Download PreAP Physics Homework Problems Unit 1: Uniform Motion and

PreAP Physics Homework Problems
Unit 1: Uniform Motion and Graphing
1. Mrs. Jensen walks 3 meters east, 2 meters south, 3 meters west and finally 2 meters
north. What is her displacement? What total distance did she walk? Which answer is a
scalar quantity and which one is a vector quantity?
2. The diagram below shows the position of a cross-country skier at various times. The
skier moves from A to B to C to D. Use the diagram to find the total distance and
displacement of the skier during the three minutes.
3. Seymour Butz views football games from under the bleachers. He frequently paces back
and forth to get the best view. The diagram below shows several of Seymour’s positions
at various times. He moves from A to B to C to D. What is his resulting displacement
after 10 minutes? What total distance does he travel during his time?
4. Consider the walk Mrs. Jensen took in problem # 1 above. If her total trip took 24
seconds, what is her average speed and her average velocity?
5. Using the diagram from #2 above, find the average speed and the average velocity of
the cross-country skier in m/min.
6. Using the diagram from #3 above, find Seymour’s average speed and average velocity
in yds/min during the 10 minute interval.
7. Eugene and Connie walk eastward with a speed of 0.98 m/s. If it takes 34 min to walk to
the store, how far have they walked? Is this a scalar quantity or a vector quantity?
8. It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the
bus stop to the museum entrance. What is your displacement?
9. A bus travels 280 km south along a straight path with an average velocity of 24 m/s to
the south. The bus stops for 24 minutes, then it travels 210 km south with an average
velocity of 20.8 m/s to the south.
a. How long does the total trip last in hours?
b. What is the average velocity for the total trip in km/h?
10. Suppose a car moving in a straight line steadily to the North increases its speed each
second, first from 35 to 40 km/h, then from 40 to 45 km/h, then from 45 to 50 km/h. What
is the car’s acceleration in km/h/s?
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PreAP Physics Homework Problems
11. List and describe the three controls of a car that cause acceleration.
12. A car moving in a straight line South increases its speed from 50 km/h to 65 km/h in 5
seconds while a truck goes from rest to 15 km/h in a straight line in the same direction.
What is the acceleration of each vehicle? Which undergoes the greater acceleration?
Position-Time Graphs
13. Start with a car moving with a constant rightward (+) velocity of +10 m/s.
Plot a position-time graph for the above motion.
14. Now consider a car moving with a changing, rightward (+) velocity which means the car
is speeding up or accelerating in the positive direction.
Plot a position-time graph for the above motion.
15. Describe the motion over each interval on the position-time graph below.
position
C
D
A
B
time
E
16. Answer the questions below concerning the position-time graph.
B
position
A
time
C
D
E
a)
b)
c)
d)
e)
f)
g)
Which maintains constant velocity?
Which accelerates?
Which changes direction?
Which is not moving?
Which is the fastest constant velocity?
Which is slowest constant velocity?
Which has the greatest acceleration?
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PreAP Physics Homework Problems
Velocity-Time Graphs
17. Start with a car moving with a constant rightward (+) velocity of +10 m/s.
Plot a velocity-time graph for the above motion.
18. Now consider a car moving with a changing, rightward (+) velocity which means the car
is speeding up or accelerating in the positive direction.
Plot a velocity-time graph for the above motion.
19. Describe the motion over each interval on the velocity-time graph below.
B
+
A
v
t
C
-
D
E
a)
b)
c)
d)
e)
f)
Which objects have constant velocity?
Which objects are accelerating?
Which objects are not moving?
Which objects change direction?
Which object has the smallest acceleration?
Which object has the greatest velocity?
20. Describe the motion over each interval on the velocity-time graph below.
Velocity
C
D
A
B
time
E
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PreAP Physics Homework Problems
21. Determine the distance traveled from 0 s to 6 s.
30
v
(m/s)
0
6
t (sec)
22. Determine the distance traveled from 0 s to 4 s.
40
v
(m/s)
0
4
t (sec)
23. Determine the distance traveled from 2 s to 5 s.
v
50
(m/s)
20
0
2 4
6
t (sec)
Acceleration-Time Graphs
24. A car is moving with a constant acceleration of +2 m/s2 for 20 seconds and then travels
at a constant velocity for 30 seconds and then travels with a constant acceleration of -4
m/s2 for 30 seconds. Sketch the acceleration vs. time graph for this situation.
25. A child is pushing a shopping cart at a speed of 1.5 m/s. How long will it take this child to
push the cart down an aisle with a length of 9.3 m? [6.2 s]
26. An athlete swims from the north end to the south end of a 50.0 m pool in 20.0 s and
makes the return trip to the starting position in 22.0 s.
a. What is the average velocity for the first half of the swim? [2.5 m/s South]
b. What is the average velocity for the second half of the swim? [2.2 m/s North]
c. What is the average velocity for the round trip? [0 m/s]
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PreAP Physics Homework Problems
27. On the graph below, what is the total distance traveled during the recorded time
interval? What is the displacement? [5m, +5m]
Position vs Time
7
Position (m)
6
5
4
3
2
1
0
0
2
4
6
8
10
12
Time (s)
28. If the average velocity of a duck is zero in a given time interval, what can you say about
the displacement of the duck for that interval?
29. Velocity can be either positive or negative, depending on the direction of the
displacement. The time interval, ∆t, is always positive. Why?
30. A bus travels from El Paso, Texas to Chihuahua, Mexico in 5.2 h with an average
velocity of 73 km/h to the south. What is the bus’s displacement? [379.60 m South]
31. A school bus takes 0.530 h to reach the school from your house. If the average velocity
of the bus is 19.0 km/h to the east, what is the bus’s displacement? [10.07 km East]
32. Two students walk in the same direction along a straight path, at a constant speed – one
at 0.90 m/s and the other at 1.90 m/s.
a. Assuming that they start at the same point and the same time, how much sooner does
the faster student arrive at a destination 780 m away? [7.60 minutes]
b. How far would the students have to walk so that the faster student arrives 5.50
minutes before the slower student? [564.3 m]
33. A shuttle bus slows to a stop with an average acceleration of -1.8 m/s2. How long does it
take the bus to slow from 9.0 m/s to 0 m/s? [5.0 s]
34. As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly
at -4.1 m/s2 as it slows from 9.0 m/s to 0 m/s. Find the time interval of acceleration for
the bus. [2.2 s]
Sketch position-time graphs that represent the following:
35. a constant positive velocity, starting at the origin
36. a constant negative velocity, starting at s=+4 m
37. a constant positive velocity, starting at s = -5 m
38. moving in the (+) direction and accelerating from a low velocity to a high velocity, starting
at the origin
39. moving in the (+) direction and accelerating from a high velocity to a low velocity, starting
to the right of the origin
40. moving in the (-) direction and accelerating from a high velocity to a low velocity, starting
at s = +6 m
41. moving in the (-) direction and accelerating from a low velocity to a high velocity, starting
at s = +4 m
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PreAP Physics Homework Problems
42. moving in the (+) direction with constant speed, first a fast constant speed and then a
slow constant speed, starting at s = +1 m
43. moving in the (+) direction with constant speed, first a fast constant speed and then a
slow constant speed, starting at the origin
44. moving in the (-) direction with constant speed, first a slow constant speed then a faster
constant speed, starting at the origin
45. moving in the (-) direction with constant speed, first a fast constant speed then a slower
constant speed, starting at s = -1 m
46. moving in the (+) direction at a slow constant speed and then in a (-) direction at a fast
constant speed, starting at the origin
47. moving in the (+) direction at a fast constant speed and then in a (-) direction at a slow
constant speed, starting to the left of the origin
48. moving in the (-) direction at a slow constant speed and then in a (+) direction at a fast
constant speed, starting at the origin
Sketch velocity-time graphs that represent the following:
49. moving with a constant speed in the positive direction, starting at v = +4 m/s
50. moving with a constant speed in the negative direction, starting at v = -5 m/s
51. an object at rest
52. moving in the (+) direction, accelerating from a slow speed to a fast speed, starting at v
= +1 m/s
53. moving in the (+) direction, accelerating from a fast speed to a slow speed, starting at v
= +5 m/s
54. moving in a (-) direction, accelerating from a slow speed to a fast speed, starting at v = 3 m/s
55. moving in a (-) direction, accelerating from a fast speed to a slow speed, starting at v = 6 m/s
56. moving with a slow, constant speed in the (+) direction, and then with a fast, constant
speed in the + direction
57. moving with a fast, constant speed in the + direction and then with a slow constant
speed in the + direction
58. moving with a constant speed in the + direction and then with a positive acceleration
59. moving with a constant speed in the + direction and then with a negative acceleration
Answer the following questions on graph paper. Use a ruler for all straight lines and
axes. Label all axes with appropriate quantities and units.
