Deck 5: Newtons Laws of Motion

Question 1

An object is dropped out of an airplane. It falls and eventually reaches a constant speed (terminal velocity). After the object reaches terminal velocity, which of the following statements is true?

A) The force of air resistance is zero.
B) The force of air resistance is equal to the weight of the object.
C) The acceleration of the object is equal to g.
D) There are no forces acting on the object.

Answer 1

The force of air resistance is equal to the weight of the object.

Question 2

$\vec { F } = m \vec { a }$ is a

A) scalar equation.
B) vector equation.
C) tensor equation.
D) none of the above.

Answer 2

vector equation.

Question 3

An object traveling along a curved path (Euclidean geometry) at constant speed

A) has no net force acting on it.
B) is not experiencing an acceleration.
C) has a net force acting on it.
D) must experience a tangential acceleration.

Answer 3

has a net force acting on it.

Question 4

Consider an object traveling at constant velocity. Which of the following statements is always true?

A) The net force must be zero.
B) The acceleration must be nonzero.
C) There must be more than one force acting on the object.
D) None of the above.

Question 5

A net force of 147 N acts on a 15-kg mass. The acceleration of the mass is

A) 0.10 m/s $2$
B) 0 m/s $2$
C) 147 m/s $2$
D) 2200 m/s. $2$

Question 6

Which of the following is an inertial reference frame?

A) The bed of an accelerating pickup truck
B) The floor of an elevator traveling upward at constant velocity
C) The seat of a Ferris wheel that is rotating at constant speed
D) The surface of an anvil that is in free fall (acceleration = g)

Question 7

The fact that a dime pulls upward on the Earth with a force equal to the weight of the dime is an example of

A) Newton's first law.
B) Newton's second law.
C) Newton's third law.
D) none of the above.

Question 8

A $3.3 \times 10 ^ { 6 }$ -kg rocket in deep space generates a thrust of $1 \times 10 ^ { 7 }$ N. What would be the force acting on a 150-kg astronaut riding in the rocket?

A) 1500 N
B) $1 \times 10 ^ { 7 }$ N
C) 450 N
D) 0 N

Question 9

A ball is thrown with some initial velocity at an angle of 42° relative to the horizontal. When the ball reaches its maximum height

A) its acceleration is zero.
B) its velocity is zero.
C) its acceleration is nonzero.
D) its velocity is at maximum value.

Question 10

A 50-kg crate is pulled across a smooth floor using a rope. The crate is accelerating at 1 m/s $2$ and the rope makes an angle of 50° with the floor. The normal force is

A) 430 N.
B) 540 N.
C) 390 N.
D) 490 N.

Question 11

The average net force to accelerate a 1-kg mass from rest to 10 m/s in one second is

A) 1 N.
B) 0.1 N.
C) 5 N.
D) 10 N.

Question 12

A catcher stops a baseball traveling at 40 m/s in a distance of 0.10 m. In doing so, she applies an average net force of 1200 N. The mass of the baseball is

A) 0.20 kg.
B) 0.15 kg.
C) 0.10 kg.
D) 0.05 kg.

Question 13

A 500-N force is required to accelerate a car from rest to 3.9 m/s in 12 seconds. We estimate the mass of the car to be

A) 5000 kg.
B) 2500 kg.
C) 4500 kg.
D) 1500 kg.

Question 14

The force that you exert on the Earth is

A) small relative to the force that the Earth exerts on you.
B) large relative to the force that the Earth exerts on you.
C) equal to your weight.
D) exactly zero.

Question 15

Two objects, A and B, experience the same net force. Object A accelerates at twice the rate of object B. Therefore the

A) mass of A is twice that of the mass of B.
B) mass of A is half that of the mass of B.
C) mass of A is one-quarter that of the mass of B.
D) mass of A is four times that of the mass of B.

Question 16

A car initially traveling at 16 m/s undergoes braking and comes to a complete stop in two seconds. During the braking an 80-kg passenger, sitting on a smooth and flat seat, exerts how much force on the seat belt?

