Unit 3 Force and Newton’s Laws
Newton’s Laws of Motion
st
1.
State Newton’s 1 Law of motion.
2.
What is inertia?
16. When a horse pulls on a cart, the cart pulls on the
horse with an equal but opposite force. How, then, is
the horse and cart able to move?
17. If the weight of a balloon is 3000 N and the lift force
3.
What is the natural tendency or state of motion of an
object that is in motion?
4.
State Newton’s 2nd Law of motion.
5.
What happens to an object in motion when it
experiences a positive net force?
6.
What happens to an object in motion when it
experiences a negative net force?
7.
Can an object move if there is no net force on it?
Explain.
provided by the atmosphere is 3300 N,
a. In which direction is the net force acting?
b. How much is the net force acting on it?
18. What is the net force acting on an object that has 50 N
acting to the right and 73 N to the left?
19. A box is pushed across the floor with a 180 N force
8.
9.
Why does it require much less force to accelerate a
low-mass object than it does to accelerate a high-mass
object the same amount?
How does the pushing force acting on an object moving
at constant velocity compare to the amount of friction
acting on it?
while there is 150 N of friction acting on the box as it is
pushed. How much is the net force acting on the box?
20. A boy pushes on a box to the right with 200 N while a
girl pulls on the box to the right with 140 N. If there is
300 N of friction acting on the box as it slides across the
floor, how much is the net force acting on the box?
21. Calculate the force of friction acting on a box that is
being pushed by a 200 N force when there is a net force
of 80 N on the box.
22. How much net force acts on a 120 kg cart that is
experiencing an acceleration of 7.5 m/s2?
10. In order to make an object positively accelerate, how
must the force of push compare to the force of friction
acting on the object?
11. In order to make an object negatively accelerate, how
must the force of push compare to the force of friction
acting on the object?
23. A 25 kg object accelerates at 6.3 m/s². Calculate the
net force acting on the object.
24. How much acceleration does a 25 kg object experience
when a net force of 100 N is applied to it?
25. What is the mass of a car that experiences an
12. Sate Newton’s 3rd Law of motion.
13. Write an action-reaction pair for each of the following:
a. a man pushes on the wall
b. a bug hits the windshield of a car
c. a leaf falls from a tree toward the grass
14. Write an action-reaction pair for each of the following:
a. a hammer drives a nail into a piece of wood
b. a hockey stick hits a puck on the ice
c. a ball falls toward Earth
acceleration of 3.2 m/s2 and a net force of 1000 N?
26. How much acceleration does a 580 kg dragster
experience if the net force acting on it is 2310 N?
27. An airplane with a mass of 12,000 kg tows a glider with
a mass of 6,000 kg. If the airplane propellers provide a
net forward thrust of 36,000 N, what is the acceleration
of the glider?
28. A 241 kg wagon is accelerated across a level surface at
0.5 m/s2. What net force acts on the wagon?
15. Write an action-reaction pair for each of the following:
a. a dog wags its tail
b. a rocket is propelled into space
c. a boy kicks a soccer ball
29. An 2845 kg elevator is supported by a steel cable. What
is the tension in the cable when the elevator is
accelerated upward at 3.00 m/s2?
30. A 100 kg object goes from 0 to 10 m/s in 2.8 s.
a.
b.
c.
d.
How much does the object weigh?
Is this object in equilibrium?
How much acceleration does it experience?
How much net force was needed to do this?
31. A 500 kg compact car is attempting to stop when
traveling at 30 m/s. The car comes to a stop after
traveling a distance of 52 m.
a. How much does the car weigh?
b. Is this object in equilibrium?
c. How much acceleration does the car experience?
d. How much net force is needed to make it stop?
32. A 1200 kg car at rest speeds up to 30 m/s in 7.3 s.
a. How much acceleration does the car experience as it
undergoes the change in speed?
b. How much net force does the engine produce in
order to cause this change?