60. Sara Sue drops an orange from the 3rd floor window. It hits the ground, splatters, and
stays at rest. Sketch and describe the position-time graph for the orange.
61. The velocity of an automobile changes over an 8 second time period as shown in the
table below.
Time (s)
0.0
1.0
2.0
3.0
4.0
a.
b.
c.
d.
Velocity (m/s)
Time (s)
Velocity (m/s)
0.0
5.0
20.0
4.0
6.0
20.0
8.0
7.0
20.0
12.0
8.0
20.0
16.0
Plot the velocity-time graph of the motion.
Determine the distance the car travels in the first 2 seconds. [8 m]
What distance does the car travel during the entire 8 seconds? [110 m]
Find the slope of the line between t = 0 s and t = 4 s. What does this slope
represent? [4 m/s2]
e. What is the slope of the line between t = 5 s and t = 7.0 s? What does this slope
indicate?
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PreAP Physics Homework Problems
Use the graph below for numbers 62 and 63.
Velocity vs Time
62.
Find the acceleration of
the object:
a. during the first 5 seconds of
travel [6 m/s2]
b. during the second 5 s of travel
[0 m/s2]
c. between the tenth and the
fifteenth second of travel [-2 m/s2]
d. between the twentieth and the
twenty-fifth second of travel [-4
m/s2]
35
Velocity (m/s)
30
25
20
15
10
5
0
0
5
10
15
20
25
30
Time (s)
63. Use the graph to find the displacement of the object:
a. between 0 s and 5 s [75 m]
b. between 5 s and 10 s [150 m]
c. between 10 s and 15 s [125 m]
d. between 0 s and 25 s [500 m]
Use the graph below for numbers 64 through 66.
Position vs. Time
64.
Use the graph to find the
distance the object travels:
a. between 0 s and 40 s [400 m]
b. between 40 s and 70 s [0 m]
c. between 90 s and 100 s [200
m]
Position (m)
500
400
300
200
100
0
0
20
40
60
80
100
Time (s)
65.
Use the graph to find the
velocity of the object:
a. during the first 40 s [10 m/s]
b. between 70 s and 90 s [-10
m/s]
c. between 90 s and 100 s [-20
m/s]
66. Construct a table showing the average velocity of the object during each 10-s interval
over the entire 100 s. (the first interval is completed for you)
Interval (s)
0-10
Time (s)
10
Displacement (m)
100
Avg velocity (m/s)
10
67. Plot a velocity-time graph using the table you just constructed.
Velocity-Time Graphs: Finding Displacement (Use a ruler and a sheet of graph paper to
complete these problems.)
68. Rennata Gas is driving through town at 25.0 m/s and begins to accelerate at a constant
rate of -1.0 m/s2. Eventually Rennata comes to a complete stop.
a. Represent Rennata’s accelerated motion by sketching a velocity-time graph.
b. Use the velocity-time graph to determine her displacement while she is
decelerating. [312.5 m]
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PreAP Physics Homework Problems
69. Otto Emissions is driving his car at 25.0 m/s. Otto accelerates at 2.0 m/s 2 for 5 seconds.
Otto then maintains this constant velocity for 10.0 more seconds.
a. Represent the 15 seconds of Otto Emissions’ motion using a velocity-time
graph.
b. Use the graph to determine the Otto’s displacement during the entire 15
seconds. [500 m]
70. Luke Autbeloe, a human cannonball artist, is shot off the edge of a cliff with an initial
upward velocity of +40.0 m/s. Luke accelerates with a constant acceleration of -10.0
m/s2.
1. Sketch a velocity-time graph for the first 10 seconds of Luke’s motion.
2. What maximum height does he reach? [80 m]
3. What total distance does he travel during the 10 seconds? [260 m]
4. What is his final position after the 10 seconds? [100 m below where he started]
71. Chuck Wagon travels with a constant velocity of 0.5 mile/min for 10 min. Chuck then
decelerates at -0.25 mile/min/min for 2 min.
1. Sketch a velocity –time graph for Chuck Wagon’s motion.
2. Use the graph to determine the total displacement of Chuck Wagon during the 12
minutes of motion. [5.5 miles]
72. Vera Side is traveling down the interstate at 45.0 m/s. Vera looks ahead and observes
an accident, which results in a pileup in the middle of the road. By the time Vera slams
on the brakes, she is 50.0 m from the pileup. She slows down at a rate of -15.0 m/s2.
a. Construct a velocity-time graph for Vera Side’s motion.
b. Use the plot to determine the distance which Vera would travel prior to
reaching a complete stop (if she does not collide with the pileup). [67.5 m]
c. Does Vera Side collide with the pileup?
73. Earl E. Bird travels 30.0 m/s for 10 seconds. He then accelerates at 3.00 m/s/s for 5
seconds.
a. Construct a velocity-time graph for Earl E. Bird’s motion.
b. Use the plot to determine the total distance traveled. [487.5 m]
74. Give a qualitative description of the motion depicted in the following x vs. t graphs:
s
s
75. Give a qualitative description of the motion depicted in the following v vs t graphs:
v
t
v
76. How can you find an object’s displacement if you are only given a v-t graph?
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t
PreAP Physics Homework Problems
77. Sketch qualitative graphs of x-t, v-t and a-t for each of the following situations:
A. Cart is released from rest and travels down the ramp away from the origin
B. Cart is released from rest and travels down the ramp towards the origin
C. Cart is given a push up the slope away from the origin
D. Cart starts from rest at top of ramp and moves away from the origin
E. Cart starts at rest from top of ramp (draw graphs only until cart reaches origin)
Page 21
PreAP Physics Homework Problems
Page 22
PreAP Physics Homework Problems
Unit 2: Kinematics
1. Ima Huryin approaches a stoplight in her car which is moving with a velocity of +30 m/s.
The light turns yellow; Ima applies the brakes and skids to a stop. If Ima’s acceleration
is -8.00 m/s/s, determine the displacement of the car during the skidding process.
[+56.25 m]
2. Ben Rushin is waiting at a stoplight in his car. When the light turns green, Ben
accelerates from rest at a rate of 6.00 m/s/s for an interval of 4.10 seconds. Determine
the displacement of Ben’s car during this time period. [+50.43 m]
3. An airplane, starting from rest, moves south and attains a lift-off speed of 56.9 m/s in
18.0 s. What is the magnitude and direction of its average acceleration? [-3.16 m/s2 or
3.16 m/s2 south]
4. A plane is sitting on a runway, awaiting takeoff. On an adjacent parallel runway, another
plane lands and passes the stationary plane at a speed of 45 m/s. The arriving plane
has a length of 36 m. By looking out of a window, a passenger on the stationary plane
can see the moving plane. For how long a time is the moving plane visible? [0.80 s]
5. If a sports car can go from rest to 27 m/s in 9.0 s, what is the magnitude of its average
acceleration? [+3.00 m/s2]
6. A soccer player runs at a constant speed of 2.6 m/s. For the next 18 m, he speeds up
with an acceleration of 0.45 m/s/s. What is his speed at the end of the run? [+4.79 m/s]
7. In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to
a speed of 6.0 m/s in 1.5 s. Assuming that the player accelerates uniformly, determine
the distance he runs. [+4.5 m]
8. A woman is running at a constant speed of 5.0 m/s to catch a bus. When she is 15 m
away, the bus pulls off with an acceleration of 0.05 m/s*s. How long does it take the
woman to catch the bus from the time when she is 15 m away? [3.28 mins]
9. A young man has a reaction time of 0.935 s. If his car can decelerate at 3.4m/s*s, how
far will he travel from the time he sees a red light until he stops completely if his initial
speed is 25 m/s? [115.29 m]
10. The "reaction time" of the average automobile driver is about 0.7 s. (The reaction time is
the interval between the perception of a signal to stop and the application of brakes.) If
an automobile can accelerate at -5 m/s/s, compute the total distance covered in coming
to a stop after a signal is observed:
a. from an initial velocity of 15 m/s [33.0 m]
b. from an initial velocity of 30 m/s [111 m]
11. A brick falls freely from a high scaffold.
a. What is its velocity after 4.0 s? [-39.2 m/s]
b. How far does the brick fall during the first 4.0 s? [-78.4 m]
12. If you drop a golf ball, how far does it fall in 0.5 s? [-1.23 m]
13. Silly Goose falls 1.0 m to the floor.
a. How long does the fall take? [0.45 s]
b. How fast is he going when he hits the floor? [-4.41 m/s]
14. A stone is thrown vertically upwards with an initial velocity of 25.4 m/s.
a. How high does the stone rise above the point of projection? [32.92 m]
b. At what times will it be 7.6 m above the projection? [0.32 s, 4.86 s]
Page 23
PreAP Physics Homework Problems
15. A ball is thrown nearly vertically upward from a point near the corner of a tall building. It
just misses the corner on the way down, and passes a point 65m below its starting point
5 seconds after it leaves the thrower's hand.
a. What was the initial velocity of the ball? [+11.5 m/s]
b. How high did it rise above its starting point? [+6.75 m]
c. What was the magnitude of its velocity as it passed a point 34 m below the
starting point? [-28.26 m/s]
d. What is the magnitude and direction of its velocity at the highest point? [0 m/s]
e. What were the magnitude and direction of its acceleration at the highest point?
