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A1 Conceptual Physics Homework Problems
Unit 1: Introduction to Physics
Math Review, Appendix and Chapter 1
1. What is the area of a rectangular room that is 3ft x 4ft?
2. What is Volume of a box that is 2m x 3m x 1m?
3. Can the following be added: If so, what are the resulting numeric answer with units.
a. 1m + 2 m
d. 2ft + 8 ft2
b. 1m + 2 m/s
e. 16087N + 58978 Nm
c. 3 m + 4.2 m
f. 16087 N + 58978 N
4. Can the following be subtracted? If so, what are the resulting numeric answer with
units.
a. 1m - 2 m
d. 2ft - 8 ft2
b. 1m - 2 m/s
e. 16087N - 58978 Nm
c. 3 m - 4.2 m
f. 16087 N - 58978 N
5. Can the following be multiplied? If so, what are the resulting numeric answer with
units.
a. (2 m) ( 4 s)
d. (100 m/s) (100s)
b. (25 N) (12.5s)
e. (99 g ) ( 3 gs)
c. (3.14 cm) (2 cm)
f. (2π) ( 2s)
6. Can the following be divided? If so, what are the resulting numeric answer with
units
a. 2 m / 4 s
d. 100 m/s / 100s
b. 25 N / 12.5N
e. 99 g / 3 gs
c. 3.14 cm/2 cm
f. 2π / 2s
7. Rearrange the following formulas to solve for the specified variable.
a. p = mv
solve for v
b. c = Lm + ½ ab2
solve for m
solve for a
c. d = m/v
solve for m
d. a = v2 – v1
t
solve for t
solve for v1
8. Write the following in scientific notion
a. 125,000
b. -21,345,939
c. 560
d. 0.912
e. 0.0005678
9. Write the following in conventional notion
a. 1.56 x 104
b. 3.6 x 10-3
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c. 1.222 x 10-2
d. 1.375 x 102
A1 Conceptual Physics Unit Homework
Unit 2: Kinematics and Linear Motion
Distance vs Displacement
1. You walk 25 m east, 67 m north, 67 m south and then 25 m west. What is your
distance traveled? [184m]
2. For #1, what is your displacement? [0m]
3. You walk 25 m east then 67 m west. What is your displacement? [42 m west]
4. An airplane travels 1000 miles on a round trip. What is it’s distance covered and
displacement? [1000m, 0m]
5. Yin walks 40m east, then 20m north, then 40 m west and finally 20 m south. What
is his displacement? Distance traveled? [0m, 120m]
Interpreting Position-Graphs
6. On the graphs below, draw two lines/curves to represent the given verbal
descriptions; label the
lines/curves as A or B.
7.
For each type of accelerated motion, construct the appropriate shape of a positiontime graph.
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8.
A1 Conceptual Physics Unit Homework
Use your understanding of the meaning of slope and shape of position-time graphs
to describe the motion depicted by each of the following graphs.
9.
Use the position-time graphs below to determine the velocity.
Speed vs Velocity
10.
11.
12.
13.
14.
Suppose you are considering three different paths (A, B and C) between the same
two locations. Along which path would you have to move with the greatest speed to
arrive at the destination in the same amount of time?
True or False: It is possible for an object to move for 10 seconds at a high speed and
end up with no overall change in position. Give an example
How much time would it take for the sound of thunder to travel 1500 meters if
sound travels at the speed of 330 m/s? [4.55 s]
A pitched baseball goes 35 m in 2.1 seconds. What is its speed? [16.67 m/s]
A car travels east on 1-10 toward Beaumont, TX, going 80 km/h. It is 125 km to
Beaumont. How long does it take for the trip? [1.56 hr]
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A1 Conceptual Physics Unit Homework
15. A bicycle rider rides her bike at 13 m/s to the South. How far will she be able to ride
in 1 hour? [46.8 km]
16. A bus goes 100 km in 2.5 hours, stops for 0.5 hours, and then goes 70 km in 1.4
hours and another 60 km in 0.75 hours. What was the bus' average speed? [44.66
km/hr]
17. A man walks 300 meters east in 420 seconds and then walks 700 meters west in
another 1130 seconds. Determine the man's distance, displacement and average
speed for the entire trip. [0.65 m/s]
18. A bug crawls in a straight line at 2.35 m/s for 15 sec. How far did the bug
crawl?[35.25 m]
19. If you walk to the right (forwards) for 200 m over 25 seconds, what is your velocity?
[8 m/s, right]
20. Suppose that you run for 10 seconds along three different paths.
a. Rank the three paths from the lowest speed to the greatest speed.
__________
b. Rank the three paths from the lowest velocity to the greatest velocity .
__________
21. You run from your house to a friend's house that is 3 miles away in 30 minutes. You
then immediately walk home, taking 1 hour on your return trip.
a. What was the average speed (in mi/hr) for the entire trip? _______________
b. What was the average velocity (in mi/hr) for the entire trip? _______________
22. A cross-country skier moves from location A to location B to location C to location
D. Each leg of the back-and-forth motion takes 1 minute to complete; the total time
is 3 minutes.
Calculate the average speed (in m/min) and the average velocity (in m/min) of the
skier during the three minutes of recreation.
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A1 Conceptual Physics Unit Homework
Interpreting Velocity-Graphs
23. On the graphs below, draw two lines/curves to represent the given verbal
descriptions; label the
lines/curves as A or B.
24. Use the velocity-time graphs below to determine the acceleration.
25. Find the displacement of objects represented on the velocity-time graphs
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A1 Conceptual Physics Unit Homework
26. For the following pos-time graphs, determine the corresponding shape of the veltime graph.
Acceleration
27. Accelerating objects are objects which are changing their velocity. Name the three
controls on an automobile which cause it to accelerate.
28. An object is accelerating if it is moving _____. Circle all that apply.
a. with changing speed b. extremely fast
c. with constant velocity
d. in a circle
e. downward
f. none of these
29. If an object is NOT accelerating, then one knows for sure that it is ______.
a. at rest
b. moving with a constant speed
c. slowing down
d. maintaining a constant velocity
30. An object with an acceleration of 10 m/s2 will ____. Circle all that apply.
a. move 10 meters in 1 second
b. change its velocity by 10 m/s in 1 s
c. move 100 meters in 10 seconds
d. have a velocity of 100 m/s after
10 s
31. Ima Speedin puts the pedal to the metal and increases her speed as follows: 0 mi/hr
at 0 seconds; 10 mi/hr at 1 second; 20 mi/hr at 2 seconds; 30 mi/hr at 3 seconds; and
40 mi/hr at 4 seconds. What is the acceleration of Ima's car?
32. Mr. Henderson's (imaginary) Porsche accelerates from 0 to 60 mi/hr in 4 seconds. Its
acceleration is ____.
a. 60 mi/hr
b. 15 m/s/s
c. 15 mi/hr/s
d. -15 mi/hr/s e. none of these
33. A car speeds up from rest to +16 m/s in 4 s. Calculate the acceleration.
34. A car slows down from +32 m/s to +8 m/s in 4 s. Calculate the acceleration.
35. The velocity of a car increases from 30 m/s at 4.0 seconds to 65 m/s at 6.0 seconds.
What is the car’s average acceleration?
36. As a car approaches a stoplight, it slows form 30 km/hr to a stop. If it decelerates at
a rate of 15 km/hr2, how long will it take for the car to stop?
37. A car accelerates uniformly from 3.0 m/s with an acceleration of 5.0 m/s2. If it does
this for 10 seconds, what will its final velocity be?
38. A car slows down for a school zone, 10 m/s. It takes him 20 seconds to slow down
at an acceleration of -1 m/s2. what was his initial velocity?
39. What is the displacement of a bus which accelerated uniformly from 10 m/s to 35
m/s in a 15.0 second interval?
40. A car starting from rest accelerates uniformly at 6.1 m/s2 for 7.0 seconds. How far
does the car move?
41. An airplane must reach a velocity of 71 m/s for takeoff. If the runway is 1.0 km
long, what must the constant acceleration be?
42. An airplane lands going 82 m/s. It slows to a halt with an acceleration of -2.5 m/s2.
How much runway is needed?
43. The Dungeon Drop at Astroworld free falls for 1.5 seconds. How far does it fall and
what is the velocity?
44. A car moving westward along a straight, level road increases its velocity uniformly
from 16 m/s to 32 m/s in 10.0 s. What is the car’s acceleration, average velocity and
displacement? ? Sketch the VT and AT Graphs [ 1.6 m/s2 ,24 m/s, 240 m]
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A1 Conceptual Physics Unit Homework
45. A ball initially at rest rolls down a hill with an acceleration of 3.3 m/s2. If it
accelerates for 7.5 seconds, how far will it move? ? Sketch the VT and AT Graphs
[92.81 m]
46. A bus slows down uniformly from 75.0 km/h to 0.0 km/h is 21 seconds. How far
does it travel before stopping? ? Sketch the VT and AT Graphs [218.75 m]
47. A penny is dropped off a tall building and hits the ground 5 seconds later. How tall
is the building? (acceleration due to gravity is -9.80 m/s2) [122.50 m] What does the
negative sign of your answer mean?