33. A 320 kg box at rest is accelerated across the floor in
6.7 s over a 22 m distance.
a. How much acceleration does the box experience as
it undergoes the change in speed?
b. How much net force acts on the box?
39. A 2784 kg truck attempts to tow a 1300 kg trailer at
rest by producing a net force of 250 N from its engine
to attempt to accelerate the system down the road. If
the engine produces this force for 4.4 s, calculate the
final velocity of the truck at the end of the 4.4 s.
Free-Body Diagrams
40. Identify whether each of the following statements is
true of false as it is currently written:
a. An object must be at rest and not be moving in
order to be in equilibrium.
b. In order to make something slide at constant
velocity there cannot be any friction.
c. If an object has no acceleration then there are no
forces acting on it at all.
d. Zero net force acts on an object in equilibrium.
e. Friction always acts in the opposite direction to
which way an object is moving.
f. The net force acting on an object that is accelerating
is a total of zero.
g. The normal force always acts straight up.
41. In the free-body diagram below, identify what each of
the four forces represents:
34. A 15 kg box at rest is accelerated across the floor in
2.7 s over a 7 m distance.
a. How much acceleration does the box experience as
it undergoes the change in speed?
b. How much net force acts on the box?
35. The net force on a boat causes it to accelerate at
1.55 m/s2. The mass of the boat is 215 kg. The same
net force causes another boat to accelerate at
0.125 m/s2.
a. What is the mass of the second boat?
b. One of the boats is now loaded on the other, and
the same net force is applied. What acceleration do
they experience?
42. In the free-body diagram shown below, identify which
of the four forces is the gravitational force.
36. A 10 kg bowling ball is released at one end of a
bowling alley lane at a speed of 7.4 m/s and slows to a
speed of 5.2 m/s over the 12.7 m long lane toward the
pins at the other end. How much net force acts on the
ball as it rolls down the bowling alley lane?
37. A 300 kg motorcycle moving at 22 m/s slows to 18 m/s
over 43.7 m. Calculate the net force acting on the
motorcycle to slow it down.
38. A 1200 kg car driving down the freeway at 37 m/s
accelerates to 41 m/s in 3.2 s. Calculate the net force
acting on the car to cause this acceleration.
43. In the drawing below, use arrows to show the two
horizontal and two vertical forces acting on the boat as
it is pulled to the shore at a constant speed.
Trigonometry
44. Draw a free-body diagram of each of the following:
a. a ball falling in the presence of air resistance
b. a ball falling without any air resistance
c. a helicopter hovering above the ground
60. For the following right triangles, find the missing side:
a.
45. Draw a free-body diagram of each of the following:
a. a book at rest on a table
b. a rock stuck in the middle of the yard
c. a box sitting on the ground
b.
46. Draw a free-body diagram of each of the following:
a. a box being pushed across the floor
b. a car being pushed across the road
c. a ball rolling across the floor
c.
47. Draw a free-body diagram for the following:
d.
Weight
e.
48. Distinguish between mass and weight.
49. How do you calculate your weight in physics?
50. How much does a 3 kg object weigh?
51. What is the mass of a cat that weighs 30.0 N?
61. For each of the following, find the missing angle(s):
a.
52. What is the weight of a 38.21 kg object?
53. What is the mass of a 105 N object?
54. What is the weight of a 1000 kg object?
b.
55. What is the mass of a 1.3 N object?
56. You are standing on a scale in an elevator. The elevator
begins to go up. What happens to your apparent
weight on the scale as it starts to move?
57. The elevator in previous problem comes to an abrupt
stop. What happens to your apparent weight on the
scale as it comes to a stop?
c.
d.
58. The elevator in the previous problem begins to go back
to down. What happens to your apparent weight on
the scale as it starts to move?
e.
59. The elevator in the previous problem comes to an
abrupt stop. What happens to your apparent weight
on the scale as it stops going down?
62. For each right triangle, find the missing sides:
64. A right triangle has a hypotenuse of length 17 cm and a
a.
leg of length 15 cm. What is the length of the other leg?