[-9.8 m/s2]
16. A balloon, rising vertically with a velocity of 5 m/s, releases a sand bag at an instant
when the balloon is 20 m above the ground.
a. Compute the position and velocity of the sandbag at the following times after its
release: 1/4s, 1/2s, 1s, 2s
b. How many seconds after its release will the bag strike the ground? [2.59 s]
c. With what velocity will it strike? [-20.48 m/s]
17. A sprinter begins from rest and accelerates at the rate of 2 m/s 2 for 200 m.
a. What is the sprinter’s velocity at the end of the 200 m? [28.28 m/s]
b. How long does it take him to cover it? [14.14 sec]
c. What is his average velocity? [14.14 m/s]
18. A motorcycle travels the first half of a 100 m track with a constant speed of 5 m/s. In the
second half of the 100 m, it experiences a flat tire and decelerates at 0.2 m/s 2. How long
does it take the cycle to travel the 100 m distance? [23.80 sec]
19. A box falls off the tailgate of a truck and slides a distance of 62.5 m before coming to a
halt. If friction slows the box at the rate of 5 m/s 2:
a. What was the speed of the truck when the box fell? [25 m/s]
b. How long does it take the box to stop? [5 s]
20. A driver traveling at 90 km/hr sees the lights of a barrier 40 m ahead. It takes the driver
0.75 seconds to apply the brakes. Once braking begins, the car slows at a maximum
rate of 10 m/s2.
a. Does the car hit the barrier? [yes, at 14m/s, or overshoots by 10m]
b. At the moment the driver notices the wall, at what maximum velocity could the
car be traveling so that it does not slam into the barrier?
21. An engineer decides to design a runway to accommodate flying squirrels. To take off,
the squirrels must attain a ground speed of 10 m/s. If they can accelerate at the rate of
1.5 m/s2.
a. How long will it take the squirrels to reach this velocity? [6.67 s]
b. What must be the minimum length of the runway? [33.37 m]
22. A bicycle traveling at 4 m/s undergoes the same acceleration during 5 seconds as a bus
whose velocity changes from 16 m/s to 20 m/s in 8 seconds. What is the bike’s final
velocity? [6.50 m/s]
23. A robber drops a bag of loot into a 30 m well. If the speed of sound is 340 m/s, how long
after dropping the bag does he hear the splash? [2.56 sec]
24. A DC-8 has a take-off speed of 80 m/s, which it reaches 35 seconds after starting from
rest.
a. How much time does the plane spend going from 0-20 m/s? [8.73 sec]
b. What distance does it cover doing so? [87.26 m]
c. How much time does it spend going from 60-80 m/s? [8.73 s]
d. What distance does it cover doing so? [611.35 m]
e. What is the minimum length of the runway? [1397.40 m]
Page 24
PreAP Physics Homework Problems
25. A penny is dropped off a tall building and hits the ground 5 seconds later. How tall is the
building? [+122.50 m]
26. A young vandal wishes to hit a truck traveling at a constant speed of 20m/s with a water
balloon. If the vandal is in a tree, 40 m from the top of the truck, how far should the truck
be from the tree when she releases the balloon so that it hits the truck when it is at a
position directly beneath her? [57.20 m]
27. The Tokyo Express accelerates at the rate of 1 m/s2 for one minute. If it begins from
rest:
a. How far will it have traveled? [1800 m]
b. What is its velocity at the end of this time? [60 m/s]
c. What is its average velocity over this distance? [30 m/s]
28. A jumping bean jumps vertically upward from the edge of a table. It has a speed of 10
m/s when it reaches half of its maximum height.
a. How high does it rise? [10.20 m]
b. What is its velocity and acceleration 1 second after it jumps? [4.3 m/s, ACC]
c. 3 seconds after? [-15.27 m/s, ACC]
d. What is its average velocity during the first half second? [11.68 m/s]
29. An ultra-light taking off has a 500 m runway. If it starts from rest, constantly accelerates,
and travels the 500 m in 30 seconds with what velocity did it take off? [33.33 m/s]
30. A juggler throws a ball upward and catches it 3.5 seconds later.
a. What is the ball’s initial velocity? [17.15 m/s]
b. What is the ball’s maximum height? [15.01 m]
31. A taxicab driver forgets to stop at a hotel. As it passes the hotel, he decelerates. Five
seconds later the cab is 80 m beyond the hotel and has slowed to 10 m/s.
a. What is the speed of the cab as it passed the stop? [22 m/s]
b. What is the acceleration of the cab? [-2.4 m/s2]
32. A flowerpot is dropped and passes by a window below. It takes 0.15 sec to travel from
the top to the bottom of the 1.6 m tall window as it falls to the ground. How far above the
window was the pot released? [5.03 m]
33. A plane accelerates from 2 m/s at the rate of 3 m/s2 over a 530 m distance.
a. How long does it take the plane to cover this distance? [17.14 s]
b. What is its velocity at the end of this 530 m distance? [56.43 m/s]
34. A television is dropped from the top of a cliff, and 1 second later a second television is
thrown downward with a velocity of 20 m/s. How far below the cliff will the second
television overtake the first? [-10.70 m]
35. Tired geese decide to land on the runway used by the flying squirrels in problem #21. If
the geese can slow at the rate of 1.2 m/s2:
a. What is the maximum velocity they can approach the runway? [8.9 m/s]
b. How long does it take them to land completely? [7.42 sec]
36. A missile is launched upward with an acceleration of 100 m/s 2. Eight seconds later, the
engine shuts off.
a. What height does the missile achieve? [35853 m]
b. What is the total time it is in flight? [175.17 sec]
c. What speed does it have when it strikes the ground? [-838.30 m/s]
d. What is the greatest speed of the missile? Why? [-838.3 m/s upon impact]
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PreAP Physics Homework Problems
37. You are traveling down the highway in a 90 km/hr zone at 100 km/hr when you look up
and see a D.P.S. car 300 m ahead. If you can slow at a maximum rate of 3 km/hr/sec:
a. Will you have slowed enough to avoid a ticket? [yes – show work as proof]
b. If you could change your deceleration, what is the minimum deceleration you
could have in order to avoid a ticket?
38. A juggler performs in a room with a 3m ceiling. He bounces the ball off the floor so that
it just reaches the ceiling.
a. With what velocity does the ball come off the floor? [7.67 m/s]
b. How long does it take to go from floor to ceiling? [0.78 s]
39. A second ball is bounced with the same velocity as the first. It leaves the floor at the
instant the first ball leaves the ceiling.
a. How long after the second ball is bounced do they pass one another? [0.39
sec]
b. How high above the floor do the two balls pass? [2.25 m]
40. The Enterprise is traveling at warp 3, which is three times the speed of light (the speed
of light is 3 x 108 m/s). Capt. James T. Kirk orders the ship to accelerate at the rate of
1.2 x 105 m/s2 for a distance of 250 light years (a light year is roughly 1.0 x 10 13 km) in
order to avoid a Klingon battle cruiser because the Captain is a chicken.
a. What is the Enterprise’s velocity at the end of the acceleration? [7.75 x 1011
m/s]
b. How many years does the Enterprise accelerate? [0.20 yr  74.67 days]
c. What is its average velocity? [3.88 x 1011 m/s]
41. A helicopter drops a care package to stranded climbers as it is ascending at 8m/s. The
package hits the ground 4 seconds later.
a. How high was the helicopter when the package dropped? [46.40 m]
b. How high was the helicopter when the package hit? [78.40 m]
42. A toy car begins from rest and accelerates at 20 cm/s 2 for 1.0 m.
a. How long does it take the stomper to cover this distance? [3.16 s]
b. What is its velocity at the end of this acceleration? [63.25 cm/s]
43. A bottle is thrown up such that it has a velocity of 19.6 m/s at half of its maximum height.
a. What is its maximum height? [39.2 m]
b. What is its velocity 1 second after it was thrown? [17.92 m/s]
44. A frantic student is running down the hall to her physics class. At 30.0m from the door
she begins to decelerate at 1.50 m/s2, but she blows it and ends up passing the door at
1.00 m/s.
