Teacher's Guide to Investigations

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					 Physics 11
Teacher’s Guide to
  Investigations
         ! Gordon R. Gore
    #404-F 3255 Overlander Drive
           Kamloops BC
          Canada V2B 0A5


      Telephone: (250) 579-5722
         Fax: (250) 579-2302
       E-mail: grgore@telus.net
                                                  2



          Investigation 1-1 Making a Pendulum Clock
Teaching Tips
Commercial pendulum clamps and drilled metal balls are usually available. Figure 1.1 in the text
illustrates a low cost alternative. This investigation provides an introduction to measurement. A
beautiful pattern emerges if care is taken with measurements of length and time.
Use a string that will not stretch significantly with the weight of the bob.
Length of the pendulum must be measured from the point of suspension to the centre of gravity
of the bob.
When counting swings, a common error is to start timing at ‘one’ swing instead of at ‘zero’. I
recommend students count down to zero, start the stopwatch, then count: One, two, three, etc.
          i.e. five, four, three, two, one, zero (Start stopwatch!), one, two, three, …..
The graph is highly curved for short lengths of the pendulum, so encourage students to take as
many readings as possible with lengths in the 10- to 30-cm range.




The graph is a parabola. Students may try to connect successive points with short straight lines.
They must be taught to draw a smooth curve through the points. Some points may be obvious
errors. If time permits, students should go back and check these readings. When the ‘curve’ is
drawn, it should pass through most of the points. Obvious errors are ignored when drawing the
‘best curve’.
                                                  3


Concluding Questions

1. (a) A one-second clock would have a length of approximately 25 cm.
   (b) A two-second clock will have a length of approximately 100 cm.
2. A two-second clock is four times as long as a one-second clock.

Challenges

1. A three-second clock must be nine times as long as a one-second clock. (Approx. 225 cm)
2. Doubling the mass will have no significant effect on the period of a pendulum.
   If students try this, make sure they check the string for stretching as the extra mass is added.
   The length may have to be adjusted.
3. The amplitude will decrease as time progresses. This should not have a significant effect on
   the period, unless the starting amplitude was very large.


 Investigation 1-2 The Frequency of a Recording Timer
Concluding Questions

1. In 5 s, the tape should record approximately 300 dots. This assumes the timer is operated on
   household current, which is 60 Hz.
2. See the example in the text.
3. See the example in the text.
4. Students should obtain a result within 10% of 60 Hz.
5. (a) Example: If the measured frequency was 60 Hz, the period T would be:
                               1          1                         -2
                                    =       -1 = 0.0167 s " 1.7 x 10 s .
                             60 Hz     60 s
   (b) (i) There are 60 dots each 1.0 s.
        (ii) There are 6 dots each 0.10 s.




  Investigation 1-3 Measuring the Speed of a Model Car

Concluding Questions

1, 2. The average speed will increase as the car accelerates, and then level off.

3. Measure the time it takes a car to travel a known distance, then divide the distance by the time
   to get the average speed.
                                                4



           Investigation 2-1                 Measuring Acceleration
Extra attention is given to the detail of Procedure, which must be followed carefully.

The acceleration calculated for successive intervals should be constant, allowing for small
experimental errors. In a later Investigation, students will graph Speed vs Time, and find
acceleration from the slope of the graph. The data from this Investigation will be re-used.




                    Investigation 2-2
    Determining Acceleration from a Speed-Time Graph
Careful attention must be given to text preceding this Investigation, where Procedure is
explained in detail.

Concluding Questions

2. The equation may have a Y-intercept if the measurements of the speed of the cart did not start
   from rest. It will have the same form as the equation for the sample graph in Figure 2.7,
   which is
                                   v = 7.0 cm/s + [69 cm/s2]t.

3. The acceleration obtained from the slope of the speed-time graph should be approximately the
   same as the acceleration obtained by calculating changes in speed in successive time intervals,
   as in Investigation 2-1. The slope method averages out the acceleration for the whole trip, in
   one calculation.
                                                 5



              Investigation 3-1                 Three Kinds of Force
Part 1 The Force of Gravity
This might be demonstrated.

Concluding Questions

1. Both steel balls fall at the same rate. Their mass makes no significant difference.
2. (a) Air friction slows the tissue much more than the steel ball.
   (b) In a vacuum (e.g. on the moon) both fall at the same rate.
3. Both the ball fired horizontally and the ball dropped vertically hit the ground at the same time.
4. Results would be similar but at 1/6th the acceleration, except the tissue would fall at the same
   rate as the steel ball. The horizontally projected ball would travel much further.

Part 2 Electrical Forces

There are many ways to demonstrate static electrical forces. Chapter 12 deals with static
electricity in more detail.

Concluding Questions

1. The electrical force is much stronger than the gravitational force. For example, before you
   charge the comb, you will notice that the gravitational attraction of the comb for the strip of
   paper or sawdust is negligible.
2. Electrical forces can be attractive or repulsive. Gravitational forces are attractive.

Part 3 Magnetic Forces

This activity should be review of what students have learned in Science 10.

Concluding Questions

1. The bar magnet will not normally attract sawdust.
2. The bar magnet attracts iron filings.
3. If the magnet was electrically charged, and insulated from your hand, it could attract either
   sawdust or filings due to its static charge. This is unlikely to happen, however.
4. Magnetic forces can be either attractive or repulsive. (Students will recall from previous
   courses that like poles repel, and opposite poles attract.)
                                                   6



             Investigation 3-2                   Another Way to Weigh
Many students will have done a similar experiment in previous science courses, where masses
were added to the end of a coiled spring. A graph of spring extension vs force of gravity gives a
fairly straight line (once the spring uncoils).

