Chapter 5 6 - PowerPoint

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					     Chapters 5, 6

Force and Laws of Motion
            Newtonian mechanics

                                             Sir Isaac Newton
                                              (1643 – 1727)
• Describes motion and interaction of objects

• Applicable for speeds much slower than the speed
of light

• Applicable on scales much greater than the atomic
scale

• Applicable for inertial reference frames – frames
that don’t accelerate themselves
                        Force

• What is a force?

• Colloquial understanding of a force – a push or a
pull

• Forces can have different nature

• Forces are vectors

• Several forces can act on a single object at a time –
they will add as vectors
             Force superposition

• Forces applied to the same object are adding as
vectors – superposition

• The net force – a vector sum of all the forces applied
to the same object
               Newton’s First Law

• If the net force on the body is zero, the body’s
acceleration is zero
             Newton’s Second Law

• If the net force on the body is not zero, the body’s
acceleration is not zero




• Acceleration of the body is directly proportional to
the net force on the body

• The coefficient of proportionality is equal to the
mass (the amount of substance) of the object
            Newton’s Second Law

• SI unit of force kg*m/s2 = N (Newton)

• Newton’s Second Law can be applied to all the
components separately

• To solve problems with Newton’s Second Law we
need to consider a free-body diagram

• If the system consists of more than one body, only
external forces acting on the system have to be
considered

• Forces acting between the bodies of the system are
internal and are not considered
                               Chapter 5
                              Problem 14
Three forces acting on an object are given by F 1 = (– 2.00^i + 2.00^j) N, F 2 =
(5.00^i – 3.00^j) N, and F3 = (–45.0^i) N. The object experiences an acceleration
of magnitude 3.75 m/s2. (a) What is the direction of the acceleration? (b) What
is the mass of the object?
             Newton’s Third Law

• When two bodies interact with each other, they exert
forces on each other

• The forces that interacting bodies exert on each
other, are equal in magnitude and opposite in
direction
          Forces of different origins

• Gravitational force

• Normal force

• Tension force

• Frictional force (friction)

• Drag force

• Spring force
        Gravity force (a bit of Ch. 13)

• Any two (or more) massive bodies attract each other

• Gravitational force (Newton's law of gravitation)




• Gravitational constant G = 6.67*10 –11 N*m2/kg2 =
6.67*10 –11 m3/(kg*s2) – universal constant
Gravity force at the surface of the Earth




                g = 9.8 m/s2
Gravity force at the surface of the Earth

• The apple is attracted by the Earth

• According to the Newton’s Third Law, the Earth
should be attracted by the apple with the force of the
same magnitude
                       Weight

• Weight (W) of a body is a force that the body exerts
on a support as a result of gravity pull from the Earth

• Weight at the surface of the Earth: W = mg

• While the mass of a body is a constant, the weight
may change under different circumstances
                   Tension force

• A weightless cord (string, rope, etc.) attached to the
object can pull the object

• The force of the pull is tension ( T )

• The tension is pointing away from the body
Free-body diagrams
                  Normal force

• When the body presses against the surface
(support), the surface deforms and pushes on the
body with a normal force (n) that is perpendicular to
the surface

• The nature of the normal force – reaction of the
molecules and atoms to the deformation of material
                  Normal force

• The normal force is not always equal to the
gravitational force of the object
Free-body diagrams
Free-body diagrams
                                Chapter 5
                               Problem 28
Two objects are connected by a light string that passes over a frictionless
pulley as shown. Draw free-body diagrams of both objects. Assuming the
incline is frictionless, m1 = 2.00 kg, m2 = 6.00 kg, and θ = 55.0° find (a) the
accelerations of the objects, (b) the tension in the string.
                  Frictional force

• Friction ( f ) - resistance to the sliding attempt

• Direction of friction – opposite to the direction of
attempted sliding (along the surface)

• The origin of friction – bonding between the sliding
surfaces (microscopic cold-welding)
     Static friction and kinetic friction

• Moving an object: static friction vs. kinetic
                Friction coefficient