a. How fast was she traveling 30.0 m from the door when she began to slow
down? [9.54 m/s]
b. What minimum velocity can she have if she wants to stop at the door instead of
passing it? [9.49 m /s]
45. A frog jumps vertically upward from a 20 m tall building with an initial velocity of 10 m/s.
a. How high above the ground with the frog reach? [25.10 m]
b. What is its velocity as it hits the ground below? [-22.18 m/s]
46. A Volvo moving at a constant speed of 20 m/s passes a Saab waiting at a red light just
as the light turns green. If the Saab begins from rest and accelerates at 2 m/s 2:
a. How far does the Saab travel before drawing even with the Volvo? [400 m]
b. How fast is the Saab traveling at this point? [40 m/s]
Page 26
PreAP Physics Homework Problems
47. A hockey player stands on the ice as an opposing player skates by with a puck, moving
at uniform speed of 12m/s. Three seconds after this, the first player decides to chase
him down and body check this guy. If he accelerates at 4 m/s 2:
a. How long does it take him to catch his opponent? [8.20 sec]
b. How far does he travel to do so? [134.40 m]
48. A skateboard starts from rest and accelerates at 2 m/s2 for 10 seconds. It then stays at a
constant speed for 30 seconds, and then slows down at 4 m/s 2 until it finally stops. What
is the total distance covered? [750 m]
49. A bobsled traveling at 24 m/s sees a spectator on the course.
a. What is the stopping distance of the sled if her reaction time is 0.75 sec and the
sled decelerates at 3.6 m/s2? [98 m]
b. If the spectator is 92 m away when the brakes are applied, what is the
acceleration needed to stop the sled in time? [-3.13 m/s2]
50. A truck accelerates from rest at 1 m/s2. At the same instant that the truck starts, a car is
1000m from the truck and moving toward it head on at 20 m/s. How far from the starting
point of the truck are the two when they meet? [420 m]
51. The driver of a bus traveling at 30 m/s sees a dump truck 200 m ahead on the road.
The truck is moving the same direction as the bus at 10 m/s. The bus driver applies his
brakes to avoid a collision which slows the bus at the rate of 1m/s 2.
a. Will there be a collision? [yes, they just touch]
b. If yes, where? [400m from where the bus hits the brakes]
52. A brown fruit bat flying toward a wall sends sound waves that travel 330 m/s when the
bat is 2 m from the wall. If the bat is flying at 20 m/s, how far will the bat fly during the
time required for the sound waves to echo off the wall and reach the bat again?
53. The maximum acceleration of a monorail train is  2m/s2 and its maximum speed is 22
m/s. What is the minimum time for it to travel 990 m between stops? [56 sec]
54. A rather quick roach travels 400 m. It starts from rest and accelerates at 1.5 m/s 2 until it
reaches a speed of 9m/s. The roach continues at this speed and then finally decelerates
at 2m/s2 until it stops. What is the time for the roach to cover this 400 m distance?
Page 27
PreAP Physics Homework Problems
Unit 3: Vectors & Projectiles Problems
Adding Parallel Vectors:
1. a. -------------------> 10 m
--------> 4 m
b. --------------------> 8 m
<---------- 4 m
Adding Perpendicular Vectors: Find the resultant and the angle of the following pairs of
vectors.
2. 3 cm East + 2.5 cm North
3. 5.9 cm East + 7.8 cm South
4. 11.6 cm West + 5.3 cm North
5. 4.5 cm West + 9.9 cm South
Vector Components: Draw the horizontal and vertical components of the vector and label
each with its magnitude.
6. 5 cm at 30o
7. 3.5 cm at 120o
8. 4.8 cm at 335o
9. 2.5 cm at 200o
Adding Non-Parallel and Non-Perpendicular Vectors: Add the following pictorially and
then calculate the magnitude and direction of the resultant vector.
10. 4.0 cm at 45o and 4.0 cm at 110o
11. 1.5 cm at 80o and 3.5 cm at 210o
12. 4.5 cm at 290o and 6.0 cm at 115o
13. 5.0 cm at 55o and 2.5 cm at 100o
Adding 3 or more non-parallel vectors: Add the following vectors, calculate the magnitude
and direction of the resultant. Use the tip-to-tail method to pictorially show the resultant
vector.
14. 1.0 cm at 30o + 2.0 cm at 40o + 3.0 cm at 50o
15. 2.5 cm at 30o + 3.5 cm at 150o + 4.0 cm at 215o
16. 2.0 cm at 195o + 3.0 cm at 30o + 1.0 cm at 25o + 4.0 cm at 85o
Add the Following Vectors (#17-21)
17. 15 cm at 30o and 10 cm at 150o
18. 14 m/s at 300 and 25 m/s at 150o
19. 25 m/s2 at 600 and 30 m/s2 at 205o
20. 150 m/s at 135o and 200 m/s at 30o
21. 200 cm at 195o and 300 cm at 300
22. A boat is moving with the current of the river (heading downstream). The boat’s speed is
25 m/s while the current speed is 2.5 m/s. What is the speed of the boat relative to the
shore?
23. Suzy is riding in a car going 45 km/h north when the car she is in passes a second car
going 38 km/h. What is Suzy’s velocity relative to the second car?
24. Joe is walking toward the engine of an approaching Amtrak train. The train is moving
due South with a speed of 75 miles per hour. Joe walks with an average speed of 5.0
miles per hour. What is his velocity:
a. relative to the train in miles per hour? [80 mi/h]
b. relative to the ground in miles per hour? [5 mi/h]
Page 28
PreAP Physics Homework Problems
25. A student walks 400 m east and then continues to walk another 200 m east. Using
vectors show the total displacement the student walked. What if that same student
walks 400 m east then 200 m west?
26. A student walks 100 m east and another 50 meters to the north. What was the distance
the student covered? What was his displacement from the starting point? Which answer
is a scalar and which is a vector? Why? [150 m, 111.8 m at 11.31o]
27. Kim is in a boat traveling 3.8 m/s straight across a river 240 m wide. The river is flowing
at 1.6 m/s. What is Kim's resultant velocity?
28. A boat sails 20 m at 45o and then 30 m at 15o and then 15 m at 60o. Calculate the
resultant displacement of the boat. [61.48 m at 34.58o]
29. An airplane flying toward 0o at 90 km/h is being blown toward 90o at 50 km/h. What is
the resultant velocity of the plane? [102.96 km/h at 29.05o]
30. A child pulls a rope attached to a sled with a force of 60 N. The rope makes an angle of
40 degrees to the ground.
a. Compute the effective value of the pull tending to move the sled along the
ground (in the horizontal direction). [45.96 N]
b. Compute the force tending to lift the sled vertically. [38.57 N]
31. A wind with a velocity of 50 km/h blows at 35 o.
a. What is the component of the wind’s velocity north? [28.68 km/h]
b. What is the component of the wind’s velocity east? [40.96 km/h]
32. Two tugboats are being used to pull a barge. One pulls with 500 N at 30o and the other
pulls with 400 N at 25o. Calculate the resultant vector. [899.15 N at 27.78o]
33. Two forces act on an object. One force is 100 N at 25o. The second force is 200 N at
135o. Find the magnitude and direction of the net force. [190.57 N at 105.46 o]
34. A ship leaves its home port expecting to travel to a port 500 km due south. Before it can
move, a severe storm comes up and blows the ship 100 km due east.
a. How far is the ship from its destination? [509.90 km]
b. In what direction must the ship travel to reach its destination? [258.69 o]
35. Diane rows a boat at 8 m/s directly across a river that flows at 6.0 m/s. What is the
resultant velocity of the boat? [10 m/s at 53.13o relative to shore]
36. Kyle is flying a plane due north at 225 km/h as a wind carries it due east at 55 km/h.
Find the magnitude and direction of the plane's resultant velocity. [231.63 km/hr at
76.26o]
37. Sue and Jenny kick a soccer ball at exactly the same time. Sue's foot exerts a force of
66 N north. Jenny's foot exerts a force of 88 N east. What is the magnitude and
direction of the resultant force on the ball? [110 N at 36.87o]
38. A weather station releases a weather balloon. The balloon's buoyancy accelerates it
straight up at 15 m/s*s. At the same time, a wind accelerates it horizontally at 6.5 m/s*s.