Note! Protect the metre sticks from damage by placing some cardboard where the clamp is
attached.

Concluding Questions

1. The graph should indicate a direct proportion [Y-intercept at (0,0)]. Students must express the
   slope in proper units [cm/N].
2. The force of gravity on the unknown should be comparable with what a spring balance reads
   for the same object. The measurement from the metre stick graph will be more precise than
   the spring balance!



       Investigation 3-3 Friction Can Be a Real Drag!
The method used here uses homemade blocks of 2"x4" wood. Teachers may wish to change the
procedure to match the equipment they have.

Part 1
Concluding Questions
1. The force of friction is directly proportional to the total force of gravity on the blocks.
2. The equation will be of the form, Ffriction = constant"Fgravity. There are no units for the constant.
3. The constant in the above equation is the coefficient of kinetic friction, given the symbol µ.
4, (a) A low coefficient of friction is desirable when a sled is pulled along an icy road, when
      pushing a heavy box along a floor, when trying to ski as fast as possible down a slope, etc.
   (b) A high coefficient of friction is desirable between brake shoes and drums, between chalk
       and a blackboard, between your shoes and the floor, etc.

Part 2
Concluding Questions

1. Surprisingly, the surface area of contact does not make a significant difference, if the force of
   gravity is kept constant.
2. It is difficult sometimes to find a surface that is consistently smooth for this experiment. Also,
   the blocks may not have identical masses.
                                                  7



                      Investigation 3-4
        How Gravitational Force Depends on Distance
Fictitious data is provided here. Students learn how to determine a power law using graphical
analysis. When students plot Fg vs d, they obtain a graph like Graph 1 below. The shape of the
graph suggests an inverse-square relation (Fg # 1/d2). Students should prepare a new Table, with
Fg and 1/d2). It will look like Table 1.
                                              Table 1
                              Fg (N)                     1/d2 x 10-4 (Mm-2)
                                9.81                            246
                                2.45                            61.6
                                1.09                            27.4
                                0.61                            15.4
                                0.39                            9.9




If Fg is plotted against 1/d2, Graph 2 is obtained. According to Graph 2, Fg = k[1/d2]. The slope,
k = 3.9 x 102 N"Mm2.

Concluding Questions
1. (a) A straight line is obtained if Fg is plotted against 1/d2.
   (b) The equation for the straight line is:
                                      Fg = 3.9 x 102 N"Mm2 [1/d2].
2. (a)                           If 4.9 N = 3.9 x 102 N"Mm2 [1/d2],
                                         3.9 x 102 N " Mm2
                                  d2 =                       = 79.6 Mm2
                                                4.9 N
                               d =     79.6 Mm2 = 8.9 Mm
                 2        2    2        3.9 x 10 2 N " Mm2              -2
(b) Fg = 3.9 x 10 N"Mm [1/d ] =                               = 9.6 x 10 N .
                                     (63.7 Mm)(63.7 Mm)
Since the distance is 10 times as great, the force should be 1/100 of what it is at Earth’s surface.
(The graphical result may differ depending on how carefully the slope is determined.)
                                                 8



            Investigation 3-5 Cohesion and Adhesion
Confession! This Investigation was included in the book mainly because it is fun to do.
(This may be against the law in some schools.)

Concluding Questions

1. Water does not adhere to wax, so the cohesive force is obviously stronger.
2. A paper towel soaks up the water! (Water adheres to the fibres of paper.)
3. The streams of water cohere to each other.
4. A partially full test tube produces a ‘concave lens’ effect, which makes the coin look smaller.
   If the water is overflowing, the bulge in the water produces a ‘convex lens’ effect, and the
   water acts as a magnifying lens.
5. Water forms a concave meniscus because of adhesive attraction to the glass. Mercury does not
   adhere to glass, so the cohesive attraction between mercury atoms causes it to form a convex
   surface.
6. Two pieces of wet glass stick together because the water between them acts as an adhesive.
   (Air pressure on both sides contributes to their ‘stick-together-ness’.)
7. The adhesive attraction of the glass is more effective in lifting a narrow column of water than
   a wider (and therefore heavier) column of water.
8. Surface tension, caused by the cohesive force between water molecules, keeps the needle
   afloat. Soap molecules floating on the surface of the water get between the water molecules,
   and reduce the cohesive force between the water molecules.
9. Soap molecules actually reduce the cohesive force between water molecules, making it
   possible for the water to form sheets or bubbles. Soapy water does adhere better to glass than
   pure water.
10. If you photograph water coming from a tap with a high-speed flash (or a strobe light) you see
   that it is actually a series of drops. Only a time exposure will make the water look like a
   steady, uninterrupted stream.



            Investigation 4-1 Inertia Demonstrations
Problem 1 Because of its inertia, the ‘passenger’ continues moving forward when the vehicle
  comes to a stop. In a real collision, the passenger will tend to go through the windshield if not
  restrained by a seatbelt or air bag.
Problem 2 If you pull gently on the string, the break will occur above the mass. If you pull
abruptly, the string breaks below the mass. The force on the top string equals the weight of the
mass plus the force you exert on the string, so the string breaks above the mass. If you pull
abruptly on the bottom string, the stretching of the string caused by your downward force does
not reach the string above the heavy mass in time. The bottom string breaks while the heavy
mass is still accelerating downward.
                                                  9


Problem 3 Because of its inertia, the train keeps going in the direction that it was going at the
instant there is no longer any track to exert an inward force (centripetal force) on it. It moves in a
direction tangent to the curve of the track.

Problem 4 Move your hand abruptly downward, so that the coin-holder’s hand is knocked
downward. Because of its inertia, the coin will tend to stay where it was, and the coin will pop
right into your hand.