48. The Tokyo Express accelerates at the rate of 1 m/s2 for 210 seconds. It begins from
rest. How far will it have traveled during the time interval and what is its velocity at
the end of this time? Sketch the VT and AT Graphs [22,050 m, 210 m/s]
49. Read the following statements and indicate the direction (up, down, east, west, north
or south) of the acceleration vector.
a. A car is moving eastward along Lake Avenue and increasing its speed from 25
mph to 45 mph.
b. A northbound car skids to a stop to avoid a reckless driver.
c. An Olympic diver slows down after splashing into the water.
d. A southward-bound free quick delivered by the opposing team is slowed down
and stopped by the goalie.
e. A downward falling parachutists pulls the chord and rapidly slows down.
f. A rightward-moving Hot Wheels car slows to a stop.
g. A falling bungee-jumper slows down as she nears the concrete sidewalk below.
50. The diagram at the right portrays a Hot Wheels track designed for a phun physics
lab. The car starts at point A, descends the hill (continually speeding up from A to
B); after a short straight section of track, the car rounds the curve and finishes its run
at point C. The car continuously slows down from point B to point C. Use this
information to complete the following table.
Point
X
Velocity Vector
Direction: _________
Reason:
Acceleration Vector
Direction: _________
Reason:
Y
Direction: _________
Reason:
Direction: _________
Reason:
Z
Direction: _________
Reason:
Direction: _________
Reason:
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A1 Conceptual Physics Unit Homework
Describing Motion with Diagrams
51. Based on the oil drop pattern for Car A and Car B, which of the following
statements are true? Circle all that apply.
a. Both cars have a constant
d. Car B is accelerating; Car A is
velocity.
not.
b. Both cars have an accelerated
e. Car A has a greater acceleration
motion.
than Car B.
c. Car A is accelerating; Car B is
f. Car B has a greater acceleration
not.
than Car A.
52. An object is moving from right to left. It's motion is represented by the oil drop
diagram below. This object has a ___velocity and a ___ acceleration.
a. rightward, rightward b. rightward, leftward
c. leftward, rightward
d. leftward, leftward
e. rightward, zero
f. leftward, zero
53. Renatta Oyle's car has an oil leak and leaves a trace of oil drops on the streets as she
drives through Glenview. A study of Glenview's streets reveals the following traces.
Match the trace with the verbal descriptions given below. For each match, verify
your reasoning.
54. Motion diagrams for an amusement park ride are shown. The diagrams indicate
the positions of the car at regular time intervals. For each of these diagrams,
indicate whether the car is accelerating or moving with constant velocity. If
accelerating, indicate the direction (right or left) of acceleration.
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A1 Conceptual Physics Unit Homework
55. Suppose that in diagram D (above) the cars were moving leftward (and traveling
backwards). What would be the direction of the acceleration? Explain your answer
fully.
Describing Motion Graphically
56. The slope of the line on a position vs. time graph reveals information about an
object's velocity. The magnitude (numerical value) of the slope is equal to the
object's speed and the direction of the slope (upward/+ or downward/-) is the same
as the direction of the velocity vector. Apply this
understanding to answer the following questions.
a. A horizontal line means___________________ .
b. A straight diagonal line means_______________ .
c. A curved line means _______________ .
d. A gradually sloped line means _____________ .
e. A steeply sloped line means_________________ .
57. The motion of several objects is depicted on the position vs. time graph. Answer
the following questions. Each question may have
less than one, one, or more than one answer.
a. Which object(s) is(are) at rest?
b. Which object(s) is(are) accelerating?
c. Which object(s) is(are) not moving?
d. Which object(s) change(s) its direction?
e. Which object is traveling fastest? Slowest?
58. The slope of the line on a velocity vs. time graph reveals information about an
object's acceleration. Furthermore, the area under the line is equal to the object's
displacement. Apply this understanding to answer the following questions.
a. A horizontal line means:
b. A straight diagonal line means:
c. A gradually sloped line means:
d. A steeply sloped line means:
59. The motion of several objects is depicted by a velocity vs.
time graph. Answer the following questions. Each question may have less than one,
one, or more than one answer.
a. Which object(s) is(are) at rest?
b. Which object(s) is(are) accelerating?
c. Which object(s) is(are) not moving?
d. Which object(s) change(s) its direction?
e. Which accelerating object has the smallest acceleration?
f. Which object has the greatest acceleration?
g. Which object(s) is(are) moving in the same direction as object E?
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A1 Conceptual Physics Unit Homework
60. The graphs below depict the motion of several different objects. Note that the
graphs include both position vs. time and velocity vs. time graphs.
The motion of these objects could also be described using words. Analyze the graphs and
match them with the verbal descriptions given below by filling in the blanks.
a. The object is moving fast with a constant velocity and then moves slow with a
constant velocity.
b. The object is moving in one direction with a constant rate of acceleration (slowing
down), changes directions, and continues in the opposite direction with a constant
rate of acceleration (speeding up).
c. The object moves with a constant velocity and then slows down.
d. The object moves with a constant velocity and then speeds up.
e. The object maintains a rest position for several seconds and the slowly accelerates
at a constant rate.
61. Consider the position-time graphs for objects A, B, C and D. On the ticker tapes to
the right of the graphs, construct a dot diagram for each object. Since the objects
could be moving right or left, put an arrow on each ticker tape to indicate the
direction of motion.
62. Consider the velocity-time graphs for objects A, B, C and D. On the ticker tapes to
the right of the graphs, construct a dot diagram for each object. Since the objects
could be moving right or left, put an arrow on each ticker tape to indicate the
direction of motion.
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A1 Conceptual Physics Unit Homework
Formula Analysis
A car is traveling down a straight road. The driver then applies the brake, and the car
decelerates with a constant acceleration until it stops. Refer to the equations below to
answer the questions.
d = ½ (vi + vf)t
vf = vi + at
d = vit + ½ at2
vf2 = vi2 + 2ad
63. What is the car’s final speed (vf)? Explain your answer.
64. You are given the distance the car travels and the length of time it takes for the car
to come to a complete stop after the driver applies the brakes. What is the
expression for the car’s initial speed?
65. You are given the car’s initial speed and the length of time it takes for the car to
come to a full stop after the driver applies the brakes. What is the expression for the
magnitude of the car’s acceleration?
66. You are given the car’s initial speed and the distance the car travels before it comes
to a complete stop after the driver applies the brakes. What is the expression for the
magnitude of the car’s acceleration?
67. You are given the magnitude of the car’s acceleration and the length of time it takes
for the car to come to a full stop after the driver applies the brakes. What is the
expression for the initial speed of the car, and what is the expression for the distance
it traveled before it came to a complete stop?
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A1 Conceptual Physics Unit Homework
Unit 3: Vector Practice Problems
Scalars Vs Vectors
1. Identify as Scalar or Vector:
a. 20 N, 30°
b. 20 N
c. 65 m/s, east
d. 27.4 J
e. 134 mm, up
f. 27 °C
Drawing Vectors – Conceptual
2. Could a vector ever be shorter than one of its components? Could it ever be equal in
length to one of its components? Explain your thinking.
3. Which of the following actions is permissible when you are graphically adding one
vector to another: move the vector, rotate the vector, change the vector’s length?
4. Using a coordinate system (system of degrees) how is the angle or direction of a
vector determined with respect to the axes of the coordinate system?
5. The Pythagorean theorem is written a2 + b2 = c2. If you use this relationship to
solve vector problems, what do a, b, and c represent? Be specific.
6. A vector drawn 15cm long represents a velocity of 30 m/s. How long should you
draw a vector to represent a velocity of 20 m/s?
7. A vector that is 1 cm long represents a displacement of 5 km. How many kilometers
are represented by a 3 cm vector drawn to the same scale?
8. What is the largest possible displacement resulting from two displacements with
magnitudes 10 m and 25 m? What is the smallest possible resultant? Draw sketches
to illustrate your answers.
Measuring vectors
9. Consider the various vectors below. Given that each square is 10 km along its edge,
determine the magnitude and direction of the components of these vectors.
10. Consider the grid below with several marked locations.
Determine the direction of the resultant displacement for a person who walks from location .
a. A to C:
b. D to B:
c. G to D:
d. F to A:
e. F to E:
f. C to H:
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A1 Conceptual Physics Unit Homework
Drawing Vectors - For each vector, select a scale and draw the vector to that scale. Be sure
to label both the magnitude and the direction of the vector, and the scale for each vector.