What is the magnitude and direction (with respect to the horizontal) of the resultant
acceleration? [16.35 m/s at 66.57o]
39. Find the horizontal and vertical components of the 125 m displacement of a superhero
that flies down from the top of a tall building at an angle of 25o below the horizontal. [x =
113.29 m, y = -52.83 m]
Page 29
PreAP Physics Homework Problems
40. Find the x and y components of the following displacements:
a. 600 cm at 27 degrees [x = 534.60 cm, y = 272.39 cm]
b. 49 m at 227 degrees [x=-33.42 m, y = -35.84]
c. 760 Km at 148 degrees [x = -644.52 km, y = 402.74 km]
d. 47.2 m at 311.9 degrees [x = 31.52 m, y = -35.13 m]
41. A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of
60 degrees with the floor. A force of 75 N is exerted on the rope. What is the
component of the force parallel to the floor? [37.50 N]
42. Joanne pulls on a trunk with a 12.6 N horizontal force. Bev pulls at an upward right
angle to Joanne. How hard must Bev pull to make the resultant force on the trunk 13 N?
[y = 3.2 N]
43. You head downstream on a river in a canoe. You can paddle at 5.0 km/h and the river is
flowing at 2.0 km/h. How far downstream will you be in 30 minutes? [3.5 km]
44. You walk 30 m south and 30 m east. Draw and add vectors for these two
displacements. Compute the resultant. [42.43 m at 315o]
45. A bomber flying horizontally at 120 m/s drops a bomb from an elevation of 240 m. How
far horizontally does the bomb travel before striking the ground? [840 m]
46. A ball is thrown horizontally off a 35 m tall tower. The ball strikes the ground 80 m from
the base of the tower.
a. What is the ball’s time in flight? [2.67 s]
b. What is its initial velocity? [29.96 m/s]
c. What is the magnitude and direction of its velocity as it strikes the ground?
[39.79 m/s at 318.84o]
47. A ball rolls off the edge of a table with a velocity of 1 m/s. If the table is 1 m tall:
a. How far from the edge of the table does the ball strike the floor? [0.45 m]
b. How long does the ball fall? [0.45 s]
48. A cannon shoots a projectile horizontally from a 24 m high cliff. The cannon ball lands
100m from the base of the cliff.
a. With what velocity is the projectile fired? [45.25 m/s]
b. What is the projectile’s velocity as it strikes the ground? [50.17 m/s at 334.42o]
49. A DC-8 flying horizontally at an altitude of 20 km and a speed of 250 m/s drops an
engine.
a. How long after it falls does it take the engine to hit the ground? [63.89 s]
b. How far horizontally has the engine traveled when it hits the ground? [15.97 km]
50. A BB gun is aimed directly at the center of a target 50 m away. If the BB is fired
horizontally at 350 m/s, how far below the bull’s-eye will the BB hit? [-0.1m]
51. A life line is to be thrown from a ship 30 m above sea level to a drowning crew person. If
the victim is 30 m horizontally from the ship, with what horizontal speed should the line
be thrown? [12.15 m/s]
52. An arrow is fired at 53o with a velocity of 15 m/s.
a. How long is it in the air? [2.44 s]
b. What is its range? [22.03 m]
53. A cannon fires a shell with a muzzle speed of 600 m/s at 30o.
a. What is the cannon’s range? [31.8 km]
b. How high does the shell rise? [4.6 km]
Page 30
PreAP Physics Homework Problems
54. A cannon’s firing angle is varied during a training exercise. If the cannon fires a shell at
700 m/s, find its range, time in flight and maximum vertical height at 45o [x = 50 km, t =
101.02 s, y = 12.5 km]
55. A football is kicked at an angle of 50o and travels a distance of 20 m before hitting the
ground.
a. What is the initial speed of the ball? [14.12 m/s]
b. How long is it flight? [2.20 s]
c. How high does it rise? [5.97 m]
56. A cat is on a 1.5 m high table and jumps at a 37o angle with a speed of 10 m/s. How far
horizontally from the edge of the table does the cat land? [11.51 m]
57. If George Washington threw a silver dollar across the Potomac River which is 300 m
wide, with what speed did he have to throw the coin? Assume a 45oangle and that
George’s arm is located 1.5 m above the ground.
58. A mortar elevated to 60o scores a hit 15 m up a building 30 m away.
a. With what speed was the shell fired? [21.85 m/s]
b. What is the velocity of the shell as it strikes the building? [13.54 m/s at 36.2 o]
59. A sniper is riding in the back of a pick-up traveling at a constant speed of 20 m/s. If he
fires the bullet straight up in the air with a speed of 100 m/s:
a. How long is the bullet in flight? [20.41 s]
b. Where does the bullet land? [408.20 m]
c. How high does it rise? [510.20 m]
60. A long jumper jumps at a 20o angle and attains a maximum altitude of 0.6 m.
a. What is her initial speed? [10.03 m/s]
b. How far is her jump? [6.60 m]
61. A bomber is climbing at a 37o angle at a speed of 250 m/s. When it reaches a height of 1
km, a bomb is released.
a. How long is the bomb in flight? [36.32 s]
b. How high above the ground does the bomb rise? [2154.86 m]
c. How far horizontally from the point it is released does the bomb travel? [7251.65
m]
d. What is the impact velocity of the bomb? [286.53 m/s at 314.17o]
62. You are traveling at a constant speed of 30 m/s in a car. You wish to release a water
balloon such that it will land in an open manhole.
a. If you release the balloon 1.5 m above the ground, how far from the hole should
you release the balloon? [16.5 m]
b. What is the impact velocity of the balloon? [30.48 m/s at 349.81o]
63. As an open elevator rises at a constant speed of 8 m/s, a boy throws an apple with a
speed of 10 m/s at a 45o angle (in the reference frame of the elevator) when the elevator
is 20 m above the ground.
a. How far horizontally from the elevator does the apple strike the ground? [28.85
m]
b. How far will the apple rise above the ground? [31.59 m]
c. How long is it in flight? [4.08 s]
d. What is the impact velocity? [-25.87 m/s at 285.86o]
Page 31
PreAP Physics Homework Problems
Unit 4: Newton’s Laws
1. What acceleration will result when a 12 N net force to the right is applied to a 3
kg object resting on a surface? What acceleration will result when the same net
force is applied to a 6 kg object?
2. A horizontal net force of 16 N causes a crate to accelerate at the rate of 5.0
m/s2. Determine the mass of the crate.
3. An object is accelerating at 2 m/s2.
a. If the net force is tripled, and the mass remains the same, what is the
new acceleration?
b. If the acceleration is still 2 m/s2, the mass is doubled and the net force
remains the same, what is the new acceleration?
c. If the acceleration is still 2 m/s2, the mass is tripled and the net force is
doubled, what is the new acceleration?
4. Write an expression for the value of FN in each situation below.
Fpush
Fpull
m
m
m
5. Using the diagram below, list at least 5 action-reaction pairs.
6. A 15 kg object is being pulled upward by a massless rope with an acceleration
of 3.0 m/s2.
a. What is the tension in the rope? [192 N]
b. The object is now accelerating downward at 3.0 m/s2. What is the tension
in the rope? [102 N]
7. A 10 kg mass rests on a horizontal surface. The frictional force opposing the
motion is 20 N. If a 100 N force is applied to the object, what will its acceleration
be? [8.0 m/s2]
8. A man stands in an elevator that accelerates up. His mass is 50 kg. The scale
reads the man is 600 N. What is the actual weight of the man? What is his
acceleration? [490 N, 2.2 m/s2]
9. A 100 N box is accelerated across the floor to the left with an applied force of 20
N. The object encounters 10 N of friction. Determine the normal force, the net
force, the coefficient of friction (µ) between the object and the surface, the mass
and the acceleration of the object. [Fnet = 10 N; FN = 100 N; m = 10.204 kg; a =
0.98 m/s2; µ = 0.10]
Page 32
PreAP Physics Homework Problems
2
10. An object is accelerating at 2 m/s . If the net force is tripled and the mass of the
object is halved, what is the new acceleration?
11. FBD for four situations are shown below. The net force is known for each
situation. Write the horizontal and vertical net force equations, then solve for the
unknown values.
12. 12. Select the correct law for the given application.
a. The driver loaded his truck with grain and it could not accelerate as
rapidly.
b. Anne steps from the boat to the dock and is surprised to see the boat
move in the opposite direction.
c. Anne and Jim stand on skateboards. Anne has a rope tied around her
waist and her hands up in the air. Jim pulls on the rope and they both
move towards each other.
d. The coffee on the dash slid to the side when the driver made a turn.
e. The book on the floor of the bus slid to the front as the driver applied the
brakes.
f. The driver drove his friend’s Mustang which had a smaller engine and
discovered it drove sluggishly.
g. The student was whirling a rubber stopper on the end of the string when
the string broke and the stopper went along a tangent to the circle and hit
the wall.
h. It took longer for the elevator to reach the top floor when it had more
people on it.
i. When the gun was fired, it pushed on the shoulder of the man.