A) 640 N
B) 800 N
C) 980 N
D) 1300 N

Question 17

An 0.08-kg bullet is fired out of a gun at 250 m/s. The length of the barrel is 0.82 m; we estimate the recoil force of the gun to be

A) 9000 N.
B) 8000 N.
C) 6000 N.
D) 3000 N.

Question 18

An 80-kg person falls out of an airplane and eventually reaches maximum speed (terminal velocity). We estimate the force of air friction at this speed to be

A) 780 N.
B) 0 N.
C) 22 N.
D) 52 N.

Question 19

A 1200-N force is required to keep an automobile traveling at 20 m/s. From this, the mass of the car

A) is 120 kg.
B) is 1200 kg.
C) is 1500 kg.
D) cannot be determined.

Question 20

A woman (mass = 70 kg) steps into an elevator. The elevator accelerates upward at 3 m/s $2$ . The force that the floor of the elevator exerts on the woman is

A) 700 N.
B) 900 N.
C) 980 N.
D) 1100 N.

Question 21

A woman who weighs 700 N steps onto a scale that is in an elevator. The elevator begins to accelerate. The woman now weighs 500 N (according to the scale). The acceleration of the elevator is

A) 2.8 m/s $2$ downward.
B) 2.8 m/s $2$ upward.
C) 4.2 m/s $2$ upward.
D) 4.2 m/s $2$ downward.

Question 22

A 5.4-kg mass, placed on a smooth incline and released, begins to slide down the incline. The acceleration of the mass along the incline is 7.1 m/s $2$ . The angle of the incline (relative to the horizontal) is

A) 41°.
B) 46°.
C) 38°.
D) 36°.

Question 23

A person who weighs 1100 N steps into an elevator. The person steps onto a scale, and the elevator begins to move down to the next floor. During the movement the person has an apparent weight of 950 N. The downward acceleration of the elevator is

A) 18. m/s $2$
B) 7.5 m/s $2$
C) 14 m/s $2$
D) 1.3 m/s $2$

Question 24

A 13.5-N net force is applied to a stationary object. The object moves a distance of 18 m in 10 seconds. The mass of the object is

A) 15 kg.
B) 21 kg.
C) 38 kg.
D) 12 kg.

Question 25

A stationary 32-kg mass has a 15-N net force applied to it. The velocity of the mass at $t = 5$ seconds is

A) 1.2 m/s.
B) 1.8 m/s.
C) 2.5 m/s.
D) 2.3 m/s.

Question 26

A 21-kg mass initially at rest on a smooth table has a horizontal force applied to it. The mass moves a distance of 30 meters in 5 seconds. The magnitude of the force is

A) 50 N.
B) 64 N.
C) 71 N.
D) 79 N.

Question 27

A 13-kg mass initially at rest has a net force applied to it. The force causes the mass to reach a velocity of 12 m/s in eight seconds. The magnitude of the force is

A) 15 N.
B) 20 N.
C) 30 N.
D) 25 N.

Question 28

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 4-kg mass (in a direction toward the 5-kg mass). The contact force between the two masses is

A) 20 N.
B) 9 N.
C) 0 N.
D) 11 N.

Question 29

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass). The contact force between the two masses is

A) 20 N.
B) 9 N.
C) 0 N.
D) 11 N.

Question 30

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass). The acceleration of the 5-kg mass is

A) 1.8 m/s $2$
B) 3.1 m/s $2$
C) 2.2 m/s $2$
D) 3.8 m/s $2$

Question 31

A 4-kg mass and a 5-kg mass are in contact with each other while resting on a smooth table. A 20-N external force is applied to the 5-kg mass (in a direction toward the 4-kg mass). The acceleration of the 4-kg mass is

A) 1.8 m/s $2$
B) 3.1 m/s $2$
C) 2.2 m/s $2$
D) 3.8 m/s $2$

Question 32

A small mass and a large mass are in contact with each other while resting on a smooth table. An external force is applied to one of the masses (in a direction toward the other mass). The contact force between the masses is

A) largest when the external force is applied to the smaller mass.
B) largest when the external force is applied to the larger mass.
C) the same whether the external force is applied to the smaller or larger mass.
D) zero in all cases.