11. 15 N at 45º
14. 7 m/s at 270º
12. 3 lbs at 150º
15. 75 ft/s at 345º
13. 10 lbs at 50º
Vector Addition
Parallel
16. A car is driven 50 miles due west on I-10, exits, re-enters I-10 traveling east and
travels 60 miles. What is the car’s displacement? [-10 miles, or 10 miles West]
17. You walk 50 steps to the left then turn and walk 30 steps to the right. What is your
displacement? [20 steps left]
18. Mrs. Jensen walked 150 m North and then 87 m North. What is her displacement?
[237 m North]
Perpendicular
19. A car is driven 125 km due west, then 65 km due south. What is the magnitude of
its displacement? (140 km)
20. A shopper walks from the door of the mall to her car 250 m down a lane of cars,
then turns 90º to the right and walks an additional 60 m. What is the magnitude of
the displacement of her car from the mall door? (300 m)
21. A hiker walks 4.5 km in one direction, then makes a 90º turn to the right and walks
another 6.4 km. What is the magnitude of her displacement? (7.82 km)
22. What is the magnitude of your displacement when you follow directions that tell you
to walk 225 m in one direction, make a 90º turn to the left and walk 350 m, then
make a 90º turn to the right and walk 125 m? (494.97 m)
23. A car is driven 125 km due west, then 65 km due south. What is the magnitude of
its displacement?
24. A shopper walks from the door of the mall to her car 250 m down a lane of cars,
then turns 90º to the right and walks an additional 60 m. What is the magnitude of
the displacement of her car from the mall door?
25. A car moves 65 km due east, then 45 km due west. What are the magnitude and
direction of its displacement? (20 km East OR 20 km @ 0°)
Relative Velocities
26. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry
to the front of the bus at 4.0 m/s relative to the bus. What is your speed relative to
the street? (6.0 m/s relative to the street)
27. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry
to the back of the bus at 4.0 m/s relative to the bus. What is your speed relative to
the street? (-2.0 m/s relative to the street)
28. A motorboat heads due east at 11 m/s relative to the water across a river that flows
due north at 5.0 m/s.
a. What is the velocity of the motorboat with respect to the shore? (12 m/s)
b. What is the direction of the motorboat with respect to due East? (24º)
29. A plane has a northward bearing (90º) and flying at 250 km/h. It soon encounters
another crosswind, this time blowing with a speed of 60 km/h at 180º with respect to
the ground. What is the plane’s new velocity with respect to the ground? (257.10
km/h, 103.5°)
30. An airplane flies due west at 185 km/h with respect to the air. There is a wind
blowing at 85 km/h north.
a. What is the plane’s speed with respect to the ground? (203.6 km/h)
b. What is the plane’s direction with respect to the ground? (155º)
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A1 Conceptual Physics Unit Homework
31. An airplane flies at 450 km/h west, and encounters a 90 km/h crosswind from the
south. What is the magnitude of the plane’s velocity resultant? (458.9 km/hr)
32. A motorboat heads due east at 15 m/s relative to the water across a river that flows
due east at 25 m/s. What is the velocity of the motorboat with respect to the shore?
(40 m/s, east)
33. A motorboat heads due east at 15 m/s relative to the water across a river that flows
due west at 25 m/s. What is the velocity of the motorboat with respect to the shore?
(10 m/s, east)
34. An airplane flies due north at 150 km/h with respect to the air. There is a wind
blowing at 75 km/h to the west relative to the ground. What is the plane’s velocity
with respect to the ground? (167.7 km/hr, 116.6° )
35. You are in a canoe paddling directly upriver (north) at a speed of 6.5 m/s relative to
the water. Viewers on the shore find that it is moving at only 0.5 m/s, north relative
to the shore. What is the speed of the river? (6.0 m/s, south)
36. You are in a canoe paddling directly upriver (north) at a speed of 12.6 m/s relative to
the water. Viewers on the shore find that it is moving at 20 m/s relative to the shore.
What is the speed of the river? (7.4 m/s, north – with the boat)
37. After being blown off course, an airplane regains its northward bearing (90º) and
resumes flying at 235 km/h. It soon encounters an easterly crosswind, this time
blowing with a speed of 80 km/h. What is the plane’s new velocity with respect to
the ground?(248.2 km/hr, 71.2 °)
Vector Resolution
38. A bus travels 23.0 km on a straight road that is 30º north of east. What are the east
and north components of its displacement? (east = 1.19 km, north = 11.5 km)
39. What are the components of a vector of magnitude 1.5 m at an angle of 35º? (1.2 m,
0.86 m)
40. A hiker walks 14.7 km at an angle of 325º. Find the east and south components of
this walk. (12 m, 8.4 m)
41. An airplane flies at 65 m/s at 149º. What are the west and north components of the
plane’s velocity? (56 m/s, 33 m/s)
42. A golf ball, hit from the tee, travels 325 m at a direction of 335°. What are the east
and south components of its displacement? (295 m, 137 m)
43. A car has a velocity of 50 km/h at 60°. Which component of the velocity vector is
larger, the x or the y?
44. A bus travels 23.0 km down I-10 at 30° in 2 hours. What are the east and north
components of its displacement? (19.92 km, 11.50 km)
45. What are the components of a vector of magnitude 1.5 m at an angle of 95º? (0.13
m, 1.49 m)
46. A hiker walks 14.7 km at an angle of 325º. Because he isn’t tired enough at the end
of his hike, he decides to calculate the east and south components of his walk. What
are they? (12.04 km, 8.43 km)
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A1 Conceptual Physics Unit Homework
Unit 4 Free Fall and Projectiles
Free Fall:
1.) A ball dropped from rest free falls. What is the velocity and displacement after 8
seconds? [-78.4 m/s, -313.6m]
2.) Aunt Sue drops a penny into a wishing well and it falls for 3 seconds before hitting
the water.
a. How fast is it going when it hits? [-29.4 m/s]
b. What is the penny’s average speed during its 3-second drop? [-14.7 m/s]
c. How far down is the water’s surface? [-44.1 m]
3.) Aunt Sue didn’t get her wish, so she does to a deeper wishing well and drops a
penny straight down into it. How far does the penny go in 3 seconds? [-44.1 m]
4.) An object falls from a high building. Ignoring air resistance, what will its velocity
be at the 6th second of falling?
5.) An object falls from a high building and hits the ground in 9 seconds. Ignoring air
resistance, what is the distance that it fell?
6.) An object falls from the Transco Tower and takes 15 seconds to reach the ground.
a. What is its velocity at impact if air resistance is ignored?
b. How tall is the building?
c. What is its acceleration at the 2nd second?
d. What is its acceleration at the 5th second?
e. If the Transco Tower were actually 3,000 meters tall, how long would an
object take to free-fall off of the top of the building? (ignoring air
resistance)
7.) Your egg protector falls from the second floor balcony and encounters air
resistance. You find out that it hit the ground at a velocity of 5 m/s. The actual
distance from the top of the balcony to the ground is 2 meters. The time of the fall is
clocked at .75 seconds.
a. Based on the actual time of the fall, what distance would it have fallen
(theoretically) if there were no air resistance?
b. Based on the actual time of the fall, at what velocity would it theoretically
hit the ground if there were no air resistance?
c. What effect did air resistance have on your results? Compare theoretical
velocity to actual velocity. Compare theoretical distance to actual distance
that the egg fell?
8.) On July 31, Sergey Bubka of the Ukraine broke his own world pole-vaulting record
by attaining a height of 6.14 m. How long did it take Bubka to return to the ground
from the highest part of his vault? [1.12 s] Describe how this time compares to the
time it took him to go from the ground to the highest point?
9.) A Christmas tree ball will break if dropped on a hardwood floor with a speed of 2.0
m/s or more. Holly is decorating her Christmas tree when her cat, Trickor, taps a
ball, causing it to fall 15 cm from a tree branch to the floor. Does the ball break?
[No]
10.) Perhaps sometime in the future, NASA will develop a program to land a human
being on Mars. If you were the first Mars explorer and discovered that when you
dropped a hammer it took 0.68 seconds to fall 0.90 m to the ground, what would
you calculate for the gravitational acceleration on Mars? [3.98 m/s2]
11.) Here is a bet you are almost sure to win! Try dropping a dollar bill through a
friend’s fingers and offer to let her keep it if she can catch it. The bill should be
started just at the finger level and your friend shouldn’t have any advanced warning
when it is going to drop. A dollar bill has a length of 15.5 cm and human reaction
time is rarely LESS than 0.20 s. Do the necessary calculations – why is this almost
a sure bet?
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A1 Conceptual Physics Unit Homework
12 A rescue team drops a box of supplies from a helicopter to some stranded tourists on
a deserted island. It takes 4.3 seconds for the box to land. How fast was the box
traveling as it hit the ground? [42.14 m/s]
13. A man is working on his roof, when he drops his hammer over the side. did it take to
hit the ground, if its velocity Gust as it hits) is 11.8 m/s? [1.20 sec]
14. A bird drops a kernel of corn from his perch on a tree branch. It takes 1.7 seconds
for the corn to land on the ground. How high above the ground was the tree branch?
[14.16 m]
15. A bank robber, in the balcony of a bank, drops a bag of money to his friend in the
lobby below. It is 30.6 meters from the balcony to the lobby. How long does it take
for the bag of money to fall? [2.50 sec]
16. For the bag of money in Question 4 above, how fast was the bag moving when it hit
the floor of the lobby? [- 24.5 m/s]
17. Divers from the cliffs in Acapulco jump vertically into the waters below. It takes 4.2
seconds for a diver to hit the water in a typical dive. How high is the cliff? [86.44 m]
18. A properly trained acrobat can safely land on the ground at a speed of 15 m/s. How
long would it take him/her to safely land from a jump or fall? [1.53 s]
19. For the acrobat in the Question above, what is the maximum height from which
he/she acrobat would safely land from a jump or fall? [11.47 m]
20. An astronaut drops a feather from a height of 1.2 meters, while he is standing on the
surface of the Moon. If the value for "g" on the Moon is one-sixth of the value of "g"
for the Earth, how long does it take for the feather to land on the Moon's surface?