13. A boy and his skateboard have a combined mass of 80 kg. If he is traveling 6
m/s, what net force is needed to stop him in 4 seconds? [-120 N]
14. An applied force of 50 N is used to accelerate an 8.164 kg object to the right
across a frictional surface. The object encounters 10 N of friction. Determine the
normal force, the net force and the acceleration of the object. [FN = 80 N; Fnet =
40 N; a = 4.9 m/s2]
15. After initially picking the stone up off the ground, a man exerts a 148 N force
upwards on a 10 kg stone. What is the acceleration of the stone? [5 m/s2]
Page 33
PreAP Physics Homework Problems
16. A man who weighs 900 N stands in an elevator on a scale and it reads 1000 N.
What direction is the elevator accelerating and what is the acceleration of the
elevator? [1.089 m/s2 upwards]
17. A man who has a mass of 50 kg stands in an elevator that is accelerating up at
3 m/s2. How much does this man weigh? What does he read on the scale as he
accelerates up?
[FW = 490 N, scale = FN = 640 N]
18. A 5 kg object is sliding to the right and is encountering a friction force which
slows it down. The coefficient of friction (µ) between the object and the surface
is 0.1. Determine the force of gravity, the normal force, the force of friction, the
net force and the acceleration. [Fnet = -4.90 N; FN = 49 N; Fg = 49 N; a = -0.98
m/s2; FFR = 4.90 N]
19. A rightward force is applied to a 6 kg object to move it across a rough surface at
constant velocity. The object encounters 15 N of frictional force. Determine the
force of gravity, the normal force, the net force and the applied force. [Fnet = 0 N;
FN = 58.8 N; Fg = 58.8 N; Fa = 15 N]
20. A .22 caliber slug moving at 360 m/s hits and embeds in a block of wood to a
depth of 0.1 m. If the slug has a mass of 1.8 g:
a. How long does it take the slug to stop? [5.56 x 10-4s]
b. What is the average retarding force? (What force causes the bullet to
stop?) [-1166.4 N]
21. A 20 kg sled rests on a horizontal surface. If it takes 75 N to start the sled in
motion and 60 N to keep it moving at a constant speed, what are the coefficients
of static and kinetic friction respectively? [µs = 0.383; µk = 0.306]
22. A leftward force is applied to a 5 kg object to move it across a rough surface with
a leftward acceleration of 2 m/s2. The coefficient of friction, µ, between the object
and the surface is 0.1. Determine the gravitational force, the normal force, the
applied force, the frictional force and the net force. [Fnet = 10 N; FN = 49 N; Fg =
49 N; Fa = 14.9 N; FFR = 4.9 N]
23. A rightward force of 25 N is applied to a 4 kg object to move it across a rough
surface with a rightward acceleration of 2.5 m/s2. Determine the gravitational
force, the normal force, the frictional force, and the coefficient of friction between
the object and the surface. [FFR = 15 N; FN = 39.2 N; Fg = 39.2 N; µ = 0.383]
24. An 8.0 kg rocket is fired and encounters a force of air resistance of 4.9 N. If the
rocket’s engines applied 100 N of thrust:
a. What is the net force on the rocket? [16.7 N]
b. What is the rocket’s acceleration? [2.09 m/s2]
25. A 1 kg object can be accelerated at 10 m/s2. If you apply this same force to a 4
kg object, what will its acceleration be? [2.5 m/s2]
26. A 15 kg cart is pushed on a frictionless surface from rest horizontally by a 30 N
force.
a. What is the cart’s acceleration? [2 m/s2]
b. How far will it travel in 10 seconds? [100 m]
c. What is its velocity at the end of 10 seconds? [20 m/s]
Page 34
PreAP Physics Homework Problems
27. The coefficient of static friction between a 100 kg box and a surface is 0.30.
What is the maximum force that can be applied to the box horizontally before it
will move? [294 N]
28. A 90 N box rests on a horizontal surface. If a force of 45 N is applied to the box,
will it move if the coefficient of static friction is 0.773? [no; FFR = 69.57 N]
29. How much force must be applied by a worker to slide a 250 N refrigerator across
the floor at a constant speed if the coefficient of sliding friction is 0.226? [56.5 N]
30. Lemon and her friends are going for a ride.
a. If their combined weight is 7.5 N and it takes 3.4 N of force to get them
going, what is the coefficient of static friction between the ground and
their box sled? [µ = 0.453]
b. How much force would be needed to keep Lemon and her friends sliding
at a constant speed if the coefficient of sliding friction is 0.230? [1.725 N]
31. A 2 kg crate with initial speed of 3 m/s slides 2 m to a stop.
a. What is the coefficient of kinetic friction? [0.230]
b. What force would be needed to keep the crate moving at a constant
speed? [4.508 N]
32. A force of 300 N is sufficient to keep a 1000 N wood crate moving at a constant
velocity across a wooden floor. What is the coefficient of kinetic friction (µk)? [µk
= 0.300]
33. A 1000 kg truck going 75 km/h slides 70 m to a stop. Find the coefficient of
kinetic friction (µk). [µk = 0.316]
34. A force of 1000 N is applied to a 10,000 N car. If the µk is 0.04, what is the car’s
acceleration? [0.588 m/s2]
35. The coefficient of kinetic friction between a rubber tire and the road is 0.5.
a. Find the minimum time in which a 1500 kg car whose initial velocity is
26.8 m/s will stop. [5.469 sec]
b. What distance will the car cover in this amount of time? [73.290 m]
36. A bowling ball with an initial velocity of 3 m/s rolls along a level floor for 50 m
before coming to a stop. What is the µk between the ball and the floor? [µk =
0.0092]
37. A tractor accelerates a 900 kg log to 15 m/s in 30 s.
a. What was the net force? [450 N]
b. If the coefficient of friction is 0.4, what was the friction force applied?
[3528 N]
c. What was the force of the tractor? [3978 N]
Page 35
PreAP Physics Homework Problems
Unit 5: Newton’s Laws Part 2
1. Find the tension in the rope and the acceleration of the system. [76.5 N, 2.16 m/s2]
2. Find the tension in the rope and the acceleration of the system. [1.31 N, 3.27 m/s 2]
a
0.1
kg
0.2
kg
3. Find the tension in the rope and the acceleration of the system. [2.85 N, 2.67 m/s 2]
a
0.6 kg
µ = 0.212
0.4
kg
4. Find the tension in the rope and the acceleration of the system. [19.28 N, 6.19 m/s2]
5. Find the mass and the tension in the string if the system accelerates at 0.55 m/s 2. [10.1
N, 1.09 kg]
a
5 kg
µ = 0.150
m
Page 36
PreAP Physics Homework Problems
6. Find the normal force, mass and acceleration if a 7 N box is pulled to the right with a 10
N force at an angle of 37o from the horizontal and the box experiences a frictional force
of 3 N. [FN = 0.98 N, a=7.02 m/s2, m=0.71 kg]
7. You are pulling a 30 kg box across the floor to the right. The coefficient of friction is 0.20.
You are pulling with a force of 112 N at an angle of 12o from the horizontal. Find the
normal force and acceleration of the box. [a = 1.85 m/s2, FN = 270.71 N]
8. A 90 kg crate is pushed with a force of 475 N at an angle of 35o with the horizontal. If the
coefficient of friction is 0.25, calculate the acceleration of the crate. [a = 1.12 m/s 2]
9. A 10 kg lawn mower is pushed along by a force applied at a 20o angle to the horizontal.
If the mower accelerates to the right at 3.4 m/s2, what is the applied force? (ignore
friction)[36.18 N]
10. A 245 N box is pushed with an applied force at an angle of 45o with the horizontal. What
is the value of the applied force needed to get the box sliding to the right if the µs = 0.45?
