Deck 8: Linear Momentum and Collisions

Question 1

A 4.0-kg mass has a velocity of 4.0 m/s east when it explodes into two 2.0-kg masses. After the explosion one of the masses has a velocity of 3.0 m/s at an angle of 60 $\degree$ north of east. What is the magnitude of the velocity of the other mass after the explosion?

A)7.9 m/s
B)8.9 m/s
C)7.0 m/s
D)6.1 m/s
E)6.7 m/s

Answer 1

7.0 m/s

Question 2

A 10-g bullet moving horizontally with a speed of 2.0 km/s strikes and passes through a 4.0-kg block moving with a speed of 4.2 m/s in the opposite direction on a horizontal frictionless surface. If the block is brought to rest by the collision, what is the kinetic energy of the bullet as it emerges from the block?

A)0.51 kJ
B)0.29 kJ
C)0.80 kJ
D)0.13 kJ
E)20 kJ

Answer 2

0.51 kJ

Question 3

A 2000-kg truck travelling at a speed of 6.0 m/s makes a 90 $\degree$ turn in a time of 4.0 s and emerges from this turn with a speed of 4.0 m/s. What is the magnitude of the average resultant force on the truck during this turn?

A)4.0 kN
B)5.0 kN
C)3.6 kN
D)6.4 kN
E)0.67 kN

Answer 3

3.6 kN

Question 4

A 12-g bullet moving horizontally strikes and remains in a 3.0-kg block initially at rest on the edge of a table. The block, which is initially 80 cm above the floor, strikes the floor a horizontal distance of 120 cm from its initial position. What was the initial speed of the bullet?

A)0.68 km/s
B)0.75 km/s
C)0.81 km/s
D)0.87 km/s
E)0.41 km/s

Question 5

A 3.0-kg ball with an initial velocity of (4 + 3 ) m/s collides with a wall and rebounds with a velocity of (-4 + 3 ) m/s. What is the impulse exerted on the ball by the wall?

A)+24 N $\cdot$ s
B)(-24 N $\cdot$ s)
C)+18 N $\cdot$ s
D)(-18 N $\cdot$ s)
E)+8.0 N $\cdot$ s

Question 6

A 2.0-kg object moving with a velocity of 5.0 m/s in the positive x direction strikes and sticks to a 3.0-kg object moving with a speed of 2.0 m/s in the same direction. How much kinetic energy is lost in this collision?

A)2.4 J
B)9.6 J
C)5.4 J
D)0.6 J
E)6.0 J

Question 7

A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position?

A)78 cm
B)66 cm
C)56 cm
D)46 cm
E)37 cm

Question 8

An 8.0-kg object moving 4.0 m/s in the positive x direction has a one-dimensional collision with a 2.0-kg object moving 3.0 m/s in the opposite direction. The final velocity of the 8.0-kg object is 2.0 m/s in the positive x direction. What is the total kinetic energy of the two-mass system after the collision?

A)32 J
B)52 J
C)41 J
D)25 J
E)29 J

Question 9

A 1.6-kg ball is attached to the end of a 0.40-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point of its swing, when it is moving horizontally, the ball collides with a 0.80-kg block initially at rest on a horizontal frictionless surface. The speed of the block just after the collision is 3.0 m/s. What is the speed of the ball just after the collision?

A)1.7 m/s
B)1.1 m/s
C)1.5 m/s
D)1.3 m/s
E)2.1 m/s

Question 10

A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest. Immediately after the collision, the 2.0-kg object has a velocity of 1.5 m/s directed 30 $\degree$ from its initial direction of motion. What is the x component of the velocity of the 1.0-kg object just after the collision?

A)3.7 m/s
B)3.4 m/s
C)1.5 m/s
D)2.4 m/s
E)4.1 m/s

Question 11

A 1.6-kg block is attached to the end of a 2.0-m string to form a pendulum. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 10-g bullet moving horizontally in the opposite direction. The bullet remains in the block and causes the block to come to rest at the low point of its swing. What was the magnitude of the bullet's velocity just before hitting the block?