[1.21 s]
21. Your friend tells you she dropped a coin from the top of a building, 200 m tall. She
said she timed it with a stop watch and it took exactly 5.43 seconds to strike the
ground. Prove whether or not she is telling the truth. [144.48 m – False]
22. In the Wizard of Oz, Dorothy awakens in Munchkinland where her house has been
blown by a tornado. If the house fell from a height of 3000.0 m, with what speed
did it hit the Wicked Witch of the East when it landed? [242.49 m/s]
23. The Tambora volcano on the island of Sumbawa, Indonesia has been known to
throw ash into the air with a speed of 625 m/s during an eruption.
a. How high could this volcanic ash plume have risen? [19925.85 m]
b. On Venus, where the acceleration due to gravity is slightly less than on
Earth, would this volcanic plume rise higher or not as high as it does on
Earth?
24. Billy, a mountain goat, is rock climbing on his favorite slope one sunny spring
morning when a rock comes hurtling toward him form a ledge 40.0 m above. Billy
ducks and avoids injury – lucky goat.
a. How fast is the rock traveling when it passes Billy? [28.00 m/s]
b. How does this speed compare to that of a car traveling down the highway at
the speed limit of 25 m/s (equivalent to 55 mi/h)?
Vertical Projectiles
25. Mrs. Jensen throws her marker straight up with a velocity of 5 m/s.
a. What is the velocity at the top? [0m/s]
b. How long does it take for the marker to reach the top? [0.204 s]
c. How long does it take for the marker to return to her hand? [0.408 s]
d. How high did it go? [1.27 m]
26. An Egg is launched from an egg launcher vertically upward.
a. What is the initial velocity if it takes 2s for the Egg to reach the top? [19.6
m/s]
b. What is the acceleration of the Egg? [-9.8 m/s2]
c. How high does it go? [19.6m]
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A1 Conceptual Physics Unit Homework
27. In frustration, you thrown your physics book down with a speed of 5 m/s. If you
are on the second floor, 5.1m from the ground, what speed does it hit the ground?
[124.96 m/s]
Horizontal Projectiles
28. Wiley Coyote is, predictably, chasing the Road Runner with an anvil. Predictably
again, he manages to overlook the fact that he is chasing him along a cliff. As Wiley
realizes that he has just run horizontally off the 472 m high cliff at 25 m/s, some
important thoughts flash through his mind…
a. How much longer do I have before I hit the ground?
b. There is a 25m wide river running directly below the cliff. Will I land in the
river, or will this anvil drill me right into the ground on the other side?
c. How fast will I be moving vertically when I hit the ground/water?
d. How fast will I be moving horizontally when I hit the ground/water?
e. What will my overall velocity be on impact?
f. What direction, relative to 0°, will I be traveling when I hit?
g. Why don’t I ever learn?
29. Mrs. Jensen is a big fan of playing Frisbee with Hank. Unfortunately, Hank is more
of a diver that a jumper, and he never seems to catch the Frisbee until it is virtually
on the ground. If Mrs. Jensen throws the Frisbee from a height of 1.5 m with a
horizontal velocity of 7.5 m/s, how far away from him will Hank be when he dives
to catch the Frisbee?
30. A baseball is dropped off a cliff and it
accelerates to the ground at a rate of -9.8 m/s2,
down. Meanwhile a cannonball is launched
horizontally from a cannon with a horizontal
speed of 20 m/s. A scale is shown along the sides
of the graphic at the right. Use the scale to locate
the position of the baseball and the cannonball.
Trace a line to indicate the trajectory of the
cannonball. Which of these two balls strike the ground first?
31. Compare the two diagrams - the vertical free-fall motion on the left and the twodimensional freefall motion on the right. Describe the effect on an object's
horizontal motion upon the object's vertical motion.
32. The diagram below shows the trajectory of a horizontally launched projectile.
Positions of the projectile at 1-second intervals are shown. Demonstrate your
understanding of the components of the displacement vector by determining the
horizontal displacement (x) and the vertical displacement (y) after the fifth second.
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A1 Conceptual Physics Unit Homework
33. A ball is launched horizontally from the top of a cliff
with an initial velocity of 20 m/s. The trajectory of
the ball is shown right. Express your understanding
by filling in the blanks.
34. If the ball in the diagram above strikes the ground
after four seconds, then (a) how high was the cliff
and (b) how far from the base of the cliff will the ball
land?
35. If the ball's initial speed in question #30 was 16 m/s, then how far from the cliff will
the ball land?
36. A ball is projected horizontally from the top of a 92.0-meter high cliff with an initial
speed of 19.8 m/s. Determine: (a) the horizontal displacement, and (b) the final
speed the instant prior to hitting the ground.
37. Determine the launch speed of a horizontally-launched projectile which lands 26.3
meters from the base of a 19.3-meter high cliff.
38. A soccer ball is kicked horizontally at 15.8 m/s off the top of a field house and lands
33.9 metes from the base of the field house. Determine the height of the field house.
Combined Projectile Motion
39. A ball is projected at an angle with an initial horizontal velocity of 8 m/s and an
initial vertical velocity of 29.4 m/s. The trajectory diagram shows the position of
the ball after each consecutive second. Express your understanding of projectiles by
filling in the blanks.
40. Determine … (a) the displacement of the ball, (b) the height above the ground at its
peak, and (c) the final speed of the ball upon hitting the ground.
41. Suppose that the horizontal component of the initial velocity had been 13 m/s and
the vertical velocity had been unchanged (in questions #36 and #16). Determine the
(a) time of flight, (b) the displacement of the ball, (c) height above the ground, and
(d) the speed upon hitting the ground.
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A1 Conceptual Physics Unit Homework
42. A physics student is driving his pick-up truck down I-10.
t(s)
x(m)
y(m)
The pick-up is equipped with a projectile launcher which
0
imparts a vertical velocity to a water-filled rubber
1
projectile. While traveling 20 m/s in an eastward direction,
2
the projectile is launched vertically with a velocity of 60
3
m/s. Fill in the table at the right. showing the horizontal
4
and vertical displacement of the projectile every second
5
for the first 12 seconds. Use the approximation that g = 10
6
m/s2, down.
7
8
9
10
11
12
43. On the diagram below, place a large dot on the location of
the projectile during each second of its trajectory. Draw a smooth curve through the
dots to indicate the
trajectory.
Will the projectile land in the truck, behind the truck or in front of the truck? (No air
resistance.)
44. A zookeeper has a monkey which he must feed daily. The monkey spends most of
the day in the trees just hanging from a branch. When the zookeeper launches a
banana to the monkey, the monkey has the peculiar habit of dropping from the trees
the moment that the banana is launched. The banana is launched with a speed of
16.0 m/s at a direction of 51.3° above the horizontal (which would be directly at the
monkey). The monkey is initially at rest in a tree 25.0-m above the ground. Use
kinematic equations to determine the horizontal and vertical displacements of the
banana and the monkey at 0.5-second time intervals. Then plot the trajectories of
both banana and monkey on the diagram below. (Use the approximation that g = 10
m/s2, down.)
Banana
Monkey
Time dx dy Height
Time dy Height
(s)
(m) (m)
(m)
(s)
(m)
(m)
0
0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
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A1 Conceptual Physics Unit Homework
45. Based on your mathematical analysis above, will the zookeeper hit the monkey if
she aims the banana directly at the monkey?
46. Use trigonometric functions to resolve the following velocity vectors into horizontal
and vertical components. Then utilize kinematic equations to calculate the other
motion parameters. Be careful with the equations; be guided by the principle that
"perpendicular components of motion are independent of each other."
Key Concepts:
A projectile is an object which has the following characteristics.
• The only force acting on it is a gravitational force; it is a free-falling object.
• The acceleration is directed downwards and has a value of 9.8 m/s2.
• Once projected, it continues its horizontal motion without any need of a force.
• As it rises, its vertical velocity (vy) decreases; as it falls, its vy increases.
• As it travels through the air, its horizontal velocity remains constant.
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A1 Conceptual Physics Unit Homework
Unit 5 Newton’s Laws
FBD’s: Draw FBD for the 1-8
1. A book is at rest on a table top.
2. A horizontal bar hangs from the ceiling suspended from two ropes. If a girl is
holding on to the bar with one hand and is hanging motionless below the bar,
diagram the forces acting on the girl and then diagram the forces acting on the bar.
3. An egg is free-falling from a nest in a tree. Neglect air resistance.
4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant
velocity. Consider air resistance.
5. A rightward force is applied to a book in order to move it across a desk with a
rightward acceleration. Consider frictional forces. Neglect air resistance.