Problem 5 The air in the bag has inertia. When you start moving the bag to the side, the air
tends to stay back where it was. When the bag is moving sideways, and suddenly brought to a
halt, the air tends to keep on going, and bunches up in the front end.
Problem 6 The glider, once moving, has no unbalanced force on it. It travels at constant speed.

Problem 7 The ball has the same forward velocity as the cart, and because of its inertia will
maintain that forward velocity, and fall right back into the ‘cannon’.



    Investigation 4-2 Newton’s Second Law of Motion
Actual data obtained will depend on the equipment used. Following are three idealized graphs,
showing the shape of graph to be expected under ideal conditions.




                   (A)                            (B)                            (C)

Concluding Questions

1. When a constant unbalanced force is applied to a cart, the speed of the cart increases at a
   uniform rate. (It has constant acceleration.)
2. Acceleration is directly proportional to the unbalanced force. (If the graph does not pass
   through (0,0), it may be because of friction, or a an undetected slope in the table.
3, Acceleration is inversely proportional to the mass of the cart.
4. It is difficult to eliminate the effect of friction between the wheels of the cart and the table.
   The carts may not have identical mass. The masses may not be correctly labelled. Timers may
   not be consistent and reliable.
                                                     10



        Investigation 4-3 Newton’s Third Law of Motion
  Discussion of Procedure

  1. (a) If the two carts, of equal mass, accelerate at the same rate (in opposite directions, of
         course), then the forces accelerating them must be of the same magnitude, but in the
         opposite direction. This follows from Newton II.
    (b) If the mass of one cart is doubled, the heavier cart will have one-half the acceleration of the
         lighter cart. The forces on the two carts are the same as before, since the forces are exerted
         by the same compressed spring. (The force depends only on how much you compress the
         spring.)
    (c) If one cart is much heavier, its acceleration will be much less, and the lighter cart will have
         a much greater acceleration. The force is the same on each cart, as before.
                                F = ma (Newton II) applies to both carts.

                                          m1a    1   = - m2   a2
  2. The ‘road’ is pushed backward, while the car goes forward. This fun demonstration shows that
     the wheels actually push backward. It is the reaction force of the road on the wheels that
     makes the car move forward.

    If an air table is not available, place a sheet of corrugated cardboard (the road) on top of a row
    of round straws or wood dowels (or fax paper cores). Place the car on the road and start it
    moving. The ‘road’ will be pushed backward.

Concluding Questions

 1. The wheels of a moving car push backward. The road pushes the wheels forward.
 2. When you do push-ups, you push down. The floor pushes you up.
   When you swim, you push backward on the water. The water push you forward.
    When you row a boat, the oars push backward on the water. The water pushes the oars and the
    boat forward.
    The earth exerts a force on you (called your ‘weight). You exert an equal but opposite force on
    the earth! (See Challenge 1.)

                       Investigation 5-1 Force Vectors
  Note! Spring scales are designed to be used in a vertical position. When used in a horizontal
  position, it may be necessary to ‘zero’ the scale.

  Force tables, available commercially, can be used to do introductory work with force vectors.
  Procedure for Investigation 5-1 requires only two spring balances, a kilogram mass and a pulley
  clamp.
                                                    11


Procedure 6 illustrates how the tension in a supporting string or wire increases dramatically
when the string or wire approaches ‘straight’ (180o).

Observations

Theoretically, Table 5.1 would look like this:

    Angle $               Force A              Force B               Force C              Resultant of
                                                                                         Forces A and B
        0o                 4.9 N                 4.9 N            9.8 N (down)             9.8 N (up)
       30o                 5.7 N                 5.7 N            9.8 N (down)             9.8 N (up)
       45o                 6.9 N                 6.9 N            9.8 N (down)             9.8 N (up)
       60o                 9.8 N                 9.8 N            9.8 N (down)             9.8 N (up)

Here is a sample vector diagram for $ = 30o:




                                       Scale was: 1 cm = 1 N




Concluding Questions

1. The resultant of forces A and B is equal in magnitude to Force C.
2. The direction of the resultant of forces A and B is opposite to the direction of Force C.
3. The resultant of forces A, B and C is zero.
                                       "        "        "
                                       FA + FB + FC = 0
4. The observation for this question depends on the strength of the string used.
5. If the string were perfectly straight (180°) , the tension in it would be infinite!
                                                 12



    Investigation 6-1 Getting Work Done with Pulleys
Theoretically, Table 6.1 might look like this:

                                            Table 6.1

 System      Load         Load        Work             My        My        Work      Mechanical
  Used       Lifted       Lifted     Done by          Effort    Effort    Done by    Advantage
                           This       Pulley          Force    Distance     Me
                         Distance    System
                N           m            J              N         m           J       (No Units)
   6.1         2.0         0.10        0.20            1.0       0.20       0.20          2
  6.2A         2.0         0.10        0.20           0.67       0.30       0.20          3
  6.2B         2.0         0.10        0.20            2.0       0.10       0.20          1
  6.3C         2.0         0.10        0.20           0.67       0.30       0.20          3
  6.4D         2.0         0.10        0.20           0.50       0.40       0.20          4

Obviously, students will not get the ‘ideal’ results, but should come close. A source of error is
stretching of the string when effort force is applied. This error can be minimized by making sure
the starting position is measured only when there is force being applied.