A)1.0 km/s
B)1.6 km/s
C)1.2 km/s
D)1.4 km/s
E)1.8 km/s

Question 12

The speed of a 2.0-kg object changes from 30 m/s to 40 m/s during a 5.0-s time interval. During this same time interval, the velocity of the object changes its direction by 90 $\degree$ . What is the magnitude of the average total force acting on the object during this time interval?

A)30 N
B)20 N
C)40 N
D)50 N
E)6.0 N

Question 13

A 3.0-kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M?

A)7.5 kg
B)5.0 kg
C)6.0 kg
D)4.2 kg
E)8.0 kg

Question 14

Two blocks with masses 2.0 kg and 3.0 kg are placed on a horizontal frictionless surface. A light spring is placed in a horizontal position between the blocks. The blocks are pushed together, compressing the spring, and then released from rest. After contact with the spring ends, the 3.0-kg mass has a speed of 2.0 m/s. How much potential energy was stored in the spring when the blocks were released?

A)15 J
B)3.0 J
C)6.0 J
D)12 J
E)9.0 J

Question 15

A 6.0-kg object moving 5.0 m/s collides with and sticks to a 2.0-kg object. After the collision the composite object is moving 2.0 m/s in a direction opposite to the initial direction of motion of the 6.0-kg object. Determine the speed of the 2.0-kg object before the collision.

A)15 m/s
B)7.0 m/s
C)8.0 m/s
D)23 m/s
E)11 m/s

Question 16

A 6.0-kg object, initially at rest in free space, 'explodes' into three segments of equal mass. Two of these segments are observed to be moving with equal speeds of 20 m/s with an angle of 60 $\degree$ between their directions of motion. How much kinetic energy is released in this explosion?

A)2.4 kJ
B)2.9 kJ
C)2.0 kJ
D)3.4 kJ
E)1.2 kJ

Question 17

A 5.0-g particle moving 60 m/s collides with a 2.0-g particle initially at rest. After the collision each of the particles has a velocity that is directed 30 $\degree$ from the original direction of motion of the 5.0-g particle. What is the speed of the 2.0-g particle after the collision?

A)72 m/s
B)87 m/s
C)79 m/s
D)94 m/s
E)67 m/s

Question 18

A 4.2-kg object, initially at rest, 'explodes' into three objects of equal mass. Two of these are determined to have velocities of equal magnitudes (5.0 m/s) with directions that differ by 90 $\degree$ . How much kinetic energy was released in the explosion?

A)70 J
B)53 J
C)60 J
D)64 J
E)35 J

Question 19

A 1.5-kg playground ball is moving with a velocity of 3.0 m/s directed 30 $\degree$ below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of 2.0 m/s directed 60 $\degree$ above the horizontal. What is the magnitude of the average resultant force on the ball?

A)14 N
B)11 N
C)18 N
D)22 N
E)3.0 N

Question 20

At an instant when a particle of mass 50 g has an acceleration of 80 m/s2 in the positive x direction, a 75-g particle has an acceleration of 40 m/s2 in the positive y direction. What is the magnitude of the acceleration of the centre of mass of this two-particle system at this instant?

A)60 m/s2
B)56 m/s2
C)40 m/s2
D)50 m/s2
E)46 m/s2

Question 21

In an elastic collision between two bodies of mass m1 and m², with m² initially at rest, mass 1 moves off at angle $\theta$ relative to the direction of its initial velocity and mass 2 at angle $\phi$ . An exam paper shows the equations below: m1v1i
0
= m1v1f cos $\theta$ + m²v2f sin $\phi$
= m1v1f sin $\theta$ + m²v2f cos $\phi$
What error(s) has the student made?

A)In the first equation, m²v2f sin $\phi$ should be m²v2f cos $\phi$ .
B)In the second equation, m²v2f cos $\phi$ should be m²v2f sin $\phi$ .
C)In the second equation, the plus sign between the terms on the right should be a minus sign.
D)All of the errors listed above.
E)Only errors (a) and (b) above.