6. A college student rests a backpack upon his shoulder. The pack is suspended
motionless by one strap from one shoulder. Diagram the vertical forces acting on
the backpack.
7. A force is applied to the right to drag a sled with a rightward acceleration across
loosely-packed snow, which has a coefficient of friction.
8. A football is moving upwards towards its peak after having been booted by the
punter. Neglect air resistance. Diagram the forces acting upon the football as it rises
upward towards its peak.
9. Free body diagrams for four situations are shown below. In each case, the net force
is known. However the magnitude of some of the individual forces is not known.
Analyze each situation individually to determine the magnitude of the unknown
forces. (the last object has a mass of 10 kg)
Problems: Use GUESS to solve each
10. Different masses are hung on a spring scale calibrated in Newtons.
a) The force exerted by gravity on 1 kg = 9.8 N.
b) The force exerted by gravity on 5 kg = ______ N.
c) The force exerted by gravity on _______ kg = 98 N.
d) The force exerted by gravity on 70 kg = ________ N.
11. What acceleration will result when a 12-N net force is applied to the right on a 3-kg
object? What would the acceleration be if the same force is applied to a 6-kg object?
[4 m/s2, 2 m/s2]
12. A net force of 16 N causes a mass to accelerate to the left at the rate of 5 m/s2.
Determine the mass of the object. [3.2 kg]
13. An object is accelerating at 2 m/s2. If the net force is tripled and the mass of the
object is doubled, what is the new acceleration? [3 m/s2]
14. An object is accelerating at 2 m/s2. If the net force is tripled and the mass of the
object is halved, what is the new acceleration? [12 m/s2]
15. A crate with a mass of 50.0 kg experiences an acceleration to the right with a
magnitude of 3.5 m/s2. Find the magnitude of the net force on the crate. [175 N]
16. A boy pushes a 0.50 kg book across a table by exerting a net force of 2.00 N on it.
Calculate the magnitude of the acceleration that the book will experience. [4m/s2]
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A1 Conceptual Physics Unit Homework
17. An applied force of 50 N is used to accelerate a 100 N object to the right across a
frictional surface. The object encounters 10 N of friction. Determine the normal
force, the net force, the mass, and the acceleration of the object. (Neglect air
resistance.) [FN = 100 N, Fnet = 40 N, a = 3.92 m/s2, m = 10.2 kg]
18. What is the frictional force when a 750 kilogram car travels on a road (coefficient of
friction of 0.4)? [2940 N]
19. A 52 Newton sled is pulled across a cement sidewalk at a constant velocity. A
horizontal force of 36 Newtons is applied. What is the coefficient of sliding friction
between the sled and the cement? [0.69]
20. Suppose the 52 Newton sled is now pulled on snow. The coefficient of friction drops
to 0.12. If a person weighing 650 Newtons sits on the sled, what force is needed to
sled across the snow at a constant velocity? [84.24 N]
21. An applied force of 20 N is used to accelerate a 20 kg object to the right across a
frictional surface. 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 force of gravity, and the acceleration of the object. (Neglect air resistance.) [F N =
196 N, Fg = 196 N, Fnet = 10 N, a = 0.5 m/s2, μ = 0.051]
22. A 5 kg object is sliding to the right and encountering a friction force which slows it
down. The coefficient of friction 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. (Neglect air resistance). [Fg = 49 N, FN = 49 N, FFR = 4.9 N, Fnet
= -4.9 N, a = -0.98 m/s2]
23. 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
gravitational force, normal force, net force, applied force and coefficient of friction.
Neglect air resistance. [Fg = 58.8 N, FN = 58.8 N, Fnet = 0 N, Fa = 15 N, μ = 0.255]
24. A rightward force is applied to a 10 kg object to move it across a rough surface at
constant velocity. The coefficient of friction between the object and the surface is
0.2. Draw an FBD and determine the weight of the object, the normal force, applied
force, frictional force and net force. Neglect air resistance. [Fg = 98 N, FN = 98 N, Fa
= 19.6 N, FFR = 19.6 N, Fnet = 0 N]
25. 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. Draw an FBD and determine the
weight of the object, normal force, frictional force, net force and coefficient of
friction between the object and the surface. Neglect air resistance. [Fg = 39.2 N, FN =
39.2 N, FFR = 15 N, Fnet = 10 N, μ = 0.383]
26. A box weighs 60 N and needs an applied force of 50 Newtons in order to overcome
friction and move at a constant velocity. What is the coefficient of static friction?
[0.833]
27. A metal crate has a mass of 50 kg and a coefficient of static friction of 0.4.
a. How much force must be applied to get the crate moving? [196 N]
b. Once it is moving, the coefficient of friction changes to 0.32. What force is
needed to keep the box moving with constant velocity? [156.8 N]
Diagrams
28. Which one(s) of the following force diagrams depict an object moving to the right
with a constant speed? List all that apply.
Page 32
A1 Conceptual Physics Unit Homework
For the 29-33 consider the velocity-time plot below for the motion of an object along a
horizontal surface. The motion is divided into several time intervals, each labeled with a
letter.
29. During which time interval(s), if any, are there no forces acting upon the object?
List all that apply.
30. During which time interval(s), if any, are the forces acting upon the object
balanced? List all that apply.
31. During which time interval(s), if any, is there a net force acting upon the object?
List all that apply.
32. During which time interval(s), if any, is the net force acting upon the object directed
toward the right? List all that apply.
33. During which time interval(s), if any, is the net force acting upon the object directed
toward the left? List all that apply.
For the 57-61, consider the dot diagram below for the motion of an object along a horizontal
surface. The motion is divided into several time intervals, each labeled with a letter.
34. During which time interval(s), if any, are there no forces acting upon the object?
List all that apply.
35. During which time interval(s), if any, are the forces acting upon the object
balanced? List all that apply.
36. During which time interval(s), if any, is there a net force acting upon the object?
List all that apply.
37. During which time interval(s), if any, is the net force acting upon the object directed
toward the right? List all that apply.
38. During which time interval(s), if any, is the net force acting upon the object directed
toward the left? List all that apply.
For the 39-43 , consider the trajectory diagram shown
below for a projectile thrown at an angle to the
horizontal. The vector arrows represent the horizontal
and vertical components of the projectile's velocity.
Use the trajectory diagram to answer the next several
questions. (Consider air resistance to be negligible.)
39. At which point(s), if any, are there no forces
acting upon the object? List all that apply.
40. At which point(s), if any, are the forces acting
upon the object balanced? List all that apply.
41. At which point(s), if any, is there a net force acting upon the object? List all that
apply.
42. At which point(s), if any, is the net force acting upon the object directed toward the
right?
Page 33
A1 Conceptual Physics Unit Homework
43. At which point(s), if any, is the net force acting upon the object directed upward?
List all that apply.
Newton’s 3 Laws
44. Newton’s 1st Law is also known as the Law of _______________.
45. Mathematically, Newton’s 1st Law states: ___________
46. Mathematically, Newton’s 2nd Law states: ________________
47. Mathematically, Newton’s 3rd Law states: ________________
48. Newton’s 3rd Law is also known as the ______________ _______________ Law
49. Imagine a place in the cosmos far from all gravitational and frictional influences.
Suppose an astronaut in that place throws a rock. The rock will:
50. An 2-kg object is moving horizontally with a speed of 4 m/s. How much net force is
required to keep the object moving with the same speed and in the same direction?
51. Mac and Tosh are arguing in the cafeteria. Mac says that if he throws his jello with a
greater speed it will have a greater inertia. Tosh argues that inertia does not depend
upon speed, but rather upon mass. With whom do you agree? Why?
52. Mr. Wegley spends most Sunday afternoons at rest on the sofa, watching pro
football games and consuming large quantities of food. What effect (if any) does this
practice have upon his inertia? Explain.
53. Ben Tooclose is being chased through the woods by a bull moose which he was
attempting to photograph. The enormous mass of the bull moose is extremely
intimidating. Yet, if Ben makes a zigzag pattern through the woods, he will be able
to use the large mass of the moose to his own advantage. Explain this in terms of
inertia and Newton's first law of motion.
54. You are standing on the floor.
a) What is the reaction force to your feet pushing on the floor?
b) What is the reaction force to your weight?
55. You are pulling on a rope. What is the reaction force?
Which Law: Each one of Newton's Laws can play a role in any one particular situation .
Pick which of Newton's most governs the situations described below.
a. First Law (inertia) b. Second Law (F = ma) c. Third Law (action-reaction)
56. A helicopter must have two sets of blades in order to fly with stability.
57. If you were in an elevator and the cable broke, jumping up just before the elevator
hit the ground would not save you. Sorry.
58. You usually jerk a paper towel from a roll in order to tear it instead of pulling it
smoothly.
59. A student desk changes the amount of force it puts on other objects throughout a
school day.
60. Heavy objects are not easier to move around in a horizontal fashion on the Moon
than on the Earth.
61. The stronger, heavier team in a tug-of-war does not create a larger tension in the
rope than the weaker, lighter team.