[Fa = 282.69 N]
11. A 20 kg sled is pulled along a frictionless horizontal surface. If the rope is pulling at a 30 0
angle to the horizontal and the sled accelerates at 2.0 m/s 2, what is the tension in the
rope? [46.19 N]
12. A 49 N block is pulled westward across a frictionless horizontal surface by a 30 N force
applied at an 87o angle above the horizontal. Find the normal force and the block’s
acceleration. [a = 0.31 m/s2, FN = 19.04 N]
13. A 150 N crate is pushed with a force of 475 N at an angle of 15o with the horizontal.
What is the coefficient of friction if the acceleration of the object is 20.5 m/s 2? [0.53]
14. A 147 N box is pushed with an applied force at an angle of 37o with the horizontal. What
is the value of the applied force needed to get the box sliding if µ s = 0.70? [270.79 N]
15. A 50 kg object is pulled over a rough horizontal surface by a 200 N force directed at an
angle of 14.0o with the horizontal. If the coefficient of kinetic friction is 0.40, find the
acceleration of the object. [0.35 m/s2]
16. A 70 kg skier is sliding up a 12o incline opposed by a 100 N frictional force. Find her
acceleration and the normal force. [a = -3.47 m/s2, FN = 671.01 N]
17. A skier slides down a 12o incline with a surface having a coefficient of kinetic friction of
0.16. What is her acceleration? [0.50 m/s2]
18. A block slides down a 10o incline at a constant speed. What is the coefficient of sliding
friction between the block’s surface and the incline? [0.18]
19. A 5 kg block is sliding up a 30o incline. What is the block’s acceleration:
a. if the incline is frictionless? [-4.9 m/s2]
b. if the incline has a coefficient of kinetic friction of 0.20? [-6.60 m/s2]
c. What applied force would be needed to offset the friction (µ = 0.20) and make
the block move up the incline at a constant rate? [32.99 N]
20. A skier has just begun descending a 30o slope.
a. Assuming µ = 0.10, what is her acceleration? [4.05 m/s2]
b. If she starts from rest, what is her speed after 4.0 seconds? [16.2 m/s]
c. Suppose the snow is now all mushy and the skier moves down the same slope
but with a constant velocity. What is the coefficient of friction? [0.58]
Page 37
PreAP Physics Homework Problems
21. Bill is unloading a 20 kg bottle of water from his delivery truck when one of the bottles
tips over and slides down the truck ramp that is inclined at an angle of 30 o to the ground.
The ramp has friction.
a. What amount of force moves the bottle down the ramp? [98 N]
b. What is the normal force on the bottle? [169.74 N]
d. If the bottle accelerates at 1 m/s2, what is the force of friction? [78 N]
e. What is the coefficient of friction between the ramp and the bottle? [0.46]
22. A 1250 kg slippery hippo slides down a mud-covered hill inclined at an angle of 18o to
the horizontal.
a. What is the hippo’s normal force? [11650.44 N]
b. If the µk between the hippo and the mud is 0.09, what force of friction impedes
the hippo’s motion down the hill? [1048.54 N]
c. What is the hippo’s force down the hill? [3785.46 N]
d. What is the hippo’s acceleration? [2.19 m/s2]
23. Lance, a 65 kg lifeguard, slides down a water slide that is inclined at an angle of 53 o to
the horizontal, into the swimming pool. If the µk = 0.05, what is Lance’s acceleration as
he slides down? [7.53 m/s2]
24. Suppose a giant hamburger slides down a ramp that has a 45o incline. The µk between
the hamburger and the ramp is 0.597, so that the net force acting on the hamburger is
6.99 x 103 N.
a. What is the mass of the hamburger? [2503 kg]
b. What is the normal force that the ramp exerts on the hamburger? [17344.91 N]
25. An extremely light, drivable car with a mass of only 9.5 kg was built in London. Suppose
that the wheels of the car are locked, so that the car no longer rolls. If the car is pushed
up a 30o slope by an applied force of 80 N, and the net acceleration of the car is 1.64
m/s2, what is the µk between the car and the incline? [0.22]
26. Find the tension in the rope and the acceleration of the system below if the coefficient of
kinetic friction is 0.33. [14.77 N, 2.67 m/s2]
27. Find the tension in the rope connecting the two
masses and the acceleration of the system if the
applied force is 180 N. Assume the surface is
frictionless. [78.77 N, 16.47 m/s2]
Page 38
PreAP Physics Homework Problems
28. Find the tension in all 3 cords if object A is a 40 N object. [T 1 = 19.65 N, T2 = 34.48 N, T3
= 40 N]
30o
60o
T1
T2
T3
A
29. Find the weight of object B and the tension in cord 2, if T 1 = 260 N. [Fg = 355.16 N, T2 =
318.43 N]
30o
45o
T1
T2
T3
B
30. Find T2 and its angle from the horizontal and T 3 if T1 = 100 N. [T2 = 31.71 N, Θ = 35o, T3
= 78.4 N]
75o
T1
T3
T2
8 kg
31. A rope extends between two poles. A 90 N boy hangs from it as shown below. Find the
tensions in the two parts of the rope. [T 1 = 346.95 N, T2 = 343.51 N]
10o
T1
5o
T2
Page 39
PreAP Physics Homework Problems
32. The tension in the horizontal cord is 30 N as shown below. Find the weight of the object.
[25.17 N]
40o
30 N
33. Find the tensions in each string. [T 1 = 31.42 N, T2 = 37.40 N, T3 = 49 N]
40o
50o
T1
T2
T3
5 kg
34. Find the tension in the cord and the acceleration of the system if the incline is
frictionless. [0.67 m/s2]
a
10 kg
20 kg
37o
35. Find the tension in the cord and the acceleration of the system below if the coefficient of
friction is 0.52. [27.11 N, 3.02 m/s2]
a
2 kg
4 kg
45o
36. Three blocks of masses 15 kg, 7 kg, and 14 kg are
connected by light strings that pass over frictionless
pulleys as shown below. The system is accelerating
to the left and the coefficient of friction between the
surface and masses is 0.40. What is the
acceleration of the system and the tensions in each
of the strings? [0.33 m/s2, T1 = 142.05 N, T2 = 112.34 N]
Page 40
PreAP Physics Homework Problems
Unit 6: Circular Motion and Gravity
1.
A mass of 1.5 kg moves in a circular path with a constant speed of 3 m/s on a horizontal
frictionless surface. The mass is held to the circular path by a light cord 2.4 m long that has one
end fixed and the other end attached to the mass. Calculate the tension in the cord. [5.625 N]
2.
An automobile of mass 1500 kg travels in a circular path of radius 20 m on a horizontal road
surface at a speed of 12.5 m/s (around 72 mph). What is the coefficient of static friction between
the tires and the road? [0.797]
3.
Determine the centripetal force acting on a 40 kg child who makes 10 revolutions around in the
Cliffhanger in 29.3 s. The radius of the barrel of the ride is 2.9 m. [533.462 N]
4.
A child whirls a stone of mass 0.5 kg in a vertical circle on the end of a string 40 cm long. At the
lowest point of the circle the velocity of the stone is 3 m/s. Calculate the tension in the string at this
point. [16.15 N]
5.
Anna Litical is riding on The Demon of Great America. Anna experiences a centripetal acceleration
of 15.0 m/s2 at the top of the loop of the roller coaster. Determine the normal force acting upon
Anna’s 1000 kg roller coaster car at the top of the loop. [5200 N]
6.
What is the direction of the centripetal force of an object in uniform circular motion? What is the
direction of the centripetal acceleration?
7.
What causes a tin can whirled on the end of a string to move in a circular path? If the string
breaks, what causes it to move in a straight-line path?
8.
An 1800 kg car rounds a curve of radius 92 m with a speed of 3.0 m/s. If its wheels are on the
verge of slipping on the road, what is the force of friction? [176.087 N]
9.
A model airplane is guided in a horizontal circular path by a cord of length 16 m. If it has a
constant speed of 18 m/s and a mass of 200 g, what is the tension in the cord? [4.05 N]
10. What is the centripetal acceleration of an object moving in a horizontal circular path of 20 m radius
with a speed of 18 m/s? [16.2 m/s]
11. An automobile travels around a circular track of radius 0.120 km at a speed of 2.5 m/s.
a. What is the centripetal acceleration? [0.052 m/s 2]
b. If the car has a mass of 1200 kg and the track is completely level, what is the coefficient
of friction between the tires and the track as the car travels on the circular track? [0.005]
12. If a car travels in a circle at a constant speed, what is the direction of the net force on the car?
What is the name of the net force for any uniform circular motion problem?
13. Anna Litical is practicing a centripetal force demonstration at home. She fills a bucket with water,
ties it to a strong rope, and spins it vertically in a circle. Anna spins the bucket when it is half-full of
water and when it is quarter-full of water. In which case is more force required to spin the bucket in
a circle? Explain using an equation as a “guide to thinking”.
14. A Lincoln Continental and a VW Beatle are making a turn. The Lincoln is four times more massive
than the Beatle. If they make the turn at the same speed, then how do the centripetal forces acting
on the two cars compare? Explain.
15. The Cajun Cliffhanger at Great America is a ride in which occupants line the perimeter of a
cylinder and spin in a circle at a high rate of turning. When the cylinder begins spinning very
rapidly, the floor is removed from under the rider’s feet. What effect does a tripling in speed have
upon the centripetal force? Explain.
16. A 95 kg halfback makes a turn on the football field. The halfback sweeps out a path which is a
portion of a circle with a radius of 12 meters. The halfback makes a quarter of a turn around the
circle in 2.1 seconds. Determine the speed, acceleration and net force acting upon the halfback.