65. Calculate the hypotenuse and interior angles for a right
triangle with the components of 12 and 7.
b.
66. Calculate the magnitude of the displacement
(hypotenuse) of a hiker that went 8 km north and
12 km west.
c.
67. An athlete runs 110 m across a level field at an angle of
30 north of east. What are the east and north
components, respectively, of this displacement?
d.
68. Find the north and east components of the velocity of a
car that is moving at 30.0 km/h in a direction 35
north of east.
69.
63. For each right triangle, find the missing angles:
a.
A skateboarder rolls 25.0 m down a hill that descends
at an angle of 20 with the horizontal. Find the
horizontal and vertical components of the
skateboarder's displacement.
70. A window washer is climbing up a ladder to wash a
b.
window. The end of the 10.5-foot ladder exactly
touches the windowsill and the ladder makes a 70.0°
angle with the ground. How far off the ground is the
windowsill?
71. A helicopter in the noon-day sun lifts off the ground
c.
d.
by rising at a 28° angle to the ground. The helicopter’s
shadow travels 120 m across the ground as it rises into
the air at an angle at which point the helicopter stops
moving and hovers above the ground. How high
above the ground is the helicopter hovering?
72. The 28 ft flagpole outside Martin Luther King, Jr.
Elementary School casts a 42 ft shadow. In degrees, at
what angle above the horizon is the Sun?
73. A hiker travels 3 km north and then turns and heads
e.
18 km to the west. What is the angular direction the
hiker should take to return home?
74. What is the resultant displacement of a dog looking
f.
for its bone in the yard, if the dog first heads 55
north of west for 10.0 m, and then turns and heads
due south for 5.00 m?
Vectors
75. An airplane traveling at 100 m/s runs into a tailwind of
65 m/s. What is the resulting velocity of the airplane
due to the tailwind?
76. An airplane traveling at 100 m/s runs into a headwind
of 65 m/s. What is the resulting velocity of the airplane
due to the headwind?
77. A jogger runs 10.0 blocks due east, 5.0 blocks due
south, and another 2.0 blocks due east. Assume all
blocks are of equal size. Use the graphical method to
find the magnitude of the jogger’s net displacement.
78. A cave explorer travels 3.0 m eastward, then 2.5 m
northward, and finally 15 m westward. Use the
graphical method to find the magnitude of the net
displacement.
86. A jogger runs 10.0 blocks due east, 5.0 blocks due
south, and another 2.0 blocks due east. Assume all
blocks are of equal size. Use the graphical method to
find the magnitude of the jogger’s net displacement.
87. A cave explorer travels 3.0 m east, then 2.5 m north,
and finally 15 m west. Use the graphical method to find
the magnitude of the net displacement.
88. A dog walks 24 steps north and then walks 55 steps
west to bury a bone. If the dog walks back to the
starting point in a straight line, how many steps will the
dog take? What is the magnitude of the displacement?
89. A runner jogs 8.0 km west, turns and jogs 10.0 km
south, and then jogs 7.0 km north. Graphically
determine the magnitude of the jogger’s displacement.
90. Two displacement vectors have equal magnitudes of
79. A student adds two vectors of 200 and 40.
a. Calculate the largest magnitude of the resultant.
b. Calculate the smallest magnitude of the resultant.
80. An ant on a picnic table travels 30 cm eastward, then
25 cm northward, and finally 15 cm westward. What is
the ant’s displacement relative to its original position?
81. A duck waddles 2.5 m east and 6.0 m north. What is the
8 km. Describe the orientation of the two vectors to
each other if their sum has the following values: 0 km,
8 km, and 16 km.
91. A photographer wants to take a picture of a particularly
interesting flower, but he is not sure how far away to
place his camera. He takes three steps forward, four
back, seven forward, then five back. Finally, he takes
the photo. In steps, what was his displacement?
Assume the forward direction is positive.
magnitude of the duck’s displacement?