62. You are in a car that is traveling on I-10. Your backpack:
a) Sits while traveling at 75 mph.
b) Slides forward when someone cuts you off and the driver hits the brakes.
c) Slides back when the driver is accelerating to merge.
d) Slides back and forth while the driver swerves quickly through traffic.
63. You are in your seat, napping during class.
64. You stand on a scale to read your weight.
65. Your hand hurts when you catch a fastball with no glove.
Page 34
A1 Conceptual Physics Unit Homework
Unit 6: Impulse and Momentum
Problems:
Impulse/Momentum:
1. A girl has a mass of 35.6 kg and her skateboard has a mass of 1.3 kg. What is the
momentum of the girl on her skateboard together if they are traveling at 9.50
m/s?[350.55 kg m/s]
2. A hockey player makes a slap shot with a force of 30 N on the hockey puck for 0.16
seconds.
a. What impulse is given to the hockey puck? [4.8 Ns]
b. What is the change in velocity of the puck if it has a mass of 0.5 kg? [9.6
m/s]
3. A force of 6 N acts on a 3 kg object for 10 seconds
a. What is the object's change in momentum? [60 kg m/s]
b. What is its change in velocity? [20 m/s]
4. A baseball with a mass of 0.14 kg is thrown by a pitcher with a velocity of + 35 m/s
a. What is the momentum of the baseball? [4.9 kg m/s]
b. For a bowling ball with a mass of 7.26 kg to have the same momentum as
the baseball, what would its velocity have to be? [0.675 m/s]
5. A baseball with a mass of 0.14 kg is thrown by a pitcher with a velocity of +38 m/s.
It is hit back by the batter at a velocity of -38 m/s.
a. What is the impulse (change in momentum)? [-10.64 Ns]
b. If the bat stays in contact with the baseball for 0.1 second, calculate the
force of the bat? [-106.4 N]
c. What is the acceleration of the ball? [-760 m/s2]
6. The brakes on a car exert a force of 640 N on a car. It was moving at 20 m/s and
finally comes to a stop. The car weighs 15,680 N.
a. What is the car's mass? [1600 kg]
b. What was the car's original momentum? [32000 kg m/s]
c. What was the change in momentum? [-32000 kg m/s]
d. How much time did it take to bring the car to a stop? [50 s]
Inelastic Collision
7. A railroad diesel engine has four times the mass of a flatcar. If a
diesel coasts at 5 km/hr into a flatcar that is initially at rest, how
fast do the two coast if they couple together? [4 km/hr]
8. A 0.105-kg hockey puck moving at 48 m/s is caught by a 75-kg
goalie at rest. With what velocity does the goalie slide on the ice
after catching the puck? [0.07 m/s]
9. A 0.35 kg bullet strikes a 5.0-kg stationary wooden block and embeds itself in the
block (the bullet remains in the block). The block and bullet move together at 8.6
m/s. What was the original velocity of the bullet? [131.46 m/s]
10. A 3000-kg truck moving East with a speed of 5 km/hr collides head-on with a 1000kg car moving West with a speed of 10 km/hr. The two vehicles stick together and
move with the same velocity after the collision. Find the post-collision velocity of
the car and truck. [1.25 km/hr, east]
11. During a goal-line stand, a 75-kg fullback moving eastward with a speed of 8 m/s
collides head-on with a 100-kg lineman moving westward with a speed of 4 m/s.
The two players collide and stick together, moving at the same velocity after the
collision. Determine the post-collision velocity of the two players. [1.14 m/s east]
Elastic Collision
12. A 0.35 kg bullet moving at 475 m/s strikes a 2.5-kg wooden block at rest. The bullet
passes through the block, leaving at 275 m/s. How fast is the wooden block moving
when the bullet leaves? Assume the mass of the wooden block does not change
significantly. [28 m/s]
Page 35
A1 Conceptual Physics Unit Homework
13. A 0.50-kg ball traveling East at 6.0 m/s collides head-on with a 1.00-kg ball moving
in the opposite direction (West) at a velocity of 12.0 m/s. The 0.50-kg ball moves
away (West) at 14 m/s after the collision. Find the velocity of the second ball. [2
m/s, left]
Problems 14-23: For problems 14-18: A car with a mass of 1000 kg is at rest at a
stoplight. When the light turns green, it is pushed by a net force of 2000 N for 10 s.
14. What is the value of the acceleration that the car experiences? [2m/s2]
15. What is the value of the change in velocity that the car experiences? [20 m/s]
16. What is the value of the impulse on the car? [20000 Ns]
17. What is the value of the change in momentum? [20000kg m/s]
18. What is the final velocity of the car at the end of 10 seconds? [20 m/s]
For problems 19-20: The car continues at this speed for a while.
19. What is the value of the change in momentum the car experiences as it continues at
this velocity? [0 kg m/s]
20. What is the value of the impulse on the car as it continues at this velocity? [0 Ns]
The brakes are applied to the car, causing it to come to rest in 4 s.
21. What is the value of the change in momentum that the car experiences? [20000 kg
m/s]
22. What is the value of the impulse on the car? [20000Ns]
23. What is the value of the force (average) that causes the car to stop? What is the
acceleration? [5000N, 5 m/s2]
Conceptual:
24. Which has the greater mass, a heavy truck at rest or a rolling skateboard? Which has
greater momentum? Why?
25. Distinguish between impact and impulse. Which designates a force and which is
force X time?
26. When the force of impact on an object is extended in time, does the impulse increase
or decrease?
27. For a constant force, suppose the impact time is doubled.
a. How much is the impulse increased?
b. How much is the resulting change in momentum increased?
28. In a car crash, why is it advantageous for an occupant to extend the time during
which the collision takes place?
29. Explain the difference between an elastic and inelastic collision.
30. Complete the following verbal statements to illustrate your understanding of the
effect of varying mass on the post-collision velocity.
a. An object of mass m and velocity v collides inelastically with an object of
mass 3m which is initially at rest, then the amount of total system mass in
motion will increase by a factor of _______ and the velocity of the system
will decrease by a factor of _______ . The new velocity (v') will be _____ v.
b. If an object of mass m collides and velocity v collides inelastically with an
object of mass 4m which is initially at rest, then the amount of total system
mass in motion will increase by a factor of ___ and the velocity of the
system will decrease by a factor of ___ . The new velocity (v') will be ___v.
c. If an object of mass 3m collides and velocity v collides inelastically with an
object of mass 4m which is initially at rest, then the amount of total system
mass in motion will increase by a factor of __ and the velocity of the system
will decrease by a factor of ____ . The new velocity (v') will be ___ v.
31. Insert these words into the four blanks of the sentence: mass, momentum,
acceleration, time, impact, weight, impulse, and force. (Not every word will be
used.)
In a collision, an object experiences a(n) ______ acting for a certain amount of ____
and which is known as a(n) _____ ; it serves to change the _______ of the object.
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A1 Conceptual Physics Unit Homework
Unit 7 Work Power and Energy
Work:
1. A 196 N suitcase is raised 3.0 m above a platform by a crane. How much work is
done on the suitcase? [588 J]
2. A tugboat pulls a ship with a constant net horizontal force of 5000 N and causes the
ship to move through the harbor. How much work is done on the ship if it moves a
distance of 3000 m? [1.50 x 107 J]
3. A weight lifter lifts a set of weights a vertical distance of 2.00 m. If a constant net
force of 350 N is exerted on the weights, what is the net work done on the weights?
[700 J]
4. A loaded sled requires a force of 250 N applied horizontally to push it across wet
snow. How far can it be pushed with 800,000 J of work? [3200 m]
5. A worker pushes a 1500 N crate with a horizontal force of 345 N a distance of 24.0
m. The coefficient of friction between the crate and the floor is 0.220.
a. How much work is done by the worker on the crate? [8280 J]
b. How much work is done by the floor on the crate? [-7920 J]
c. What is the net work done on the crate? [360 J]
d. What is the net force on the crate? [15 N]
e. What is the crate’s acceleration? [0.098 m/s2]
6. A delivery clerk carries a 34 N package from the ground to the fifth floor of an
office building, a total height of 15 m. How much work is done by the clerk? [510
J]
7. What work is done by a forklift raising a 583 kg box 1.2 m.? [6856.08 J]
8. You and a friend each carry identical boxes to a room one floor above you and down
the hall. You choose to carry it first up the stairs, then down the hall. Your friend
carries it down the hall, then up another stairwell. Who does more work? [same
amount]
9. What work is done if a boy pushes a box that has a mass of 30 kg with a force of 50
Newtons over a distance of 6 meters in 4 seconds?
10. A 196 N suitcase is raised 3.0 m above a platform by a crane at constant velocity.
How much work is done on the suitcase? [588 J]
11. A tugboat pulls a ship with a constant net horizontal force of 5000 N and causes the
ship to move through the harbor. How much work is done on the ship if it moves a
distance of 3000 m? [1.50 x 107 J]
12. A weight lifter lifts a set of weights a vertical distance of 2.00 m. If a constant net
force of 350 N is exerted on the weights, what is the net work done on the weights?