[8.976 m/s, 6.714 m/s2, 637.835 N]
Page 41
PreAP Physics Homework Problems
17. A 1.5 kg bucket of water is tied by a rope and whirled in a circle with a radius of 1.0 m. At the top
of the circular loop, the speed of the bucket is 4.0 m/s. Determine the acceleration, the net force
and the individual force values when the bucket is at the top of the circular loop. [16 m/s 2, T = 9.3
N, Fnet = 24 N, Fg = 14.7 N]
18. Noah Formula is riding a roller coaster and encounters a loop. Noah is traveling 6 m/s at the top of
the loop and 18.0 m/s at the bottom of the loop. The top of the loop has a radius of curvature of
3.2 m and the bottom of the loop has a radius of curvature of 16.0 m. Use Newton’s second law to
determine the normal force acting upon Noah’s 80 kg body at the top and at the bottom of the
loop. [FNtop = 116 N, FNbottom = 2404 N]
19. Anna Litical is riding a wooden roller coaster. Anna encounters the bottom of a small dip having a
radius of curvature of 15.0 m. At the bottom of this dip Anna is traveling with a speed of 16.0 m/s
and experiencing a much larger than usual normal force. Determine the normal force acting upon
Anna’s 50 kg body. [1343.33 N]
See Chart of Standards in Appendix as needed:
20. Determine the speed of the Hubble Telescope orbiting at a height of 5.96 x 105 m above the
earth’s surface.
21. The moon orbits the earth once every 27.3 days. What is the centripetal acceleration of the moon?
22. A spacecraft orbits the moon in a circular orbit of radius 8.01 x 10 8 m. What is the velocity of the
spacecraft as it orbits?
23. What is the gravitational attraction between the earth and the moon? Which force is the largest,
the earth pulling on the moon or the moon pulling on the earth?
24. What is the value of g (acceleration due to gravity) at a height of 1500 km above the earth’s
surface? [6.42 m/s2]
25. Calculate the velocity that a satellite shot from Earth must have to orbit Earth 150 km above the
surface of Earth. [7815.503 m/s]
b. How long (in seconds) would it take the satellite to return to where it was shot? [5.25 x 10 3 sec]
26. The sun revolves around the center of the galaxy with a radius of 2.2 x 10 20 m. The time for one
rotation is 2.5 x 108 years.
a. Find the speed with which the sun moves around the center of the galaxy. [1.753 x 105
m/s]
b. Find the mass of the galaxy. [1.014 x 1041 kg]
c. Assuming that an average star in the galaxy has the mass of the sun, find the number of
stars in the galaxy. [5.095 x 1010 stars]
27. Two tennis balls weigh 1.64 kg and their centers are 0.020 m apart. Solve for the gravitational
force between them. [4.485 x 10-7 N]
28. Two balls have their centers of mass 2 m apart. One has a mass of 5 kg and the other has a mass
of 8 kg.
a. What is the gravitational force between them? [6.67 x 10 -10 N]
b. The distance between the balls is now cut in half. What is the gravitational force between
them? [2.668 x 10-9 N]
29. Calculate the acceleration due to gravity on the surface of the earth. [9.799 m/s 2]
30. Calculate the acceleration due to gravity on the surface of the moon. [1.619 m/s2]
31. The planet Venus has a mass of 4.88 x 1024 kg and has a radius of 6.073 x 106 m.
a. Find the velocity of a satellite in orbit 377 km above its surface. [7103.837 m/s]
b. Calculate the period of the satellite. [5704.881 s]
32. What is the force of gravity acting on a 5000 kg space craft when it orbits three earth radii from the
earth’s center? [5.44 x 103 N]
33. Two balls have their centers 5.0 m apart. One has a mass of 11.0 kg and the other has a mass of
7.0 kg. What is the gravitational force between them? [2.054 x 10-10 N]
Page 42
PreAP Physics Homework Problems
Unit 7: Momentum and Impulse
1. A compact car, mass 725 kg, is moving at +100 km/h. What is its momentum?
[20139.05 kg m/s]
2. A snowmobile has a mass of 2.5 x 102 kg. It is acted upon by a force so that its velocity
changes from 6.0 m/s to 28 m/s. What is the change in its momentum? [5500 kg m/s]
3. Jenny has a mass of 35.6 kg and her skateboard has a mass of 1.3 kg. What is the
momentum of Jenny and her skateboard together if they are going 9.50 m/s? [350.55 kg
m/s]
4. A 0.20 kg baseball is pitched horizontally with a speed of +40 m/s. When it hits the bat a
force of 1.7 x 104 N acts on the ball to send it soaring in the opposite direction. If the bat
and ball are in contact for 8.0 x 10-3 s, what is the impulse delivered to the ball by the
bat? [136 N s]
5. A hockey player makes a slap shot, exerting a force of 30.0 N on the puck for 0.16 s.
What impulse is given to the puck? [4.8 N s]
6. A basketball of mass 0.23 kg is thrown horizontally against a rigid vertical wall with a
velocity of 20 m/s. It rebounds with a velocity of 15 m/s.
a. Calculate the impulse of the force of the wall on the basketball. [-8.05 N s]
b. What is the force of the wall on the basketball if it remains in contact with the
wall for 0.5 s? [-16.1 N]
7. A 125 g snowball is traveling with a speed of 22 m/s when it hits the fence. If the
snowball is completely stopped by the fence and does not rebound, what is the impulse
of the force of the fence on the snowball? [-2.75 N s]
8. A woman of mass 50 kg is swimming with a velocity of 1.6 m/s. If she stops stroking and
glides to a stop in the water, what is the impulse of the force that stops her? [-80 N s]
9. A 0.41 kg football that is initially at rest acquires a velocity of 35 m/s when it is kicked. If
the kicker’s boot remains in contact with the ball for 0.08 s, what is the average force of
the kick? [179.375 N]
10. A 1.5 kg object moving with a speed of 2.5 m/s strikes a wall and the ball rebounds with
a speed of 1.5 m/s. The ball is in contact with the wall for 0.045 s. What is the magnitude
of the average force exerted on the ball by the wall? [-133.333 N]
11. A 1525 kg car traveling 30 m/s crashes into a concrete wall. The front of the car
crumples and the car comes to rest in 0.12 s. Calculate the average force exerted on the
car by the wall. [-381250 N]
12. A woman, driving a golf ball off of the tee, gives the ball a speed of 20.0 m/s. The mass
of the ball is 45 g and the duration of the impact with the golf club is 6.0 x 10-3 s.
a. What is the change in the momentum of the ball? [0.9 kg m/s]
b. Determine the average force applied by the club. [150 N]
13. A 0.144 kg baseball is pitched horizontally at +38 m/s. After it is hit by a bat, it moves
horizontally at -38 m/s.
a. What impulse did the bat deliver to the ball? [-10.944 kg m/s]
b. If the bat and ball were in contact 8.0 x 10-4 s, what was the average force the
bat exerted on the ball? [-13680 N]
c. Find the acceleration of the ball during its contact with the bat. [-95000 m/s2]
14. A 32 g bullet strikes a 5 kg block of wood that is initially at rest and embeds in the wood.
If the subsequent velocity of the block is 3.8 m/s, calculate the initial velocity of the
bullet. [597.55 m/s]
Page 43
PreAP Physics Homework Problems
15. A 0.105 kg hockey puck moving at 48 m/s is caught by a 75 kg goalie at rest. With what
speed does the goalie slide on the ice? [0.0671 m/s]
16. A 35.0 g bullet moving at 475 m/s strikes a 2.5 kg wooden block. The bullet passes
through the block, leaving at 275 m/s. The block was at rest when it was hit. How fast is
it moving when the bullet leaves? [2.8 m/s]
17. A 0.5 kg ball traveling at 6.0 m/s collides head on with a 1.00 kg ball moving in the
opposite direction at a velocity of -12.0 m/s. The 0.50 kg ball moves away at -14.0 m/s
after the collision. Find the velocity of the second ball. [-2.0 m/s]
18. A 95 kg fullback, running at 8.2 m/s collides in midair with a 128 kg defensive tackle
moving in the opposite direction. Both players end up with zero speed.
a. What was the fullback’s momentum before the collision? [779 kg m/s]
b. What was the change in the fullback’s momentum? [-779 kg m/s]
c. What was the tackle’s original momentum? [-779 kg m/s]
d. What was the change in the tackle’s momentum? [779 kg m/s]
19. Two 75 kg campers are in the middle of a creek in a 45 kg boat without a paddle. All
they have on board the boat is a quantity of 0.50 kg cans of beans. One of the campers
is able to throw a can with a speed of 26.8 m/s. How many cans of beans must the
camper throw to give the boat a speed of 1.0 m/s? Ignore friction. Since mass of cans is
so much less than the mass of the boat initially, can ignore mass of cans initially as well.
[15 cans]
Page 44