92. For the winter, a duck flies with a velocity of 2.5 m/s
82. A plane flies from city A to city B. City B is 1540 km west
and 1160 km south of city A. What is the total
displacement of the plane?
due south against a 10.0 m/s gust of wind. What is the
resultant velocity of the duck?
93. A lightning bug flies at a velocity of 0.25 m/s due east
83. A hiker walks 4.5 km north. Then the hiker walks 4.5 km
south. What is the magnitude of hiker’s total
displacement?
84. A quarterback takes the ball from the line of scrimmage
and runs backward for 10 m then sideways parallel to
the line of scrimmage for 15 m. The ball is thrown
forward 50 m perpendicular to the line of scrimmage.
The receiver is tackled immediately. How far is the
football displaced from its original position?
85. While following directions on a treasure map, a person
walks 45.0 m south, then turns and walks 7.50 m east.
Which single straight-line displacement could the
treasure hunter have walked to reach the same spot?
toward another lightning bug seen off in the distance. A
light easterly breeze blows on the bug at a velocity of
0.25 m/s. What is the resultant velocity of the bug?
94. Determine the magnitude and direction of the velocity
of a plane that is flying west at 100.0 km/h with respect
to the air while the wind is blowing toward the north at
65.0 km/h relative to the ground.
95. A pilot wants to fly a plane at 500.0 km/h, directly
north. The wind is blowing at 90.0 km/h from the east.
Find the magnitude of the course the pilot should fly.
96. A soccer ball is rolling east at an average velocity of
6.0 m/s when a kick deflects it to the north at an
average velocity of 7.0 m/s. What is the magnitude of
the ball’s change of velocity?
97. A diver is standing on a diving board that is 15 meters
above the surface of the water. He jumps 0.50 meters
straight up into the air, dives into the water and goes
3.0 meters underwater before returning to the
surface.
a. Assume that "up" is the positive direction. What is
the vertical displacement of the diver from when
he is on the diving board to when he emerges from
the water?
b. Now assume that "down" is the positive and again
determine the displacement.
106. A 0.125 kg frozen hamburger patty has two forces
acting on it that determine its horizontal motion. A
2.30 N force pushes it to the left, and a 0.800 N force
pushes it to the right.
a. What is the net force acting on it?
b. What is its acceleration?
107. 56. A 2,000 kg sailboat has two forces acting on it that
determine its horizontal motion. A 700 N force pushes
it to the left, and a 540 N force pushes it to the right.
a. What is the net force acting on it?
b. What is its acceleration?
98. A string attached to an airborne kite was maintained
at an angle of 40.0° with the ground. If 120 m of string
was reeled in to return the kite back to the ground,
what was the horizontal displacement of the kite?
(Assume the kite string did not sag.)
99. Julie is a citizen of Country A and she is describing the
nearby geography: "Our capital is at the origin. Our
famous beaches are 200 km directly west of our
capital. Country B's capital is 200 km directly east of
our capital. Country B's largest mountain is 700 km to
the east of Country A's capital."
a. Draw the four geographical features on a number
line from Julie's perspective.
b. A citizen of Country B begs to differ. He believes
that his capital is the origin. Draw the features on a
number line from his perspective.
Equilibrium
100. A car goes forward along a level road at constant
velocity. How much additional force is needed to bring
the car into equilibrium?
101. When a brick rests on a flat, stationary, horizontal
table, there is an upward normal force on it from the
table. Explain why the brick does not accelerate
upward in response to this force.
102. What is the tension in a rope that is supporting a 4.2 kg
bucket?
103. A net force of 125 N acts on an object. Find the single
force that will produce equilibrium.
104. What is the net force acting on an object that is
experiencing a force of 5 N to the north, 7 N to the
south, and 3 n to the north?
105. In a game of tug-of-war, a rope is pulled to the left with
a force of 75 N and to the right with a force of 102 N.
What is the magnitude and direction of the net external
force on the rope?
108.A 125 N sign is supported equally by two cables that
form a 140 angle between each other.
a. What is the net vertical force acting on the sign?
b. What is the tension in either of the cables?