Question 33

A heavy truck is towing a small car. The mass of the truck is four times larger than the mass of the car. If the force that the truck is exerting on the car is 5000 N, the force that the car is exerting back on the truck is

A) 1300 N.
B) 20,000 N.
C) 2000 N.
D) 5000 N.

Question 34

A small car is towing a heavy truck. The mass of the truck is four times larger than the mass of the car. If the force that the car is exerting on the truck is 2000 N, the force that the truck is exerting back on the car is

A) 1300 N.
B) 8000 N.
C) 2000 N.
D) 500 N.

Question 35

A steel cable is tightly tied (horizontally) to two trees that are 8 meters apart. A 40-kg child hangs from the center of the cable-causing the center of the cable to be 1 cm below the original location (before the child grabbed the cable). The tension in the cable is

A) 78,000 N.
B) 400 N.
C) 1200 N.
D) 12,000 N.

Question 36

A steel cable is tightly tied (horizontally) to two trees that are 10 meters apart. A child hangs from the center of the cable, causing the center of the cable to be 2 cm below the original location (before the child grabbed the cable). The tension in the cable is 70,000 N. The mass of the child is

A) 41 kg.
B) 66 kg.
C) 57 kg.
D) 48 kg.

Question 37

A 4-kg mass is connected to a 6-kg mass by a massless cord. A 120-N upward force is applied to the 4-kg mass, causing both masses to accelerate upward. The tension in the massless cord is

A) 60 N.
B) 48 N.
C) 40 N.
D) 72 N.

Question 38

A 4-kg mass is connected to a 6-kg mass by a massless cord. A 120-N upward force is applied to the 4-kg mass, causing both masses to accelerate upward. The upward acceleration of the masses is

A) 12 m/s $2$
B) 2.2 m/s $2$
C) 9.8 m/s $2$
D) 5.8 m/s $2$

Question 39

A 6-kg mass is connected to a 4-kg mass by a massless cord. A 120-N upward force is applied to the 6-kg mass, causing both masses to accelerate upward. The tension in the massless cord is

A) 60 N.
B) 40 N.
C) 72 N.
D) 48 N.

Question 40

Object A, having mass $m _ { A }$ , is connected to object $\mathrm { B }$ , having mass $m _ { B }$ , by a massless cord. An upward force $P$ is applied to mass A, causing both masses to accelerate upward. Find the tension in the massless cord.

A) $P \times \left[ m _ { A } / \left( m _ { A } + m _ { B } \right) \right]$
B) $P \times \left[ \left( m _ { A } + m _ { B } \right) / m _ { B } \right]$
C) $P \times \left[ m _ { B } / \left( m _ { A } + m _ { B } \right) \right]$
D) $P \times \left[ \left( m _ { A } + m _ { B } \right) / m _ { A } \right]$

Question 41

A 5-kg mass slides down a smooth incline. The acceleration of the mass along the surface of the incline is 4.2 m/s $2$ . The angle of the incline (relative to the horizontal) is

A) 20°.
B) 16°.
C) 29°.
D) 25°.