Question 22

Two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls?

A) $\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{B}}\right|<\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{A}}\right|$ .
B) $\left|\Delta \overrightarrow{\mathbf{p}}_{B}\right|=\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{A}}\right|$ .
C) $\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{B}}\right|>\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{A}}\right|$ .
D) $\overrightarrow{\mathbf{p}}$ B = $\Delta$$\overrightarrow{\mathbf{p}}$ A.
E) $\overrightarrow{\mathbf{p}}$ B > $\Delta$$\overrightarrow{\mathbf{p}}$ A.

Question 23

Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision

A)each car has half the momentum.
B)car A stops and car B has momentum mv.
C)car A stops and car B has momentum 2mv.
D)the momentum of car B is four times as great in magnitude as that of car A.
E)each car has half of the kinetic energy.

Question 24

A steel ball bearing of mass m1 and speed of magnitude v1 has a head-on elastic collision with a steel ball bearing of mass m² at rest. Rank the speed v1 of m1 relative to v2, the magnitude of the speed of m², after the collision when: i) m1 > m²; ii) m1 = m²; and iii) m1 < m².

A)v1 < v2; v1 < v2; v1 < v2
B)v1 < v2; v1 = v2; v1 > v2
C)v1 < v2; v1 > v2; v1 > v2
D)v1 > v2; v1 = v2; v1 < v2
E)v1 > v2; v1 > v2; v1 > v2

Question 25

A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s2) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed?

A)56 kN
B)48 kN
C)52 kN
D)44 kN
E)36 kN

Question 26

If you know the impulse that has acted on a body of mass m you can calculate:

A)its initial velocity.
B)its final velocity.
C)its final momentum.
D)the change in its velocity.
E)its acceleration during the impulse.

Question 27

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are:

A)their changes in momentum.
B)the force each exerts on the other.
C)their changes in kinetic energy.
D)all of the above.
E)only (a) and (b) above.

Question 28

A 3.00-kg stone is dropped from a 39.2 m high building. When the stone has fallen 19.6 m, the magnitude of the impulse the Earth has received from the gravitational force exerted by the stone is:

A)9.80 N $\cdot$ s.
B)19.6 N $\cdot$ s.
C)29.4 N $\cdot$ s.
D)58.8 N $\cdot$ s.
E)118 N $\cdot$ s.

Question 29

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer?

A)Nothing. The spaceship takes up the momentum of the hammer.
B)He moves away from the spaceship.
C)He moves towards the spaceship.
D)He moves towards the spaceship as he pulls the hammer back and moves away from it as he swings the hammer forward.
E)He moves away from the spaceship as he pulls the hammer back and moves toward it as he swings the hammer forward.

Question 30

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than $\frac{\pi}{2} \mathrm{R}$ , one quarter circle, the centre of mass of the two cars:

A)remains at the initial point.
B)travels along a diameter of the circle at speed v' < v.
C)travels along a diameter of the circle at speed v' = v.
D)travels along a diameter of the circle at speed v' > v.
E)remains at the centre of the circle.

Question 31

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m high ladders. The centre of mass of the Earth (mE = 5.90 $\times$ 1024 kg) is then displaced:

A)0 m.
B)1.84 *10-23 m.
C)1.84 * 10-14 m.
D)1.80 * 10-13 m.
E)2 m.

Question 32

Refer to Exhibit 8-1 below.Exhibit 8-1 Two birds of prey hurtling after the same rabbit collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60 $\degree$ angle to the ground. What is the magnitude of their velocity, in m/s, immediately after the collision?

A)0
B)13
C)15
D)26
E)30

Question 33

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (-2, -2) m. Where must a 20-g particle be placed so that the centre of mass of the three-particle system is at the origin?