• Experiments show that friction is related to the
magnitude of the normal force

• Coefficient of static friction μs




• Coefficient of kinetic friction μk


• Values of the friction coefficients depend on the
combination of surfaces in contact and their
conditions (experimentally determined)
Free-body diagrams
Free-body diagrams
                              Chapter 5
                             Problem 42
Three objects are connected on a table. The rough table has a coefficient of
kinetic friction of 0.350. The objects have masses of 4.00 kg, 1.00 kg, and 2.00
kg, as shown, and the pulleys are frictionless. Draw a free-body diagram for
each object. (a) Determine the acceleration of each object and their directions.
(b) Determine the tensions in the two cords.
                    Drag force

• Fluid – a substance that can flow (gases, liquids)

• If there is a relative motion between a fluid and a
body in this fluid, the body experiences a resistance
(drag)

• Drag force (R)
                    R = ½DρAv2
• D - drag coefficient; ρ – fluid density; A – effective
cross-sectional area of the body (area of a cross-
section taken perpendicular to the velocity); v - speed
                Terminal velocity

• When objects falls in air, the drag force points
upward (resistance to motion)

• According to the Newton’s Second Law

          ma = mg – R = mg – ½DρAv2
• As v grows, a decreases. At some point acceleration
becomes zero, and the speed value riches maximum
value – terminal speed

                   ½DρAvt2 = mg
                      Terminal velocity

        • Solving ½DρAvt2 = mg we obtain




vt = 300 km/h




                               vt = 10 km/h
     Drag force proportional to speed

• In dense fluids (liquids) a resistance force can be
proportional to speed


• b depends on the property of the medium, and on
the shape and dimensions of the object

• The negative sign indicates that the force is in the
opposite direction to motion
         Spring force (a bit of Ch. 7)

• Spring in the relaxed state




• Spring force (restoring force) acts to restore the
relaxed state from a deformed state
                    Hooke’s law

• For relatively small deformations
                                              Robert Hooke
                                              (1635 – 1703)



• Spring force is proportional to the deformation and
opposite in direction

• k – spring constant

• Spring force is a variable force

• Hooke’s law can be applied not to springs only, but
to all elastic materials and objects
                Centripetal force

• For an object in a uniform circular motion, the
centripetal acceleration is




• According to the Newton’s Second Law, a force
must cause this acceleration – centripetal force




• A centripetal force accelerates a body by changing
the direction of the body’s velocity without changing
the speed
                Centripetal force

• Centripetal forces may have different origins

• Gravitation can be a centripetal force
• Tension can be a centripetal force
• Etc.
                Centripetal force

• Centripetal forces may have different origins

• Gravitation can be a centripetal force
• Tension can be a centripetal force
• Etc.
Free-body diagram
                               Chapter 6
                              Problem 14
A roller-coaster car has a mass of 500 kg when fully loaded with passengers.
(a) If the vehicle has a speed of 20.0 m/s at point A, what is the force exerted by
the track on the car at this point? (b) What is the in maximum speed the vehicle
can have at point B and still remain on the track?
Answers to the even-numbered problems

Chapter 5

Problem 2
(a) 1/3;
(b) 0.750 m/s2
Answers to the even-numbered problems

Chapter 5

Problem 6
(a) 534 N down;
(b) 54.5 kg
Answers to the even-numbered problems

Chapter 5

Problem 18
(b) 1.03 N;
(c) 0.805 N to the right
Answers to the even-numbered problems

Chapter 5

Problem 36
0.306; 0.245
Answers to the even-numbered problems

Chapter 6

Problem 2
215 N horizontally inward
Answers to the even-numbered problems

Chapter 6

Problem 4
(a) 1.65 km/s;
(b) 6.84 × 103 s
Answers to the even-numbered problems

Chapter 6

Problem 12
(a) 1.33 m/s2;
(b) 1.79 m/s2 forward and 48.0° inward
Answers to the even-numbered problems

Chapter 6

Problem 26
(a) 6.27 m/s2;
(b) 784 N up;
(c) 283 N up
Answers to the even-numbered problems

Chapter 6

Problem 40
8.88 N

				
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