Concluding Questions

1. The work you do is slightly greater than the work accomplished by the pulley system, due to
   friction between the rope and the pulleys.
2. Pulleys and other simple machines never ‘save you work’. They may reduce the effort force
   needed to move a load.
3. See Table 6.1.
4. The theoretical mechanical advantage equals the number of rope sections sharing the load.
   (Do not count a section where you are pulling down.)
                                   Effort Distance
5. Ideal Mechanical Advantage =                    .
                                    Load Distance
Challenge #1 This is three pulleys ‘in series, with a combined MA of 2 x 2 x2 = 8! Try it!
Challenge #2 See Answer to Exercise 5, page 120 at the back of the text.
                                                 13



                         Investigation 6-2
                Measuring the Power of a Small Motor
Kits for this experiment are available from science suppliers. Northwest Scientific calls it the
Energy Transfer Apparatus, catalogue number 24-2333.

Sample Calculation: The mass being lifted is 0.050 kg, so the force of gravity that must be
balanced is (0.050 kg)(9.8 N/kg) = 0.49 N. If the time it takes to lift the mass through a distance
of 1.0 m at constant speed is 2.0 s, then the power of the motor in this application would be:

                                Work Done   (0.49 N)(1.0 m)
                      Power =             =                 = 0.25 W.
                                  Time           2.0 s



        Investigation 7-1 Heat Transfer by Conduction

Part 1 (Demonstration)

Gentle heating with an alcohol lamp is advised. With the typical apparatus, copper conducts best,
then aluminum, brass and iron. The metal rods are usually labelled.

Part 2 (Demonstration)

With careful heating using a low flame, you can make the water at the top of the test tube boil,
while the ice at the bottom remains frozen. Water is a poor conductor of heat.

Part 3 (Demonstration)
 (a) The copper gauze conducts heat very well. Initially, gas burns at A but not at B or C. The
     heat from the gas burning at A is conducted through the gauze. (Eventually the gas above the
     gauze will light, so do the demonstration quickly, then shut off the gas.
(b) The gas burns at B only.
(c) The gas burns at C only.

Concluding Questions
1. Copper is best, then aluminum, brass and iron.
2. Copper, aluminum and iron are used to make cooking utensils because they are good
   conductors.
3. Wool, cotton, Styrofoam%, still air, and fibreglass, are a few insulators.
4. Water is a poor conductor. It transfers heat by convection, so it is a poor insulator as well.
5. The copper gauze conducts so much heat away from the gas, the gas does not reach its ignition
   temperature.
                                                 14



                        Investigation 7-2 Convection
Both demonstrations use commercial apparatus. This equipment may have been seen by students
back in grade 8 science. The demonstrations should provide a quick review of convection.

Concluding Questions

1. When a fluid (such as air or water) is warmed, the molecules gain kinetic energy, so they
   move faster. The fluid expands, so it is less dense than the cooler fluid around it. The denser,
   cooler fluid buoys the warmer fluid up, moves in to take its place, and is itself warmed. A
   convection current results.
2. If the bottom of the test tube is heated, warmed water will rise to the top of the test tube by
   convection, melting the ice.


       Investigation 7-3 Absorbing Infrared Radiation
There are variations on this approach, so teachers may wish to modify the experiment to match
the equipment available.

Caution! Oil built up on a surface will absorb radiation. Keep the containers free of fingerprints.

Concluding Questions

1. The black container warms up more than the shiny one (or a white one).
2. Dark-coloured surfaces absorb infrared radiation more efficiently than shiny or white surfaces.
                                                  15



  Investigation 7-4 Measuring the Power of a Hot Plate




The above sample graph uses ‘manufactured’ data to show how the student graph might look.
The power of the hot plate, according to the manufacturer, is 300 W.


For the sample graph, the slope is
                                        40 o C " 20 o C
                                  k =                   = 0.20 C o /s .
                                          100s " 0
The useful power of this hotplate is, therefore,
                           "T                             J            Co
                 P = mc         = (0.300 kg)(4200            )(0.20       ) = 252 W
                           "t                           kgCo            s

Concluding Questions

1. The calculated power rating for the sample above is 252 W.

2. The percentage difference between the calculated power rating and the manufacturer’s rating
      300 W " 252 W
   is                  x 100% = 16%.
          300 W

                  252 W
3. Efficiency =         x 100% = 84 %.
                  300 W

4. Much of the thermal energy from the hot plate surface goes to the surrounding air instead of
   directly into the beaker of water. In turn, energy is lost from the water itself to the air.
                                                16



          Investigation 8-1 An Introduction to Waves
Concluding Questions

1. The cause of sound coming from the fork is the vibrations of the fork.
2. The vibrations in the glass make the water vibrate, too. Tiny waves can be seen on the surface
   of the water.




                     Investigation 8-2
        Observing Transverse and Longitudinal Waves
Observations in this Investigation are intended to qualitative.

Concluding Questions

1. Transverse waves travel faster in the small diameter spring.
2. Longitudinal waves also travel faster in the small diameter spring.
3. Amplitude of the waves does not have a noticeable effect on the speed of travel through the
   springs.
4. When the tension in the spring is increased, wave speed increases.
5. The medium does not ‘’travel’. The disturbance in the medium does travel.
6. The wave is inverted when it reflects from a solid, fixed end of the medium (the spring).




                   Investigation 8-3
    Wavelength, Frequency and Speed of Water Waves
Observations in this Investigation are intended to qualitative.

Concluding Questions

1. The speed of a circular wave is constant in all directions. We know this because the wave
   stays circular as it spreads out in a uniform medium.
2. As the frequency of the wave increases, the wavelength decreases.
                                                17



                Investigation 8-4 Properties of Waves
This Investigation is a lengthy one, which may be done over more than one class period.


        Teachers may wish to use the attached student Data Sheets for Investigation 8-4.
                          These may be photocopied if you wish.




Part 1 Reflection of Circular Water Waves

The circular wave reflects with less curvature than the incident wave. The curvature is such that
the reflected wave appears to come from a point behind the mirror, at a distance equal to the
distance from the point source to the mirror.