109.A 205 N sign is supported equally by two cables that
form a 130 angle between each other.
a. What is the net vertical force acting on the sign?
b. What is the net horizontal force acting on it?
c. What is the tension in either of the cables?
d. Is this object in equilibrium?
110.A 20 kg sign is hung by two cables that form a 100
angle between each other.
a. What is the net vertical force acting on the sign?
b. What is the net horizontal force acting on it?
c. What is the tension in either of the cables?
111.A 90 kg sign is supported equally by two cables that
form a 60 angle between each other.
a. What is the net vertical force acting on the sign?
b. What is the tension in either of the cables?
112.A 300 N sign is supported equally by two cables that
form a 60 angle between each other. What is the
tension in either cable?
113.A 15 kg tire swing is supported equally by two ropes
that form a 20 angle between each other. What is
the tension in either of the ropes?
114.A 40 kg object is supported by two ropes where the
rope on the left forms a 20 angle to the horizontal
and the rope on the right forms a 40° angle to the
horizontal. What is the tension in the two ropes?
115.A 50 kg object is supported by two ropes where the
rope on the left forms a 45° angle to the horizontal
and the rope on the right forms a 30° angle to the
horizontal. What is the tension in the two ropes?
116.A 320 N sign is supported by two cables where cable A
forms a 40° to the wall on the left and cable B which
goes perfectly horizontal to the right (As Shown
Below). How much force of tension is on cable B?
Net Force Applied Through Angles
121. As the angle of an inclined plane increases, what
happens to the magnitude of the parallel component of
the weight force and the perpendicular component of
the weight force?
122. A 180 N sled is drug across the snow at constant
117.A 200 N sign is supported by a pole that pushes up and
a cable (C) that pulls up as shown in the picture below.
What is the tension in the cable (C)?
velocity by a force of 86 N through a rope that makes
an 40 angle with the ground. What is the horizontal
component of the pulling force being used to drag the
sled?
123. A lawnmower is pushed with a force of 250 N on the
handles that form a 63 angle with the ground. What
is the vertical component of the pushing force being
used to push the lawnmower?
124. A traveler rushes to catch a plane, pulling a suitcase
40
o
50
with a force directed 30 above the horizontal. If the
horizontal component of the force on the suitcase is
60.6 N, what is the force exerted on the handle?
C
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P
Bob's
Jingle
Shop
118. A 200 N sign is supported by two cables where cable A
forms a 40° to the wall on the left and cable B which
goes perfectly horizontal to the right (as shown in the
picture below). How much force of tension is acting in
cable A in keeping the sign motionless?
125. A 250 N sled is drug across the snow at constant
velocity with a rope that makes a 35 angle with the
ground with the tension in the rope being 50 N.
a. How much is the normal force on the sled?
b. How much friction is acting on the sled?
126. A sled is pulled at a constant velocity across a
horizontal snow surface. If a force of 80 N is being
applied to the sled rope at an angle of 53 to the
ground, what is the force of friction on the sled?
127. A 450 N suitcase is drug across the floor at constant
119.A 230 N lamp is supported by a rope and a pole as
shown in the picture below. How much force of
tension is acting in the rope to keep it motionless?
velocity by a handle that makes a 30 angle with the
ground with a pulling force of 250 N.
a. How much is the normal force on the suitcase?
b. How much friction is acting on the suitcase?
128. A mule uses a rope to pull a box that weighs 300 N
across a level surface with constant velocity. The rope
makes an angle of 30 above the horizontal, and the
tension in the rope is 100 N. What is the normal force
of the floor on the box?
129. A 20 kg box is pulled across the ground at constant
120.A trapeze artist weighs 800 N. The artist is
momentarily held to one side of a swing by a partner
so that both of the swing ropes are at an angle of 30
with the vertical. In such a condition of static
equilibrium, what is the horizontal force being applied
by the partner?
velocity with a force of 200 N through a rope that
makes a 15 angle to the ground.
a. How much does the box weigh?
b. How much is the vertical component of the pull?
c. How much is the horizontal component of the pull?
d. How much is the normal force acting it?
e. How much friction is acting on the box?