Question 42

A 7-kg mass slides down a smooth incline. The incline makes an angle of 30° with the horizontal. The acceleration of the mass along the incline is

A) 4.9 m/s $2$
B) 8.2 m/s $2$
C) 6.5 m/s $2$
D) 9.1 m/s $2$

Question 43

A 7-kg mass slides down a smooth incline. The incline makes an angle of 30° with the horizontal. The acceleration of the mass in the vertical direction is

A) 9.8 m/s $2$
B) 2.5 m/s $2$
C) 7.2 m/s $2$
D) 4.1 m/s $2$

Question 44

A 7-kg mass slides down a smooth incline. The incline makes an angle of 30° with the horizontal. The acceleration of the mass in the horizontal direction is

A) 0 m/s $2$
B) 3.5 m/s $2$
C) 4.2 m/s $2$
D) 5.1 m/s $2$

Question 45

A 5-kg mass is pulled up a smooth incline at a constant speed by a rope. The rope is parallel with the surface of the incline. If the incline is 50° relative to the horizontal, the tension in the rope is

A) 38 N.
B) 41 N.
C) 44 N.
D) 49 N.

Question 46

A 5-kg mass is pulled up a smooth incline at a constant speed by a rope. The rope is parallel with the surface of the incline. If the incline is 50° relative to the horizontal, the normal force exerted by the incline on the mass is

A) 28 N.
B) 38 N.
C) 31 N.
D) 45 N.

Question 47

An 8-kg mass is pulled across a smooth floor using a rope. The rope makes an angle of 28° with the floor. If the tension in the rope is 45 N, the acceleration of the 8-kg mass is

A) 7.8 m/s $2$
B) 7.2 m/s $2$
C) 6.2 m/s $2$
D) 5.0 m/s $2$

Question 48

An 8-kg mass is pulled across a smooth floor using a rope. The rope makes an angle of 28° with the floor. If the tension in the rope is 45 N, the normal force exerted by the floor on the mass is

A) 57 N.
B) 65 N.
C) 78 N.
D) 69 N.

Question 49

A 5.5-kg object, moving at constant velocity, is acted on by three forces. One force is 20 N along the +x axis. The second force is 25 N along the +y axis. What is the magnitude of the third force?

A) 23 N
B) 32 N
C) 28 N
D) 35 N

Question 50

A 5.5-kg object, moving at constant velocity, is acted on by three forces. One force is 20 N along the +x axis. The second force is 25 N along the +y axis. What is the direction of the third force (measured counterclockwise from the x +axis)?

A) 231°
B) 129°
C) 269°
D) 246°

Question 51

A truck has a 300-kg load that is not secured. The maximum frictional force between the load and the truck bed is 400 N. What is the maximum acceleration that the truck can have so that it does not lose the load?

A) 0.8 m/s $2$
B) 1.8 m/s $2$
C) 2.3 m/s $2$
D) 1.3 m/s $2$

Question 52

A truck has a 300-kg load that is not secured. The truck pulls away from a stoplight with a maximum acceleration of 2.3 m/s $2$ ; during this acceleration the load does not slip. What was the maximum frictional force developed between the load and the truck bed?

A) 2900 N
B) 1900 N
C) 990 N
D) 690 N

Question 53

A particle of mass $5.7 \mathrm {~kg}$ , initially at rest, experiences a time-varying force, $f ( t ) = c t ^ { 2 } + h t$ , where $c = 1.3 \mathrm {~N} / \mathrm { s } ^ { 2 }$ and $h = 5.6 \mathrm {~N} / \mathrm { s }$ . What is the velocity of the particle at time $t = 4$ seconds?

A) 35 m/s
B) 19 m/s
C) 13 m/s
D) 25 m/s

Question 54

A particle of mass $5.7 \mathrm {~kg}$ , initially at rest, experiences a time-varying force, $f ( t ) = c t ^ { 2 } + h t$ where $c = 1.3 \mathrm {~N} / \mathrm { s } ^ { 2 }$ and $h = 5.6 \mathrm {~N} / \mathrm { s }$ . What is the acceleration of the particle at time $t = 4$ seconds?

A) 9.5 m/s $2$
B) 8.8 m/s $2$
C) 5.4 m/s $2$
D) 7.6 m/s $2$

Question 55

A particle of mass $5.7 \mathrm {~kg}$ , initially at rest, experiences a time-varying force, $f ( t ) = c t ^ { 2 } + h t$ , where $c = 1.3 \mathrm {~N} / \mathrm { s } ^ { 2 }$ and $h = 5.6 \mathrm {~N} / \mathrm { s }$ . What is the displacement of the particle at time $t = 4$ seconds?

