# Draw vs diagram with constant slope

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```					If we knew what we were doing, it wouldn't be
called research, would it?

-- Albert Einstein
Genius is 99 percent perspiration and 1 percent
inspiration.

-- Thomas Edison
Kinematics Problem:
A placekicker must kick a football from a point 36.0
m from the goal. Half the crowd hopes the ball will
clear the crossbar, which is 3.05 m high. When
kicked, the ball leaves the ground with a speed of
20.0 m/s at an angle of 53.0 to the horizontal. By
how much does the ball clear or fall short of clearing
the crossbar?
Kinematics Problem:

A placekicker must kick a football
from a point 36.0 m from the goal.
Half the crowd hopes the ball will
clear the crossbar, which is 3.05 m
high. When kicked, the ball leaves the
ground with a speed of 20.0 m/s at an
angle of 53.0 to the horizontal. By
how much does the ball clear or fall
short of clearing the crossbar?
Kinematics Problem:

A placekicker must kick a football
from a point 36.0 m from the goal.
Half the crowd hopes the ball will
clear the crossbar, which is 3.05 m
high. When kicked, the ball leaves the
ground with a speed of 20.0 m/s at an
angle of 53.0 to the horizontal. By
how much does the ball clear or fall
short of clearing the crossbar?
Kinematics Problem:

A placekicker must kick a football
from a point 36.0 m from the goal.
Half the crowd hopes the ball will
clear the crossbar, which is 3.05 m
high. When kicked, the ball leaves the
ground with a speed of 20.0 m/s at an
angle of 53.0 to the horizontal. By
how much does the ball clear or fall
short of clearing the crossbar?
Force Problem:
An object of mass M is held in place by an
applied force and a pulley system as shown.
The pulleys are massless and frictionless. Find
the tension in each section of rope.
Force Problem:
An object of mass M is held in
place by an applied force and a
pulley system as shown. The
pulleys are massless and
frictionless. Find the tension in
each section of rope.
Force Problem:
An object of mass M is held in
place by an applied force and a
pulley system as shown. The
pulleys are massless and
frictionless. Find the tension in
each section of rope.
Force Problem:
An object of mass M is held in
place by an applied force and a
pulley system as shown. The
pulleys are massless and
frictionless. Find the tension in
each section of rope.
Energy Problem:
A block of mass m1 = 20.0 kg is connected to a block of mass
m2 = 30.0 kg by a massless string that passes over a light,
frictionless pulley. The 30.0-kg block is connected to a spring
that has negligible mass and a force constant of k = 250 N/m as
shown. The spring is unstretched when the system is as shown
in the figure, and the incline is frictionless. The 20.0-kg block is
pulled a distance h = 20.0 cm down the incline of angle  =
40.0 and released from rest. Find the speed of each block
when the spring is again unstretched.
Energy Problem:
A block of mass m1 = 20.0 kg is
connected to a block of mass m2 = 30.0
kg by a massless string that passes
over a light, frictionless pulley. The
30.0-kg block is connected to a spring
that has negligible mass and a force
constant of k = 250 N/m as shown. The
spring is unstretched when the system
is as shown in the figure, and the
incline is frictionless. The 20.0-kg block
is pulled a distance h = 20.0 cm down
the incline of angle  = 40.0 and
released from rest. Find the speed of
each block when the spring is again
unstretched.
Energy Problem:
A block of mass m1 = 20.0 kg is
connected to a block of mass m2 = 30.0
kg by a massless string that passes
over a light, frictionless pulley. The
30.0-kg block is connected to a spring
that has negligible mass and a force
constant of k = 250 N/m as shown. The
spring is unstretched when the system
is as shown in the figure, and the
incline is frictionless. The 20.0-kg block
is pulled a distance h = 20.0 cm down
the incline of angle  = 40.0 and
released from rest. Find the speed of
each block when the spring is again
unstretched.
Energy Problem:
A block of mass m1 = 20.0 kg is
connected to a block of mass m2 = 30.0
kg by a massless string that passes
over a light, frictionless pulley. The
30.0-kg block is connected to a spring
that has negligible mass and a force
constant of k = 250 N/m as shown. The
spring is unstretched when the system
is as shown in the figure, and the
incline is frictionless. The 20.0-kg block
is pulled a distance h = 20.0 cm down
the incline of angle  = 40.0 and
released from rest. Find the speed of
each block when the spring is again
unstretched.
Help Sessions
Office
Groups: 2 pts extra credit
If an object has an acceleration of 0 m/s2, then one can be sure
that the object is not ____.