[700 J]
13. A loaded sled requires a force of 250 N applied horizontally to push it across wet
snow. How far can it be pushed with 800,000 J of work? [3200 m]
Power:
14. A rock climber wears a 7.5 kg knapsack while scaling a cliff. After 30 minutes, the
climber is 8.2 m above the starting point.
a. How much work does the climber do on the knapsack? [602.7 J]
b. If the climber weighs 645 N, how much work does she do lifting herself and
the knapsack? [5891.7 J]
c. What is the average power developed by the climber? [3.27 W]
15. An electric motor develops 65 kW of power as it lifts a loaded elevator 17.5 m is
35.0 seconds. How much force does the motor exert? [130,000.19 N]
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A1 Conceptual Physics Unit Homework
16. Ben and Will are in the weight room. If Ben lifts the 75 N barbell over his head 11
times in 45 seconds and Will lifts the same barbell over his head 10 times in 35
seconds.
a. Who has more work?
b. Who demonstrates more power?
17. How long does it take a 19 kW steam engine to do 6.8 x 107J of work? [3578.95 s]
18. A 1500 kg car accelerates uniformly from rest to 10.0 m/s in 3.0 s.
a. What is the work done on the car in this time interval? [75000 J]
b. What is the power delivered by the engine in this time interval? [25000 W]
19. A 60 kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs
is 4.5 m. What is the jogger’s power output? [661.5 W]
20. A student with a mass of 80 kg runs up three flights of stairs in 12 seconds. The
student has gone a vertical distance of 8 meters.
a. Determine the amount of work done by the student to elevate his body to
this height.
b. Determine the power exerted by the student.
21. A girl pushes a 6 kg box for a distance of 3 meters with a force of 4 N in 2 seconds.
What is the power of the girl?
Kinetic Energy:
22. A comet with a mass of 7.85 x 1011 kg strikes Earth at a speed of 25,000 m/s. What
is the kinetic energy of the comet? [2.45 x 1020 J]
23. If the work is done over a distance of 0.75 m, what is the average force on the
bullet? [267.43 N
24. A 6.0 kg cat runs after a mouse at 10 m/s. What is the cat’s kinetic energy? [300 J]
25. A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the
bowling ball have? [31.5 J]
b. How fast must a 2.45 g table-tennis ball move in order to have the same kinetic
energy as the bowling ball? [160.357 m/s]
26. Calculate the speed of an 8.0 x 104 kg airliner with a kinetic energy of 1.1 x 109 J.
[165.831 m/s]
27. Two bullets have masses of 3.0 g and 6.0 g, respectively. Both are fired with a speed
of 40.0 m/s. Which bullet has more kinetic energy?
28. A car has a kinetic energy of 4.32 x 105 J when traveling at a speed of 23 m/s. What
is its mass? [1633.270 kg]
29. If the velocity of a car is doubled, how is its kinetic energy affected? Why?
Gravitational Potential Energy:
30. Larry, who weighs in at 630 N, climbs up a ladder to a height of 5.0 m.
a. Does Larry do work?
b. How much work does Larry do?
c. What is Larry’s gravitational potential energy before he starts climbing?
d. What is Larry’s gravitational potential energy at the top of the ladder?
31. A 90 kg rock climber climbs 45 m upward to the top edge of Enchanted Rock.
a. What is his gravitational potential energy at the top of his climb? [39690 J]
b. He climbs back down to the ground, 85 m below the top of Enchanted Rock.
Using his initial height as the reference point, calculate his gravitational
potential energy at the bottom of his climb. (Hint: Draw a sketch - it is ok
to have a negative PEg) [-35280 J]
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A1 Conceptual Physics Unit Homework
32. A spoon is raised 21.0 cm above a table. If the spoon and its contents have a mass of
30.0 g, what is the gravitational potential energy associated with the spoon at that
height relative to the surface of the table? [0.0617 J]
33. Calculate the increase in gravitational potential energy of a 75 kg hiker who climbs a
1500 m peak. [1.103 x 106 J]
34. If 2.0 J of work is done in raising a 180 g apple, how far is it lifted? [1.134 m]
35. If a force of 15 N is used to drag the loaded cart along the
incline for a distance of 0.90 m, then how much work is done
on the loaded cart?
b. What is the cart’s potential energy when the cart is 1.2
meters above the ground?
Spring Potential Energy:
36. A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a
mass is attached to the end of the spring and allowed to come to rest, the vertical
length of the spring is 3.57 m. Calculate the elastic potential energy stored in the
spring. [3.261 J]
37. The staples inside a stapler are kept in place by a spring with a relaxed length of
0.115 m. If the spring constant is 51.0 N/m, how much elastic potential energy is
stored in the spring when its length is 0.150 m? [0.031 J]
Work Energy Theorem:
38. A rifle can shoot a 0.0042 kg bullet at a speed of 965 m/s.
a. What is the kinetic energy of the bullet? [1955.57 J]
b. How much work is done on the bullet if it starts from rest? [1955.57 J]
39. If a car has of mass 1000kg is moving at 25 m/s
a. How much Kinetic energy does it start with? [312500 J]
b. How much work is required to stop the car? [312500 j]
c. If the tires can exert a total force of 25000N, how far does it take to stop?
[12.5m]
Conservation of Energy:
40. A bike rider approaches a hill w/ a speed of 8.5 m/s. The total mass of the bike and
rider is 85 kg.
a. What is the kinetic energy of the bike and rider at the base of the hill?
[3070.63 J]
b. The rider coasts to the top of the hill. What is his kinetic energy at the top
of the hill? Explain your answer. [0 J]
c. How much work does the rider do? [- 3070.63 J]
d. Assuming there is no friction, at what height will the bike come to a stop?
[3.67 m]
41. Starting from rest, a child zooms down a frictionless slide from an initial height of
3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25
kg. [7.668 m/s]
42. A pendulum bob is released from some initial height such that the speed of the bob
at the bottom of the swing is 1.9 m/s. What is the initial height of the bob? [0.184 m]
43. A boy holds a 15 kg box on a cliff that is 45 meters off of the ground and lets it go.
Gravity pulls it to the ground directly below where it was dropped.
a. What was the potential energy of the box before it was dropped?
b. What was the kinetic energy of the box at the point that it hit the ground?
c. What was velocity of the ball at impact? (Use mgh = ½ mv2)
d. What was the work done by gravity?
e. What was the force of the box at impact with the ground?
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A1 Conceptual Physics Unit Homework
44. What is the potential energy of a pendulum that hangs 4 meters above the ground
and has a mass of 2 kg?
a. If the pendulum starts to move. At the bottom of the swing it is going 5 m/s.
What is its kinetic energy at that point?
b. At the bottom of the swing of the pendulum, the pendulum hits a brick. The
brick moves 3 meters. With what force did the pendulum hit the brick?
45. Draw a diagram of a pendulum, label the points where there is the maximum
potential energy, the maximum kinetic energy, zero potential energy, zero kinetic
energy and where there are both kinetic and potential energy present. How is work
related?
46. Draw a diagram of a mass on spring, label the points where there is the maximum
potential energy, the maximum kinetic energy, zero potential energy, zero kinetic
energy and where there are both kinetic and potential energy present. How is work
related?
Mixed Practice: Show all work, including a sketch, formula, work, and final answer in a
box.
47. A worker pushes a 1500 N crate with a horizontal force of 345 N a distance of 24.0
m. If the force of friction is 330 N, find:
a. How much work is done by the worker on the crate? [8280 J]
b. How much work is done by the floor on the crate? [-7920 J]
c. What is the net force on the crate? [15 N]
d. What is the net work done on the crate? [360 J]
e. If the mass of the crate is 153.06 kg, what is the crate’s acceleration? [0.098
m/s2]
48. A delivery clerk carries a 34 N package from the ground to the fifth floor of an
office building, a total height of 15 m. How much work is done by the clerk? [510
J]
What work is done by a forklift raising a 583 kg box 1.2 m.? [6856.08 J]
49. You and a friend each carry identical boxes to a room one floor above you and down
the hall. You choose to carry it first up the stairs, then down the hall. Your friend
carries it down the hall, then up another stairwell. Who does more work? Why?
[same amount]
50. A rock climber wears a 7.5 kg knapsack while scaling a cliff. After 30 minutes, the
climber is 8.2 m above the starting point.
a. How much work does the climber do on the knapsack? [602.7 J]
b. If the climber weighs 645 N, how much work does she do lifting herself and
the knapsack? [5891.7 J]
c. What is the average power developed by the climber? [3.27 W]
51. An electric motor develops 65 kW of power as it lifts a loaded elevator 17.5 m is
35.0 seconds. How much force does the motor exert? [130,000 N]
52. A 60 kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs
is 4.5 m. What is the jogger’s power output? [661.5 W]
53. A student with a mass of 80 kg runs up three flights of stairs in 12 seconds. The
student has gone a vertical distance of 8 meters.
a. Determine the amount of work done by the student to elevate his body to this
height. [522.67 J]
b. Determine the power exerted by the student. [43.56 W]
54. How long does it take a 19 kW steam engine to do 6.8 x 107J of work? [3578.95 s]
55. What work is done if a boy pushes a box that has a mass of 30 kg with a force of 50
N over a distance of 6 meters in 4 seconds? [300 J]
56. If the velocity of a car is decreased by a factor of 2, how is its kinetic energy
affected? [1/4]
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A1 Conceptual Physics Unit Homework
Unit 8: Circular Motion and Newton’s Universal Gravity
Problems
Circular Motion
1. What is the acceleration of a piece of dust on an old-fashioned record album, 15 cm
from the center, if the record is spinning at 33.3 rpm?