A)(-3, -1) m
B)(+1, +3) m
C)(+3, -1) m
D)(-1, -3) m
E)(-0.5, -2) m

Question 34

When two bodies of different masses collide, the impulses they exert on each other are:

A)equal for all collisions.
B)equal but opposite for all collisions.
C)equal but opposite only for elastic collisions.
D)equal but opposite only for inelastic collisions.
E)equal but opposite only when the bodies have equal but opposite accelerations.

Question 35

A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?

A)42 kN
B)39 kN
C)45 kN
D)48 kN
E)35 kN

Question 36

Two bodies with masses m1 and m² are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the centre of mass of this system of two bodies is:

A)less than v1.
B)equal to v1.
C)equal to the average of v1 and v2.
D)greater than v1 and less than v2.
E)greater than v2.

Question 37

Refer to Exhibit 8-1 below.Exhibit 8-1 Two birds of prey hurtling after the same rabbit collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60 $\degree$ angle to the ground. What is the horizontal component of their momentum, in $\frac{\mathrm{kg} \cdot \mathrm{~m}}{\mathrm{~s}}$ , immediately after the collision?

A)0
B)6.1
C)7.5
D)13
E)15

Question 38

When the rate of burn and the exhaust velocity are constant, a rocket ascends with:

A)decreasing acceleration.
B)decreasing velocity.
C)constant velocity.
D)constant acceleration.
E)increasing acceleration.

Question 39

Refer to Exhibit 8-1 below.Exhibit 8-1 Two birds of prey hurtling after the same rabbit collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60 $\degree$ angle to the ground. What is the magnitude of their total momentum, in $\frac{\mathrm{kg} \cdot \mathrm{~m}}{\mathrm{~s}}$ , immediately after the collision?

A)0
B)6.5
C)7.5
D)13
E)15

Question 40

A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40 $\degree$ angle to the ground. The magnitude of the horizontal impulse the catapult receives from the rock is:

A)5.1* 104 N $\cdot$ s.
B)6.1 * 104 N $\cdot$ s.
C)8.0 * 104 N $\cdot$ s.
D)5.0 * 105 N $\cdot$ s.
E)6.0 * 105 N $\cdot$ s.

Question 41

The linear density of a rod, in g/m, is given by $\lambda=40.0+30.0 x$ . The rod extends from the origin to x = 0.400 m. What is the mass of the rod?

A)0.213 g
B)3.50 g
C)3.84 g
D)18.4 g
E)20.8 g

Question 42

High-speed stroboscopic photographs show that the head of a golf club of mass 200 grams is travelling at 55.0 m/s just before it strikes a 46.0-gram golf ball at rest on a tee. After the collision, the clubhead travels (in the same direction) at 40.0 m/s. Find the speed of the golf ball just after impact.

Question 43

A uniform thin wire has a length $L=\pi R$ and is bent into a semicircular arc of radius R. If the wire starts at (x, y) = (R, 0) and curves counterclockwise to (x, y) = (-R, 0), what is the y coordinate of its centre of mass?

Question 44

A child bounces a 50-gram superball on the sidewalk. The velocity of the superball changes from 21 m/s downward to 19 m/s upward. If the contact time with the sidewalk is 1/800 s, what is the magnitude of the force exerted on the superball by the sidewalk?

Question 45

A bowler claims he can throw a cricket ball with as much momentum as a 3.00-g bullet moving with a speed of 1500 m/s. A cricket ball has a mass of 0.145 kg. What must be its speed if the bowler's claim is valid?

Question 46

The linear density of a rod, in g/m, is given by $\lambda=40.0+30.0 x$ . The rod extends from the origin to x = 0.400 m. What is the location of the centre of mass of the rod?

A)x = 0.213 m
B)x = 0.315 m
C)x = 0.384 m
D)x = 0.184 m
E)x = 0.208 m

Question 47

A U-238 nucleus (mass = 238 units) decays, transforming into an alpha particle (mass = 4.00 units) and a residual thorium nucleus (mass = 234 units). If the uranium nucleus was at rest, and the alpha particle has a speed of 1.50 * 107 m/s, determine the recoil speed of the thorium nucleus.