130. A 300 N sled is drug across the snow at constant
velocity by a force of 86 N through a rope that makes
an 18 angle with the ground.
a. What are the vertical and horizontal components of
the ropes force?
b. How much is the normal force acting on it?
c. How much friction is acting on the sled?
131. A 230 N sled is pulled across the ground at constant
velocity by a force of 86 N through a rope making an
25 angle with the ground.
a. What are the components of the rope’s force?
b. Is this sled in equilibrium?
c. How much is the normal force acting on it?
d. How much friction is acting on the sled?
25 incline. What are
the vertical and horizontal components of the boxes
weight?
132. A 28 kg box remains at rest on a
133. A book with a mass of 2.0 kg is held in equilibrium on a
board with a slope of 60 by a horizontal force. What
normal force is exerted by the book?
134. A crate weighing 823 N rests on a plank that makes a
25 angle with the ground. Find the components of
the crate’s weight force parallel and perpendicular to
the plank.
135. A sled weighing 100 N is held in place on a frictionless
20 slope by a rope attached to a stake at the top. The
rope is parallel to the slope. What is the normal force
of the slope acting on the sled?
136. A man pushes a 300 N crate up a
34 incline with a
force of 200 N at a constant velocity.
a. What is the net horizontal force acting it?
b. What are the vertical & horizontal components of
the weight?
c. What is the magnitude of the friction force?
d. What is the magnitude of the normal force?
137. A 27 kg trunk slides down an incline that makes a 30
with the floor and slides at constant velocity.
a. What is the weight of the trunk?
b. How much is the normal force acting on it?
c. How much friction is acting on the trunk?
139. A 15 kg suitcase slides at constant velocity down a
luggage chute that makes an incline of 30 .
a. What is the weight of the suitcase?
b. How much is the normal force acting on it?
c. How much friction is acting on the suitcase?
140. A 45 kg rock sits at rest an incline of
30 .
a. What is the weight of the rock?
b. How much is the normal force acting on it?
c. How much friction is acting on the rock?
141. A man pushes a 210 N crate up a 14 incline with a
force of 100 N at a constant velocity.
a. Find the vertical components of the weight?
b. Find the horizontal component of the weight?
c. Is this crate in equilibrium?
d. How much is the net vertical force on the crate?
e. How much is the net horizontal force on it?
f. What is the magnitude of the friction force?
g. Calculate the normal force acting on the crate?
45 incline with a
force of 200 N at a constant velocity.
a. What are the vertical and horizontal components of
the crate’s weight?
b. What is the magnitude of the friction force
c. What is the magnitude of the normal force?
142. A man pushes a 300 N crate up a
143. A 230 N box is sliding down a 40 incline at a constant
velocity. A man in front of the box pushes upward to
keep if from sliding faster with a force of 50 N.
a. What is the net horizontal force on the box?
b. What are the vertical & horizontal components of
the weight?
c. What is the magnitude of the friction force?
d. What is the magnitude of the normal force?
144.A 34 kg suitcase accelerates as it slides down a
luggage chute that makes an incline of 30 and
experiencing 50 N of friction.
a. What is the weight of the suitcase?
b. Is this suitcase in equilibrium?
c. How much is the normal force acting on it?
d. How much is net horizontal force on it?
e. How much acceleration does the suitcase
experience?
145.A 12 kg suitcase accelerates as it slides down a
138. A man pushes a 20 kg crate up a
20 incline with a
force of 100 N at a constant velocity.
a. What is the weight of the crate?
b. What are the vertical & horizontal components of
the weight?
c. What is the magnitude of the friction force?
d. What is the magnitude of the normal force
luggage chute that makes an incline of 50 .
a. What is the weight of the suitcase?
b. How much is the normal force acting on it?
c. If 50 N of friction is produced by the chute, how
much is net horizontal force on the suitcase?
d. How much acceleration does the suitcase
experience sliding down the chute?