Deck 11: Collisions

Question 1

A golf ball having mass of 0.05 kg rests on a tee. The ball is then struck with a club having a mass of 0.3 kg. The ball acquires a velocity of 30 m/s. The impulse imparted to the ball by the club is

A) 1.5 N.s.
B) 5.5 N.s.
C) 9.0 N.s.
D) 90. N.s

Answer 1

1.5 N.s.

Question 2

A golf ball having mass of 0.05 kg rests on a tee. The ball is then struck with a club having a mass of 0.3 kg. The club is in contact with the ball for 0.008 seconds. If the ball acquires a velocity of 30 m/s, the average force imparted to the ball by the club is

A) 1.5 N.
B) 5.5 N.
C) 90. N.
D) 190 N.

Answer 2

190 N.

Question 3

A time-varying force is given by $f ( t ) = 6.3 t ^ { 2 }$ , where $f ( t )$ is in $\mathrm { N }$ and $t$ is in seconds. The impulse this force imparts to a $7.8 - \mathrm { kg }$ mass during the time interval $t = 0$ to $t = 5$ seconds is

A) 150 kg.m/s.
B) 170 kg.m/s.
C) 260 kg.m/s.
D) 230 kg.m/s.

Answer 3

260 kg.m/s.

Question 4

A 2.5-kg mass A travels at 4 m/s in the x direction. A 5-kg mass B traveling in the -x direction at 2 m/s collides with mass A. After the collision both masses stick together; their velocity is

A) 1.0 m/s in the -x direction.
B) 0.5 m/s in the -x direction.
C) 0.0 m/s.
D) 1.0 m/s in the x direction.

Question 5

A 2.5-kg mass A travels at 4 m/s in the x direction. A 5-kg mass B also traveling in the x direction at 2 m/s collides with mass A. After the collision both masses stick together, and their final velocity is

A) 0.3 m/s in the -x direction.
B) 2.7 m/s in the -x direction.
C) 0.3 m/s in the x direction.
D) 2.7 m/s in the x direction.

Question 6

A 2.5-kg mass A travels in the -x direction. A 3-kg mass B traveling in the x direction at 2 m/s is involved in a collision with mass A. After the collision both masses stick together and have a velocity of 1 m/s in the -x direction; from this, the initial speed of mass A is

A) 0.2 m/s.
B) 2.1 m/s.
C) 0.09 m/s.
D) 4.6 m/s.

Question 7

A 2.1-kg ball traveling at 5 m/s directly hits a concrete wall. The ball bounces off the wall and then travels in the opposite direction (perpendicularly) at 5 m/s. The impulse, in the direction of the ball's final velocity, that the concrete wall exerts on the ball is

A) 0 N.s.
B) 21 N.s.
C) 5 N.s.
D) 11 N.s.

Question 8

A massive projectile traveling at 23 m/s elastically collides (in one dimension) with a very light target mass ( $m _ { \text {projectile } } > > m _ { \text {target } }$ ) that was initially at rest. After the collision, the velocity of the target mass

A) is 23 m/s.
B) is 33 m/s.
C) is 46 m/s.
D) cannot be determined (masses not given).

Question 9

A massive projectile traveling at 23 m/s elastically collides (in one dimension) with a very light target mass ( $m _ { \text {projectile } } > > m _ { \text {target } }$ ) that was initially at rest. After the collision, the velocity of the projectile

A) is 23 m/s.
B) is 0 m/s.
C) is 46 m/s.
D) cannot be determined (masses not given).

Question 10

A very light projectile traveling at 23 m/s elastically collides (in one dimension) with a massive target ( $m _ { \text {projectile } } < < m _ { \text {target } }$ ) that was initially at rest. After the collision, the velocity of the projectile

A) is -23 m/s.
B) is 0 m/s.
C) is -46 m/s.
D) cannot be determined (masses not given).

Question 11

A very light projectile traveling at 23 m/s elastically collides (in one dimension) with a massive target ( $m _ { \text {projectile } } < < m _ { \text {target } }$ ) that was initially at rest. After the collision, the velocity of the target mass

A) is -23 m/s.
B) is 0 m/s.
C) is -46 m/s.
D) cannot be determined (masses not given).