A) 20 m
B) 15 m
C) 10 m
D) 25 m

Question 56

The position of a $3.2 - \mathrm { kg }$ particle is given by $x ( t ) = b t ^ { 3 }$ , where $b = 6.5 \mathrm {~m} / \mathrm { s } ^ { 3 }$ . What is the force acting on the particle at time $t = 8$ seconds?

A) 1000 N
B) 670 N
C) 520 N
D) 800 N

Question 57

The velocity of a $3.2 - \mathrm { kg }$ particle is given by $v ( t ) = c t ^ { 2 }$ , where $c = 2.1 \mathrm {~m} / \mathrm { s } ^ { 3 }$ . What is the force acting on the particle at time $t = 5$ seconds?

A) 48 N
B) 67 N
C) 34 N
D) 41 N

Question 58

The acceleration of a $3.2 - \mathrm { kg }$ particle is given by $a ( t ) = h t ^ { 2 }$ , where $h = 8.4 \mathrm {~m} / \mathrm { s } ^ { 4 }$ . What is the force acting on the particle at time $t = 7$ seconds?

A) 1500 N
B) 1600 N
C) 1300 N
D) 1100 N

Question 59

An archer pulls the string of her bow back with her hand with a force of 200 N. The two halves of the string (above and below her hand) make an angle of 110° with each other. What is the tension in the string?

A) 170 N
B) 200 N
C) 350 N
D) 140 N

Question 60

A 3-m-long heavy chain, mass of 30 kg, is lowered from a barn loft by a farmer. The downward acceleration of the chain is 3 m/s $2$ . What is the tension in the chain at its midpoint of 1.5 m from an end?

A) 0 N
B) 200 N
C) 150 N
D) 100 N

Question 61

A 3-m-long heavy chain, mass of 30 kg, is lowered at constant speed from a barn loft by a farmer. What is the tension in the chain at its midpoint of 1.5 m from an end?

A) 0 N
B) 200 N
C) 150 N
D) 100 N

Question 62

A 3-m-long heavy chain, mass of 30 kg, is held by one end from a barn loft by a farmer. The farmer then lets go of the chain. What is the tension in the chain at its midpoint (1.5 m from an end) as it is falling?

A) 0 N
B) 200 N
C) 150 N
D) 100 N

Question 63

A heavy cable of length $l$ and linear mass density $\lambda$ (mass/length) hangs vertically from a high bridge. What is the tension in the cable at its midpoint of $l / 2$ ?

A) $g \lambda l$
B) $\frac { 1 } { 4 } g \lambda l ^ { 2 }$
C) $\frac { 1 } { 2 } g \lambda l$
D) $\frac { 1 } { 4 } g \lambda l$

Question 64

A person has a mass of 110 kg on Earth. What is the weight of this person on Jupiter, which has a surface gravity of $2.53 \mathrm {~g}$

A) 430 N
B) 2700 N
C) 880 N
D) 1080 N

Question 65

A person has a mass of 110 kg on Earth. What is the mass of this person on Jupiter, which has a surface gravity of $2.53 \mathrm {~g}$

A) 43 kg
B) 110 kg
C) 330 kg
D) 280 kg

Question 66

A 1.3-kg pendulum hangs from the roof of a stationary car. The car accelerates, and the string of the pendulum now makes an angle of 13 - (relative to its initial position). What is the acceleration of the car?

A) 4.5 m/s $2$
B) 4.1 m/s $2$
C) 3.2 m/s $2$
D) 2.3 m/s $2$

Question 67

A 5.0-kg mass hangs by a thin massless string from a tree branch. A strong breeze blowing in the horizontal direction imparts a force of 40 N on the mass. What is the angle of the string (relative to its initial vertical position)?