Concluding Question

The distance from the ‘image’ to the mirror equals the distance from the ‘object’ to the mirror.

Part 2 Reflection of Straight Water Waves

Concluding Questions

1. The angle of incidence equals the angle of reflection.

2. When the waves reflect, there is no change in their speed, wavelength or frequency.
                                                 18




Part 3 Reflection of Waves from a Curved ‘Mirror’
Concluding Questions
1. Straight waves reflect from the parabolic mirror, forming circular waves that pass through a
   focus, then diverge from there. Parabolic mirrors are used in telescopes, flashlights, and
   headlights. They are used in parabolic microphones used in televised sports events.
2. A circular wave generated at the focus of a parabolic mirror reflects off the mirror as a straight
   wave. Spotlights, flashlights and headlights use this idea.

Part 4 Diffraction of Water Waves
                                                 19




Concluding Questions

1. Diffraction is more noticeable with long wavelengths.

2. Diffraction is more noticeable with small openings.

3. Straight waves are diffracted into circular waves.

4. (a) Waves passing by a relatively small obstacle diffract around it with little change.

  (b) Some diffraction is noticed when the wavelengths and the obstacle are of comparable size.

  (c) Short waves passing a large obstacle form a distinct ‘shadow’, with little noticeable
      diffraction.

5. One can see a ‘starburst’ effect when one looks at a distant streetlight through a mesh curtain.
   One can hear someone talking around a corner. Water waves diffract around obstacles in the
   water.
                                                20


Part 5 Refraction of Water Waves




Concluding Questions
1. Water waves slow down as they enter deeper water.
2. The wavelength of the waves gets shorter as they enter deeper water.
3. The wave frequency is determined by the wave generator causing the waves.
4, Waves parallel to a boundary reflect parallel to the boundary. The direction is reversed, but the
   waves remain parallel to the boundary.
5. The angle of refraction is less than the angle of incidence.
6. The angle of refraction leaving the water is equal to the original angle of incidence when the
   waves entered the shallower water. The waves leave the shallow region in the same direction
   they were travelling before they entered the shallow region.

Part 6 Interference
(a) Interference in a Stretched Spring




Concluding Questions

1. Waves A and B interfere constructively in text Figure 8.15(a), producing a wave with double
   the amplitude.

2. Waves A and B interfere destructively in text Figure 8.15(b), producing zero amplitude.
                                               21


Part (b) Interference in Water Waves




Concluding Questions

1. A crest from one source will cancel a trough from another source arriving at the same point
   simultaneously. You see a ‘flat’ spot on the screen.

2. Crests arriving simultaneously with crests, and troughs arriving simultaneously with troughs,
   constructively interfere. You see a bright area on the screen.

3. If the distance from one source is n&, and you observe a nodal line (destructive interference),
                                              1 3 5
   then the other source could be a distance &, &, &, etc., because a crest from one source is
                                              2 2 2
   arriving simultaneously with a trough from the other source. If the nodal line is a distance n&
                                              1
   from one source, then it is a distance (n ± &) from the other source.
                                              2

4. If one source is a distance m& from one source, and a maximum is observed, then the
   maximum is a distance (m ± n)& from the other source, where m and n is are integral numbers.
                                            22


Observations for Investigation 8-4               Name____________________
Part 1 Reflection of Circular Water Waves




Part 2 Reflection of Straight Water Waves
                                          23


Part 3 Reflection of Waves from a Curved ‘Mirror’




Part 4 Diffraction of Water Waves
                                         24




Part 5 (a) The Effect of Water Depth on Wave Speed
                                         25


Part 5 (b) Refraction of Water Waves




Part 6 Interference

(a) Interference in a Stretched Spring




(b) Interference in Water Waves
                                                 26



                    Investigation 8-5
        Measuring Wavelength Using Young’s Method

Part A Wavelength of Water Waves

Students are asked to measure the wavelength of the water waves directly, by making the waves
‘stop’ using a hand stroboscope. This may be a new technique to most students, so the instructor
might wish to spend some time beforehand giving students practice in ‘stopping’ such things as a
recording timer or an electric fan.

Part B Wavelength of Light

A helium-neon (red) laser is used here. A laser pointer will do the job, and is much cheaper.
The twin slits can be prepared as in the text, or you can purchase prepared double slit slides,
which are probably more accurate.

It is difficult to prepare the double slit slide using the graphite paint. Usually several trials are
needed to obtain a usable slide. If too much pressure is used in scratching the slits with the razor
blades, the blades may separate and the distance between the slits may no longer be equal to one
razor blade width.

Students will need practice in using micrometer calipers.



   Investigation 9-1 What Frequencies Can You Hear?
Young people can usually hear sounds between 20 Hz and 20 000 Hz. Old, old teachers may not
be able to hear the full range.


    Investigation 9-2 Does Sound Travel in a Vacuum?
There are variations on this demonstration, one being the doorbell suspended in a bell jar by two
bell wires that pass through a rubber stopper. It is difficult to achieve total silence, because
vibrations are transmitted through the wires to the glass bell jar, which transmits some sound to
your ear. Students can certainly hear the fall in volume as air is pumped out, and the increasing
volume as air is allowed back into the bell jar.

Unfortunately, if you do not already have a vacuum pump and bell jar, with stand to support it,
the combination is extremely expensive to purchase.
                                               27



             Investigation 9-3 ‘Seeing’ Sound Waves
This Investigation requires the use of an oscilloscope, or an equivalent set-up using a computer.
It is sometimes possible to obtain usable results using a piezoelectric speaker as a microphone,
which is connected directly to the input of the oscilloscope.

A low-pitch sound will have a longer wavelength on the screen that a high-pitch sound.