2. What is the tension in a 0.500 meter rope which carries a 2.50 kg rock in a
horizontal circle with a velocity of 3.00 m/s.
3. Determine the minimum coefficient of friction required to keep a 920.-kg car on a
turn with a radius of 26.8 m. The car is traveling 29.9 m/s and the roadway is level.
4. With what speed (in mi/hr) must you drive your car across the crest of a hill of
radius 37.1-m in order to feel weightless (1.00 m/s = 2.24 mi/hr)?
5. What is the reading of a bathroom scale when a man of mass 72 kg stands on it
while riding in an elevator accelerating upwards at 5.4 m/s2?
6. Use the following information to determine the orbital velocity at treetop level (2m)
on the surface of the moon. Mass of moon = 7.36 x 1022 kg Radius of Moon =
1.74 x 106 m
7. What is the period of rotation of Venus in earth years if it is a distance of 1.08 x
1011meters from the sun? (The earth-sun distance is 1.5 x 1011m.)
8. Which of the following statements are true of an object moving in a circle at a
constant speed? Include all that apply.
a. The object experiences a force which has a component directed parallel to
the direction of motion.
b. Inertia causes objects to move in a circle.
c. There can be a force pushing outwards on the object as long as the net force
in inwards.
d. Because the speed is constant, the acceleration is zero.
e. The acceleration and the net force vector are directed perpendicular to each
other.
f. If the net force acting upon the object is suddenly reduced to zero, then the
object would suddenly depart from its circular path and travel tangent to the
circle.
g. The acceleration of the object is directed tangent to the circle.
9. A physics teacher ties an eraser to the end of a string and then whirls it in a counterclockwise circle. If the teacher lets go of the string, then the eraser
hits a student (or several students) in the classroom. If the string is
let go when the eraser is at point X on the diagram at the right,
then which student(s) in the class will the eraser hit?
Newton’s Gravity
10. Two objects attract each other with a force of gravity (Fgrav) of 36 N. If the distance
separating the objects is doubled, then what is the new force of gravitational
attraction?
11. Two objects attract each other with a force of gravity (Fgrav) of 36 N. If the distance
separating the objects is doubled and the masses one of the objects is tripled, then
what is the new force of gravitational attraction?
12. Two objects attract each other with a force of gravity (Fgrav) of 36 N. If the distance
separating the objects is increased by a factor of 4 and the masses of both objects are
tripled, then what is the new force of gravitational attraction?
13. Suppose that a planet was located 12.0 times further from the sun than the earth's
distance from the sun. Determine the period of the planet.
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A1 Conceptual Physics Unit Homework
14. Suppose that the acceleration of gravity on the surface of planet X is 12 m/s2.
Determine the acceleration of gravity at a location ...
a. of 2 radii from the center of planet X.
b. of 4 radii from the center of planet X.
c. of 2 radii from the surface of planet X.
d. on the surface of planet X if the planet mass were twice as large (same
radius).
e. on the surface of planet X if the planet mass were one-half as large (same
radius).
15. The acceleration of gravity on the moon is approximately one-sixth the value on
earth's surface. If a person weighs 60.0 N on the moon's surface, what is his/her
approximate mass on Earth?
16. Determine the force of gravitational attraction between a 52.0-kg mother and a 3.0kg child if their separation distance is 0.50 meters.
17. What is the gravitational attraction between the proton and electron in an Hydrogen
atom if they are 5.3 x 10-11 meters apart? (mproton= 1.67 x 10-27 kg; melectron= 9.11x1031
kg)
18. Use the following information to help determine the orbital velocity and orbital
period of a satellite at a location of 15000 miles above the surface of the earth. Mass
of Earth = 5.98 x 1024 kg, Radius of Earth = 6.37 x 106 m
1609 m = 1.00 mi
For Questions #18-21, identify the type of force which causes the following bold-faced
objects to travel along a circular path.
a. gravity
b. normal
c. tension
d. applied
e. friction
f. spring
g. electrical
h. magnetic
19.
20.
21.
22.
An eraser is tied to a string swung in a horizontal circle.
The moon orbits the earth
A car makes a sharp right-hand turn along a level roadway.
A roller coaster car passes through a loop. Consider the car at the bottom of the
loop.
23. Which of the following statements are true about gravitational force? Identify all
that apply.
a. The gravitational force only acts between very, very massive objects.
b. The gravitational force between an object and the earth is inversely related
to the distance between the object's and the earth's center.
c. The gravitational force can ALWAYS be accurately calculated by
multiplying the object mass by the acceleration of gravity (m•g).
d. The gravitational force acting upon an object is the same as the weight of
the object.
e. The gravitational force between two objects is independent of the mass of
the smaller of the two objects.
f. If object A gravitationally attracts object B with a force of X Newtons, then
object B will also gravitationally attract object A with the same force of X
Newtons.
g. The doubling of the separation distance (measured from the center) between
two objects will halve the gravitational force between the objects.
h. It an object is placed two earth-radii above the surface of the earth, then the
force of gravitational attraction between the object and the earth will be onefourth the magnitude as on earth's surface.
i. Orbiting astronauts do not experience a force of gravity; this explains why
they feel weightless.
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A1 Conceptual Physics Unit Homework
24. Which of the following statements are true about the acceleration of gravity?
Identify all that apply.
a. The acceleration of gravity experienced by objects located near to (and far
from) from the earth depends upon the mass of the object.
b. The acceleration of gravity experienced by objects located near to (and far
from) from the earth depends upon the mass of the Earth.
c. The acceleration of gravity experienced by objects located near to (and far
from) the earth is inversely related to the distance between the center of the
object and the center of the earth.
d. Increasing the mass of an object will increase the acceleration of gravity
experienced by the object.
e. Doubling the distance between an object and the earth's center will decrease
the acceleration of gravity by a factor of four.
f. The acceleration of an orbiting satellite is equal to the acceleration of
gravity at that particular location.
g. If the mass of the Earth were doubled (without an alteration in its radius),
then the acceleration of gravity on its surface would be approximately 20
m/s2.
h. If the mass of the Earth were doubled and the radius of the earth were
doubled, then the two changes would offset each other and the acceleration
of gravity on its surface would still be approximately 10 m/s2.
Satellites
25. Which of the following statements are true about satellites? Identify all that apply.
a. Satellites are falling projectiles.
b. All satellites follow circular paths.
c. The orbital velocity required of a satellite is dependent upon the mass of the
satellite; a more massive satellite would require a greater orbital speed.
d. The orbital velocity of a satellite does not depend upon the mass of the
planet around which it orbits.
e. A high-altitude satellite will require a greater orbital speed than a lowaltitude satellite.
f. By definition, a geosynchronous satellite orbits the earth in a perfect circle,
maintaining the same distance above the surface of the earth.
g. Satellites travel faster along their orbital path when they are closest to the
earth.
h. The acceleration of a satellite varies inversely with its distance from the
center of the earth. More distant satellites have smaller accelerations.
26. Which of the following statements are true about the motion of planets about the
sun? Identify all that apply.
a. The force of gravity is the only force which acts upon the planets.
b. Their trajectories are highly elliptical.
c. The planets which are furthest from the sun have the greatest period.
d. For any given planet, the speed is greatest when the planet is closest to the
sun.
e. The velocity vector is directed tangent to the elliptical path.
f. The net force vector is at all times directed perpendicular to the velocity
vector.
g. To keep the planet from escaping the sun's gravitational field, the net force
vector is greatest when the planet is furthest from the sun.
Short Answer
27. Explain how something can be moving at a constant speed yet be accelerating at the
same time.
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A1 Conceptual Physics Unit Homework
28. How did Newton come up with the idea that the moon is actually "falling" toward
the Earth.
29. Distinguish between true- and apparent-weightlessness.
30. Describe the apparent weight of a person in an elevator while upward, accelerating
downward, and not accelerating.
Diagramming and Analysis
31. In the diagram at the right, draw vector arrows (straight lines with arrowheads)
which indicate the following for an object which is moving in a horizontal clockwise
circle.
a. the net force at point A.
b. the acceleration at point B.
c. the velocity at point C.
32. Construct a free-body diagram showing the direction and types of forces acting upon
the car at the top and the bottom of a loop. Be sure to label the forces according to
type.
33. Pete Zaria is riding the Cliff Hanger at Great America. Pete enters a cylindrical
barrel which makes 18.5 revolutions every minute. The diameter of the barrel is 6.92
m. Pete's mass is 64.7 kg. Construct a free-body diagram showing the forces acting
upon Pete. Calculate the acceleration and net force acting upon Pete Zaria. Finally,
determine the coefficient of friction between Pete and the walls that would be
required to support Pete's weight.
Page 44