Question 12

Stationary mass $m _ { 2 }$ is involved in an elastic, one-dimensional collision with mass $m _ { 1 }$ . If $m _ { 1 }$ had an initial velocity three times greater than (and in the same direction as) the final velocity of $m _ { 2 }$ , the mass of $m _ { 2 }$ is

A) 3 $m _ { 1 }$
B) 4 $m _ { 1 }$
C) 6 $m _ { 1 }$
D) 5 $m _ { 1 }$

Question 13

A bullet with momentum of $10 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ embeds itself into a large, heavy block of wood: $m _ { \text {wood } } = 12.6 \mathrm {~kg}$ and $m _ { \text {wood } } > > m _ { \text {bullet } }$ . The block of wood is tied to a string connected to the ceiling, forming a ballistic pendulum. The maximum (vertical) height that the block of wood + bullet rises to is

A) 8 cm.
B) 5 cm.
C) 3 cm.
D) 9 cm.

Question 14

A bullet with momentum of $10 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ embeds itself into a large, heavy block of wood: $m _ { \text {wood } } = 12.6 \mathrm {~kg}$ and $m _ { \text {wood } } > > m _ { \text {bullet } }$ . The block of wood is tied to a string connected to the ceiling, forming a ballistic pendulum. The initial velocity of the bullet was $1000 \mathrm {~m} / \mathrm { s }$ . During the collision, the loss of mechanical energy is

A) 0 J.
B) 50 J.
C) 500 J.
D) 5000 J.

Question 15

Consider an elastic collision in two dimensions. A 0.5-kg ball at rest, located at the origin, is struck by another ball (of equal mass) moving in the +x direction. After the collision, one of the balls is moving with a velocity of 2 m/s at an angle of 30º above the +x axis. The y momentum of the other ball is:

A) -1.0 y kgm/s. .
B) +0.5 y kgm/s. .
C) +1.0 y kgm/s. .
D) -0.5 y kgm/s. .

Question 16

In a general collision problem, one that may include the existence of an external impulse, the conservation law that must always hold true is

A) conservation of total energy.
B) conservation of total momentum.
C) conservation of kinetic energy.
D) conservation of potential energy.

Question 17

In an elastic collision problem, what additional conservation law is valid?

A) Conservation of potential energy
B) Conservation of thermal energy
C) Conservation of kinetic energy
D) None of the above

Question 18

In a problem involving a golf club striking a stationary golf ball, if we define our system to be just the ball, the momentum of the ball

A) is conserved.
B) is not conserved.
C) is conserved only if the final momentum of the ball is known.
D) cannot be determined.

Question 19

In a problem involving a golf club striking a stationary golf ball, if we define our system to be both the golf club and the ball, the momentum of the system

A) is conserved.
B) is not conserved.
C) is conserved only if the final momentum of the ball is known.
D) cannot be determined.

Question 20

In a process in which the impulse on a system is zero, the law that must hold true is

A) conservation of kinetic energy.
B) conservation of potential energy.
C) conservation of momentum.
D) none of the above.

Question 21

If the impulse acting on a system is known and the total time is also known, then we also know

A) the average force acting on the system.
B) the instantaneous force acting on the system.
C) the final momentum.
D) the initial momentum.

Question 22

Consider the plot of the instantaneous force acting on a system versus the time. The area under the instantaneous force is the

A) mass times the impulse.
B) impulse divided by the time.
C) change in the momentum.
D) total energy in the system.

Question 23

Collisions demand forces that

A) occur over a small time interval.
B) act through a nonzero distance.
C) necessitate direct contact.
D) must not change with time.

Question 24

Elastic collisions between two bodies satisfy all of the following except

A) relative velocity of approach = relative velocity of separation.
B) relative speed of approach = relative speed of separation.
C) momentum is conserved.
D) kinetic energy is conserved.

Question 25

If a body (otherwise isolated) receives a single (nonzero) impulse, it must change all of the following except its

A) position.
B) kinetic energy.
C) momentum.
D) rest mass (inertia).