          Investigation 9-4 Visualizing Sound Quality
A musical sound will have a regular, repeating pattern. See Text Figure 0.7. It may be simple or
complex.
‘Noise’ has a pattern like this:




                        Investigation 9-5 Resonance
re: Resonating Tubes: In my experience, Meker burners give the best result with carpet tubes.
Keep a spray bottle full of water handy in case the cardboard gets overheated. This has never
happened to me, but it is a worthwhile precaution.
‘Singing Pipes’, available from Educational Innovations, Inc Catalogue # HS-14A, produce a
fine result. Try their website at www.teachersource.com.
Two carpet tubes or two singing pipes with slightly different lengths, played simultaneously,
produce loud and dramatic ‘beats’.

Concluding Questions
1. Resonance occurs when an object has the same natural frequency as another object that is
   transmitting sound or other vibrations.
2. Students have told me that in the music room a snare drum, for example, may start vibrating
   on its own, resonating with some other musical instrument.
3. You tune your radio by making its circuit have the same natural frequency as the transmitter.
   The tuner is a variable capacitor.
4. If the soldiers happen to march in step with the same frequency as the rope suspension bridge,
   the bridge may resonate to an extent that disastrous results occur!
                                                 28



              Investigation 10-1 Pinhole Photography
Concluding Questions

1. Only two rays are needed to predict where an image will form and how large it will be.




2. A letter b will be inverted, laterally and vertically. The image will look like a q. The diagram
   for Question 1 illustrates how a pinhole inverts an image in the Y-direction. The same thing
   happens in the Z-direction.


              Investigation 10-2 Looking into Mirrors
Part 1
Concluding Questions
1. The image is behind the mirror. The image distance is (approximately) equal to the object
   distance.
2. Reflection occurs mainly at the rear surface of the ‘mirror’, but a weak second image can be
   seen, caused by reflection from the front surface of the mirror.

Part 2
Concluding Questions
1. The object distance (approximately) equals the image distance. When light enters and leaves
   the mirror, its direction changes direction slightly (due to refraction).
2. The light originates at the object, but it reflects from the mirror to your eyes. Your brain ‘sees’
   the projection of the reflected rays as if the rays came from the (virtual) image.
3. The angle of incidence equals the angle of reflection. This is consistent with wave behaviour
   observed earlier.
                                                  29



                   Investigation 10-3 Multiple Images
                                            Observations

                                   Angle Between       Number of
                                     Mirrors            Images
                                       180°               1
                                       120°               2
                                        90°               3
                                        72°               4
                                        60°               5
                                        45°               7
                                        40°               8
                                        36°               9
                                        30°               11
                                        24°               14
                                        20°               17
                                        15°               23
                                         0°               '

Concluding Questions

1. A rule for predicting how many images you will see between two mirror surfaces forming an
   angle $ is:
                                                     360o
                                Number of Images =         - 1.
                                                       "

2. If the mirrors are set at 90°, you will see the object plus 3 images, so the pattern will be seen 4
   times.




             Investigation 10-4(A) Refraction of Light
Typical Observations

        Angle of
                              0°      10°       20°       30°       40°      50°       60°       70°
       Incidence, i
        Angle of
                              0°      7.5°      15°       22°       29°      35°      40.5°      45°
       Refraction, r
                                                  30



Angle of Incidence Vs Angle of Refraction for Light Entering Water from Air




If glass or Plexiglas% is used the graph is similar, but has a slope of 1.5.

Concluding Questions

1. When light travels from air into water or Plexiglas, the beam refracts toward the normal.

2. The slope of the straight part of the above graph, for light travelling from air into water, is
   1.33. For Plexiglas, the slope is 1.50. Plexiglas (or glass) refracts light more than water does.

3. Water waves refract in a very similar manner. A wave model of light explains refraction.




             Investigation 10-4(B) Refraction of Light
A graph of sin i vs sin r gives a straight line for all angles of incidence.

For light travelling from air into water, the slope of the graph is 1.33. For light travelling from air
into Plexiglas, the slope is 1.50.
                                                  31


              Graph of sin i vs sin r for Light Entering Water from Air




The slope of this graph is 0.670/0.500 = 1.34. If Plexiglas is used, the slope is approximately
1.50.


                         Investigation 10-5
              Internal Reflection and the Critical Angle
Concluding Questions

1. The critical angle for water is 48.6°. Critical angle for Plexiglas is 41.8°.




2. Light entering the optical pipe is reflected repeatedly from the inside walls. This illustrates the
   principle behind fibre optics.
                                                  32



               Investigation 10-6 Polarization of Light
Concluding Questions

1. The wave theory seems to explain polarization of visible light quite nicely.
2. The light causing ‘glare’ is horizontally polarized.
3. A polarizing filter eliminates the glare from the water wave surfaces, and brings out their
   shape and texture better.
4. A calcite crystal allows double refraction, and acts as a polarizing filter. Light passing through
   calcite is refracted in two planes at right angles to one another. By rotating a polarizing filter
   through 90°, you can pick out one or the other of the two refracted images.



                        Investigation 10-7
             Dispersion and Other Colour Phenomena
Suggestion: Use a discarded CD to disperse the light from various sources.

Concluding Questions

1. Light of different frequencies (colours) is refracted different amounts. Strictly speaking, each
   frequency has its own index of refraction.

2. Glass refracts red light less than other colours, so the index of refraction for red light will be
   less than the index of refraction for violet light.

3. (a) The white light is dispersed into: red, orange, yellow, green, blue, indigo and violet. Don’t
       worry if you cannot distinguish indigo.

  (b) The three primary light colours--- red, blue and green --- together produce white.

4. Red and green lights produce yellow. Blue and green produce cyan. Red and blue produce
   magenta. Red, green and blue produce white.