A) 39 N
B) 55 N
C) 33 N
D) 35 N

Question 68

A 1500-kg car on a snow-covered road starts from rest and accelerates at a constant rate for 12 seconds until traveling at 40 m/s. What is the frictional force imparted to the car by the snow-covered road?

A) 15,000 N
B) 7500 N
C) 5000 N
D) 2500 N

Question 69

A 5-kg mass is attached to a massless cord. The cord is wrapped around a massless pulley, and the other end of the cord is attached to a 3-kg mass. The two masses are released. Find the acceleration of the masses.

A) 4.1 m/s $2$
B) 1.9 m/s $2$
C) 2.5 m/s $2$
D) 3.1 m/s $2$

Question 70

A 5-kg mass is attached to a massless cord. The cord is wrapped around a massless pulley, and the other end of the cord is attached to a 3-kg mass. The two masses are released. Find the tension in the cord.

A) 37 N
B) 17 N
C) 29 N
D) 49 N

Question 71

A heavy object having mass $m _ { a }$ is attached to a massless cord. The cord is wrapped around a massless pulley, and the other end of the cord is attached to a lighter object having mass $m _ { b } \left( m _ { a } > m _ { b } \right)$ . The two masses are released. Find the acceleration of the masses.

A) $2 g m _ { b } / \left( m _ { a } + 2 m _ { b } \right)$
B) $2 g m _ { a } / \left( m _ { a } + m _ { b } \right)$
C) $g \times \left( m _ { b } - m _ { a } \right) / \left( 2 m _ { a } + m _ { b } \right)$
D) $g \times \left( m _ { a } - m _ { b } \right) / \left( m _ { a } + m _ { b } \right)$

Question 72

A 21-kg mass is pushed up a smooth incline using a horizontal force. The incline makes an angle of 35° with the horizontal, and the acceleration of the mass along the incline is 1.5 m/s $2$ . Find the horizontal force.

A) 120 N
B) 180 N
C) 230 N
D) 210 N

Question 73

A 21-kg mass is pushed up a smooth incline using a horizontal force. The incline makes an angle of 35° with the horizontal, and the acceleration of the mass along the incline is 1.5 m/s $2$ . Find the normal force exerted by the incline.

A) 210 N
B) 330 N
C) 390 N
D) 270 N

Question 74

Two masses, 5 kg and 3 kg, are connected by massless string. A cord is then attached to the 5-kg mass and the two masses are pulled across a smooth flat table. If the masses are moving at constant speed, what is the tension in the massless string (between the two masses)?

A) 0 N
B) 50 N
C) 20 N
D) 30 N

Question 75

Two masses, 5 kg and 3 kg, are connected by massless string. A cord is then attached to the 5-kg mass, and the two masses are pulled across a smooth flat table. If the masses accelerate at 2 m/s $2$ , what is the tension in the massless string (between the two masses)?

A) 10 N
B) 4 N
C) 5 N
D) 6 N

Question 76

Two masses, 5 kg and 3 kg, are connected by massless string. The two masses are then placed on a smooth incline and released. The acceleration of the two masses along the incline is 2 m/s $2$ . Find the tension in the massless string between the two masses.

A) 10 N
B) 4 N
C) 0 N
D) 6 N

Question 77

A person receives a 7-kg bag of groceries from the store clerk. The person then exerts an upward force of 28 N on the bag of groceries. The acceleration of the bag of groceries is

A) 4.0 m/s $2$ upward.
B) 4.0 m/s $2$ downward.
C) 5.8 m/s $2$ upward.
D) 5.8 m/s $2$ downward.

Question 78

A 10-kg mass is placed at the top of a smooth incline. The incline makes an angle of 30° with the horizontal. What should be the minimum horizontal acceleration of the incline so that the normal force exerted by the incline (acting on the mass) is zero?

A) 9.8 m/s $2$
B) 11 m/s $2$
C) 6.2 m/s $2$
D) 17 m/s $2$