Question 26

In an inelastic collision of two bodies, a change occurs in the

A) total energy in the universe.
B) total kinetic energy of the colliding bodies.
C) momentum in the universe.
D) velocity of the center of mass.

Question 27

During (that is, from before contact until after contact) an isolated, totally elastic two-body collision, the pair of parameters that remains unchanged is

A) the center-of-mass velocity and the center-of-mass speed.
B) the center-of-mass speed and the speed of either body with respect to the center of mass.
C) the speed of either body with respect to the center of mass and the velocity of either body with respect to the center of mass.
D) the velocity of either body with respect to the center of mass and the center-of-mass velocity.

Question 28

Suppose M > m. The small mass m (initially moving) strikes the massive body M (initially at rest). After the collision, m could never (with respect to the lab)

A) rebound at roughly the same speed.
B) glance off at roughly 90 degrees to the original direction.
C) continue approximately forward with roughly its original velocity.
D) impart to M a speed roughly equal to that originally present in m.

Question 29

Suppose M > m. The large mass M (initially in motion) strikes the body of mass m, initially at rest. After the collision, M could never (with respect to the lab)

A) reverse its direction, traveling at roughly its initial speed.
B) cause m to rebound, with M glancing off at roughly 90 degrees to the original direction.
C) continue approximately forward with roughly the original speed.
D) impart to m a speed roughly equal to that originally present in M.

Question 30

A projectile of mass M_p hits a target (initially at rest) of mass M_t. When the collision is not completely elastic, all of the following (measured with respect to the lab frame) are reduced from their respective values for the elastic case except

A) if M_p = M_t, the maximum angle of separation (measured between the final velocity vectors for the two masses).
B) if M_p > M_t, the maximum deflection angle of M_p.
C) lf M_p < M_t, the maximum final speed of M_t.
D) if M_p = M_t, the center-of-mass speed.

Question 31

Two identical masses (one initially at rest) collide elastically. After the collision, all of the following are true with respect to the lab except

A) the masses separate at an angle of 90 degrees.
B) the sum of the squares of the final speeds = the square of the initial speed.
C) the vector sum of the final velocities = the initial velocity.
D) the sum of the final speeds cannot exceed the sum of the initial speeds.

Question 32

After a two-body collision, the velocity vectors associated with the separating bodies form a right angle, independent of the specific final direction of the motion of body 1. Necessary assumptions include all of the following except

A) equal masses.
B) one mass initially at rest.
C) perfectly elastic collision.
D) collision confined to a horizontal plane.

Question 33

Let V be the speed of a baseball bat just before the instant of initial contact with a baseball. Let v be the initial speed of the ball just before impact. Neglecting spin effects of the ball and treating both the ball and the bat as point masses (assuming the mass of the bat > the mass of the ball), the maximum speed (with respect to the ground) at which a pitched ball can be "launched" by a bat is

A) $| v + V |$
B) $| \mathrm { v } - \mathrm { V } |$
C) $| 2 v + V |$
D) $| 2 V - v |$

Question 34

Before collision, the velocity vectors of two bodies (each moving initially) define an initial plane. After collision

A) the motion of both bodies must be confined to the initial plane.
B) the motion of both bodies must be in a plane differing from the initial plane.
C) whether or not one body moves in the initial plane depends on whether or not the other one does so.
D) one body may move in the initial plane independent of whether or not the other body does so.

Question 35

During a partially elastic two-body collision, a piece breaks off one of the two bodies, creating a three-body interaction. Nevertheless, all of the following remain unchanged except

A) the velocity of the center of mass.
B) the speed of the center of mass.
C) the confinement of the final velocities of the two main particles to a single plane.
D) the total (vector) change in momentum.

Question 36

Case I: Two identical cars, each traveling at 30 mph, approach each other in a head-on totally inelastic collision. Case II: An automobile, traveling at 60 mph, hits an indestructible brick wall (mounted in concrete, so that it remains essentially unmoved) head-on, undergoing a totally inelastic collision. The ratio of the total kinetic energy before collision in the two cases (II to I-that is, TKE_II/TKE_I) is equal to

A) 1/4.
B) 1/2.
C) 2.
D) 4.