Suggestion

If time permits, try the Challenges at the end of this Investigation.

Caution!

Students who suffer from epilepsy may be adversely affected by a strobe light. (Challenge #4)
                                                  33



  Investigation 11-1 An Introduction to Curved Mirrors

Concluding Questions

Part 1 Convex Mirrors
1. Light diverges (spreads out) after reflecting from a convex mirror.
2. Because of its convex shape, the light reflected to your eyes comes from a much wider angle.
3. The image in a diverging mirror is virtual, diminished and erect.
4. In a cylindrical, vertical mirror, you would look thinner than normal.

Part 2 Concave Mirrors
1. Light converges (comes together) after it reflects from a concave mirror.
2. Parallel light rays from distant stars can be focused to a small area by a concave mirror.
3. A cylindrical mirror reflects light to a small area, but not to a point. A parabolic mirror is
   needed to do this.

Part 3 Finding the Focal Length of a Spherical Concave Mirror

1. Light from a close source is diverging. It will focus to a point, but it won’t be at the principal
   focus.
2. Light from a distant source is, for all practical purposes, parallel, and will focus at the
   principal focus of the mirror.



Investigation 11-2 Locating Images in Concave Mirrors
Concluding Questions

1. Drawings for Question 1




                   .
                              Image is real, diminished and inverted.
                                                  34




                      Image is real, the same size as the object, but inverted.




                                Image is real, enlarged and inverted.




  There is no image. The reflected rays are parallel, so they cannot converge to form a real
  image. In real life, the object is not dimensionless, and some part of it will be outside F, so
  an image may be formed of an object like a candle that is placed at the focus of the mirror.

2. In an astronomical telescope, the object is ‘at infinity’, and the parallel rays form an image at
   the focus of the mirror.

3. The filament of the light bulb in a headlight is at the focus.

4. See the comment under diagram (d), above.

5. Real images are formed when the object distance is greater than the focal length.

6. Virtual images are formed when the object distance is less than the focal length.
                                    35


Images Formed by a Concave Mirror Name___________________




               This page may be photocopied for student use.
                                                36



              Investigation 11-3 Focussing on Lenses
This is an informal introduction to lenses. For some students, it may be review of work done
several years ago. The activity in Figure 11.20 may be puzzling. When the air-filled round-
bottom flask is immersed in water, you will see a diminished, erect, virtual image of whatever is
on the other side of the aquarium. Even though the flask is convex in shape, light travels faster in
air than in water, and refraction is such that the flask acts like a diverging lens.



                       Investigation 11-4
            Locating Images Formed by Convex Lenses
You may photocopy the attached worksheet for students, if you wish. It is a copy of text Figure
11.26.

Part 1

Concluding Questions
1. (a) In a camera, (a) would be most common, but (b) and (c) are possibilities.
   (b) In an enlarger, (c) is used.
   (c) A slide or movie projector uses (c).
   (d) An overhead projector uses (c).
   (e) A camera shooting an object the same size uses (b).

2. (a) A point-size object at F will form no image, because the parallel rays do not converge. For
       a real-sized object, some part of it will be just outside F, and an enlarged image may be
       seen.
   (b) A small, bright source placed at F will produce a spotlight.

3. (a) An object placed between F and the lens can only form a virtual image.
   (b) A magnifying glass is used this way.

Part 2
Concluding Questions
1. The slide must be inverted vertically and laterally. From behind, the letter will look like a d.
2. The overhead projector has more than just a single lens. A mirror system re-inverts the image.
3. In a lens-type solar furnace, the object to be heated is at the focus of the lens.
4. The spider is at the centre of curvature of the lens (two focal lengths from the lens), and the
   film is the same distance from the lens on the other side.
                                  37


Predicting Image Formation by a Lens Name__________________
                    (This page may be photocopied.)
(a)




(b)




(c)




(d)




(e)
38
                                                  39



     Investigation 12-1                    Two Kinds of Electric Charge
This Investigation may be review for some students. The objective is to show that there are two
kinds of static charge. Static electricity experiments work best on a day when the humidity is
low.




      Investigation 12-2 The Van de Graaff Generator
These demonstrations are favourites of students. For the ‘hair-raising’ demonstration, I have
found that the plastic single-step-stools sold by stores such as Canadian Tire work very well.
        The Van de Graaff generator may be positive or negative, so check it out. The smaller
versions are usually positive, and the larger ones usually negative. At the BIG Little Science
Centre, I have two large ones, one negative and one positive. This way, I can demonstrate
‘lightning’ discharges between the two.
        Whose hair works best is sometimes unpredictable. At the BIG Little Science Centre in
Kamloops, I found that students coming from the nearby pool with their hair still damp worked
extremely well. I keep a an old Windex bottle full of distilled water handy, and sprinkle a fine
mist on their hair if it won’t work otherwise. This works every time.




                        Investigation 12-3
               Charging by Conduction and Induction
Part 1 Charging by Conduction
Concluding Questions
1. (a) The first can is given a negative charge by the vinyl strip.

  (b) The second can is given a positive charge by the acetate strip.

  (c) The graphite ball is initially neutral.

2. The neutral ball is attracted to one can or the other, and picks up the charge of that can. Let us
   assume the first can it touches is negative. The ball carries negative electrons to the positive
   can, where it loses them by conduction, and becomes positively charged. It is repelled back to
   the negative can, and the process repeats until excess electrons from the first can have been
   removed, making the first can neutral. The second can is also neutralized by the electrons
   transported to it by the vibrating ball.
                                                  40


Part 2 Charging by Induction
Concluding Questions

1. (a) The vinyl strip is negatively charged.

  (b) The side of the can near the vinyl is positively charged, because electrons are repelled to
      the far side, where your finger is.