1.moving.
2.changing position.
3.changing velocity.
4.All of the above.
5.None of the above.
Below is a graph of position vs. time.
x (m)

B
A

C

t (s)

D
At which point is my speed the
greatest?
x (m)

B
A

C

t (s)

D
At which point is my speed the
least?
x (m)

B
A

C

t (s)

D
What is average velocity?
x (m)

B
A

C

t (s)

D
x (m)

B
A

C

t (s)

D
Below is a graph of velocity vs.
time.
v (m/s)

B
A

C

t (s)

D
At which point am I nearest the
origin?
v (m/s)

B
A

C

t (s)

D
Which point has the greatest
speed?
v (m/s)

B
A

C

t (s)

D
Which point has the least speed?
v (m/s)

B
A

C

t (s)

D
At which point(s) is the object
traveling in the positive direction?
v (m/s)

B
A

C

t (s)

D
At which point is the magnitude of
my acceleration the greatest?
v (m/s)

B
A

C

t (s)

D
At which point is the magnitude of
my acceleration the least?
v (m/s)

B
A

C

t (s)

D
What is my average acceleration?
v (m/s)

B
A

C

t (s)

D
v (m/s)

B
A

C

t (s)

D
The ball shown below is initially moving 0.30 m/s and
accelerates at 2.50 m/s2 while on the sloped section.

Graph the:
position vs. time
velocity vs. time
acceleration vs. time

0.20 m

0.40 m                 0.20 m
A rocket initially stationary on the ground maintains constant
acceleration upward for a distance of 300 m.

If it takes the rocket 5 sec. to reach 300 m, graph the:
position vs. time
velocity vs. time
acceleration vs. time
A race car accelerates from 0 mph to 100 mph in 8 sec. It then
travels at a constant speed for 30 sec. Finally, the driver hits
the brakes, causing the car to stop in 15 sec.

Graph the:
position vs. time
velocity vs. time
acceleration vs. time
1. A soccer ball rolls slowly across the road and down a hill as shown below.

Which of the following sketches of ax vs. t is a reasonable representation of the
horizontal acceleration of the ball as a function of time?

(1)                 (2)                    (3)                  (4)

(5) None of the above.
(6) Can not be determined.
2. A person throws a ball straight up in the air. The ball rises to a maximum height
and then falls back down so that the person catches it. Consider the ball while it is in
the air.
Which of the following statements are true? (There may be multiple answers.)

A. Just after the ball leaves the person’s hand the direction of the acceleration is up.
B. The acceleration is zero when the ball reaches its maximum height.
C. The acceleration is about 9.8 m/s2 (down) when the ball is falling.
3. Jane is riding in a hot air balloon that is rising vertically at a constant speed of 3
m/s over a lake. She drops a rock from the balloon when the distance from the
rock to the water is 50 m. Use g=10 m/s2, and let up be the positive direction.
What is the initial velocity of the rock?

a)   3 m/s
b)   0
c)   -3 m/s
d)   -10 m/s
e)   -500 m/s
f)   None of the above.
g)   Cannot be determined.
4. If I throw ball A upward and a ball B downward with the same initial speed, which
ball is traveling the fastest just before hitting the floor?
5. What can be said about an object that has a velocity of 0 m/s?

a)   It is at the origin.
b)   It is not moving.
c)   It is not accelerating.
d)   Its motion is constant.
e)   None of the above.
6. A water balloon is dropped from the top of Paine. Draw graphs for:

Position vs. time
Velocity vs. time
Acceleration vs. time

Note: include only the freefall time.
7. A bullet is fired straight up into the air. Draw graphs for:

Position vs. time
Velocity vs. time
Acceleration vs. time

Note: include only the freefall time.
8. A basketball is thrown up, hits the ceiling, falls down, and bounces off the floor.
Draw graphs for:

Position vs. time
Velocity vs. time
Acceleration vs. time

Note: include only the time after the ball is released.
The ball shown below is initially moving 0.30 m/s and
accelerates at 2.50 m/s2 while on the sloped section.

Write an expression for the final velocity.

0.20 m

0.40 m               0.20 m
A rocket initially stationary on the ground maintains constant
acceleration upward for a distance of 300 m.

If it takes the rocket 5 sec. to reach 300 m, write an expression
for the acceleration.
A race car accelerates at a constant rate from 0mph to 100mph
in 8sec. It then travels at a constant speed for 30sec. Finally,
the driver hits the brakes, causing the car to stop in 15sec.

Write an expression for the total distance traveled (in miles).
9. Jane is riding in a hot air balloon that is rising vertically at a constant speed of 3
m/s over a lake. She reaches out and drops a rock from the balloon when the
distance from the rock to the water is 50 m. Use g=10 m/s2, and let the up
direction be positive. About how long after Jane drops the rock will it splash into
the water?
a) 2.0 sec
b) 2.6 sec
c) 3.5 sec
d) 5.0 sec
e) 6.8 sec
f) >8 sec
10. A crane is lifting a batch of bricks on a pallet to an upper floor of the building.
Suddenly a brick falls off the rising pallet. You clock the time it takes for the brick
to hit the ground at 2.5 seconds. The crane, fortunately, has height markings and
you see the brick fell off the pallet at a height of 22 meters above the ground. A
falling brick can be dangerous, and you wonder how fast the brick was going
when it hit the ground. Since you are taking physics, you quickly calculate the