  (c) The side near your finger is negatively charged.

2. Electrons are conducted from the can to your body.

3. (a) The final charge on the can after you touch it is positive.

  (b) The strip is not affected.

  (c) The can obtained its charge by induction.




        Investigation 13-1 Measuring Electric Current
Procedure: If you use digital meters, start with Procedure 3.
The readings for Procedure 2 are as follows:
(a) 3.8 A
(b) 760 mA
(c) 190 mA
(d) 19 mA
(e) 7.6 mA
(f) 3,8 mA
(g) 0.76 mA

The attached Observations sheet may be photocopied. Students can write the currents right on
the diagrams.

Concluding Questions

1. As more light bulbs are added in series, the current decreases. Due to temperature effects, the
   current with two bulbs will not be quite one-half, and the current with three bulbs will not be
   quite one-third.

2. As more light bulbs are added in parallel, the current approximately doubles, and then
   approximately triples.
                                       41


Observations for Investigation 13-1          Name_____________________




          (a)                    (b)                      (c)




           (d)                         (e)                 (f)




                       This page may be photocopied.
                                                 42



                       Investigation 13-2
              Measuring Current Using Electroplating
Teaching Tips
This investigation is not part of the B.C. physics curriculum. The author includes it because it
gives students an idea of how electric current can be measured indirectly, and how an ammeter
might be calibrated.

Comments on Procedure

1. Sometimes carbon rods have a copper deposit on them from previous year’s
   student experiments. This may be removed by setting up an electrolytic cell with the
   carbon as the positive electrode, and a copper strip as the negative electrode. Let
   the current from the battery exist for as long as it takes to remove the copper from the
   carbon and put it back on the copper strip.

2. Find the mass of a clean, dry carbon rod before starting this step.

3, 4, 5. Here is some typical student data:

                           Mass of carbon rod before plating 31.51 g
                           Mass of carbon rod after plating   31.75 g
                           Mass of copper plated in 20 minutes 0.24 g

Concluding Questions

                   1 mole Cu 6.02 x 1023 atoms Cu
1. (a) 0.24 g Cu x           x                        = 2.27 x 1021 atoms Cu .
                   63.5 g Cu         1 mole Cu
                21             -
   (b) 2.27 x 10 atoms Cu x 2 e /atom Cu = 4.54 x 1021 e- transferred.

  (c) 4.54 x 1021 e- x 1.60 x 10-19 C/e- = 7.26 x 102 C transferred.

                   Q   7.26 x 10 2 C
2. Current = I =     =               = 0.61 A .
                   t    1.2 x 10 3 s

3. Assume the measured current happened to be 0.58 A (average).

                                          0.61 A - 0.58 A
                         %Difference =                    x 100% = 5%.
                                               0.58 A

Sources of error include: meter errors, carbon rod still wet when weighed, loss of copper
from the carbon rod.
                                                  43



                Investigation 13-3 Measuring Voltage
This Investigation provides practice in reading a voltmeter, and illustrates how a potentiometer
(potential divider) works. The potential divider consists of a nichrome wire stretched between the
two ends of a metre stick. Students will find the voltage proportional to the length of wire tapped
off. A typical laboratory potentiometer has the nichrome wire wound on a doughnut-shaped roll.



                 Investigation 13-4 Voltage in Circuits

Concluding Questions
1. When more cells are added in series, the voltage increases proportionally with the number of
   cells.
2. (a) When cells are arranged in parallel, the voltage remains the same as the voltage of one cell.
   (b) The main reason for connecting cells in parallel is to make a battery that lasts longer.
3. In a series circuit, the battery voltage equals the sum of the voltages across the external circuit.
4. In a parallel circuit, the battery voltage equals the voltage across each branch of the circuit.
5. The voltage across each branch of a parallel circuit is the same.


                       Investigation 13-5 Ohm’s Law

Concluding Questions
1. Voltage across a resistor is proportional to the current in a resistor.
4. Major sources of error include: imperfect calibration of the ammeter and voltmeter.
   If the resistor is overheated, its resistance will change.


                  Investigation 13-6 Special Resistors

This is an optional Investigation. Students who did the other Investigations in previous courses
might be asked to try this one.

Concluding Questions
1. Light decreases the resistance of a photo resistor.
2. A photo resistor can be used in a circuit that detects when the sun has gone down, and then
   turns on a streetlight or porch light.
4. A single diode changes AC into pulsating DC.
5. Light-emitting diodes (LED’s) are used in almost all electronic appliances.
                                                44



                    Investigation 13-7 Series Circuits
Concluding Questions
Part 1
2. When more resistors are added in series, the resistance increases additively.

Part 2
1. Current is the same everywhere in a series circuit.

Part 3
1. The source voltage equals the sum of the voltages across the resistors in series.
3. The Law of Conservation of Energy suggests that the source voltage should equal the sum of
    the voltages across the resistors in series.
4. Sources of error include incorrect calibration of the meters.

General Conclusions
1. Current is the same everywhere in a series circuit.
2. Source voltage equals the sum of the voltages across the components of the circuit.
3. Total resistance equals the sum of the individual resistances.
4. Each lamp has a voltage of (120 V) ÷ 8 = 15 V.




                  Investigation 13-8 Parallel Circuits
Concluding Questions

Part 1

1. Current increases when more resistors are added in parallel.
2. Resistance decreases when more resistors are added in parallel.

Part 2

1. Voltage is the same in each branch of a parallel circuit.
2. Total current is the sum of the currents in the branches of a parallel circuit.
3. In each branch, the current is determined by the voltage across that branch and the resistance
   of that branch. (Ohm’s Law applies.)
4. Total current entering a junction equals the total current leaving that junction.

				
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