Question 37

The ratio of the kinetic energy per vehicle in the two cases (II to I-that is, [KE_II/v]/[KE_I/v]) is equal to

A) 1/4.
B) 1/2.
C) 2.
D) 4.

Question 38

Based on the previous answers, the potential for damage and harm to the occupants of the vehicle in case II, compared to that of the occupants of the vehicle in case I, will be

A) less.
B) greater.
C) equal.
D) zero.

Question 39

If the previous scenarios were modified solely in that the collisions were totally elastic, the potential damage sustained by the occupants would be

A) less.
B) greater.
C) equal.
D) zero.

Question 40

Consider an ideal collision between a superball and an immovable wall. For Questions 40-42, assume a head-on collision. In the frame of reference of the wall (the lab frame), the initial velocity of the ball is V. In the lab frame, the final speed of the ball is

A) < V.
B) = V.
C) > V.
D) unknown; insufficient information is given for an unambiguous answer.

Question 41

From a reference frame moving along the surface of the wall at speed v, the initial speed of the ball is

A) $< | V - v |$
B) < {v² + V² }^1/2.
C) = {V² + V² }^1/2.
D) > {v² + V² }^1/2.

Question 42

From the reference frame moving along the surface of the wall at speed v (see the previous question), the final speed of the ball is

A) $< | V - v |$
B) < {v² + V² }^1/2.
C) = {V² + V² }^1/2.
D) > {v² + V² }^1/2.

Question 43

If the collision is not head-on, but the angle that the initial velocity vector of the superball makes with the wall is $\theta$ , the angle the final velocity vector makes with the same plane is

A) < $\theta$
B) = $\theta$
C) > $\theta$
D) unknown; insufficient information is given for an unambiguous answer.

Question 44

Consider a partially inelastic collision between a superball and an immovable wall. For Questions 44-46, assume a head-on collision. Also assume that there are no other sources of energy (such as explosives). In the frame of reference of the wall (the lab frame), the initial speed of the ball is V. Let the final speed of the ball be defined as V'. In the lab frame, V' is

A) < V.
B) = V.
C) > V.
D) unknown; insufficient information is given an for unambiguous answer

Question 45

From a reference frame moving along the surface of the wall at speed v, the initial speed of the ball is

A) $< \left| \mathrm { V } ^ { \mathrm { T } } - \mathrm { v } \right|$
B) < {v² + V² }^1/2 .
C) = {v² + V² }^1/2.
D) > {v² + V² }^1/2.

Question 46

From the reference frame moving along the surface of the wall at speed v (see the previous question), the final speed of the ball is

A) $< \left| \mathrm { V } ^ { \mathrm { T } } - \mathrm { v } \right|$
B) < {v² + V'² }^1/2 .
C) = {v² + V'² }^1/2.
D) > {v² + V'² }^1/2.

Question 47

If the collision is not head-on, but the angle that the initial velocity vector of the superball makes with the wall is $\theta$ , the angle the final velocity vector makes with the same plane is

A) < $\theta$
B) = $\theta$
C) > $\theta$
D) unknown; insufficient information is given for an unambiguous answer.

Question 48

Consider a two-body collision in which the target (of mass M_t) is initially at rest and the projectile (of mass M_p) moves with speed V. To increase the possible mass of potential new particles (to be created by the collision), each of the following (single) changes in the initial parameters of the experimental arrangement are appropriate except

A) using a target with a smaller mass M_t.
B) giving the target body initial motion toward the projectile body.
C) increasing the velocity of the projectile body.
D) using a projectile with a larger mass M_p.

Question 49

We may choose to think of friction as a force rendering the collision between a superball and wall partially inelastic. The direction of the impulse given by friction to the ball when it strikes a wall obliquely (note that there exists relative motion in such a case between the ball and the wall in a direction parallel to the surface of the wall) is

A) in the direction of the component of the ball motion parallel to the wall surface.
B) opposite the direction of the component of the ball motion parallel to the wall surface.
C) perpendicular to the direction of the component of the ball motion parallel to the wall surface and directed toward the wall.
D) perpendicular to the direction of the component of the ball motion parallel to the wall surface and directed away from the wall.

Question 50

If the angle that the initial velocity vector of the superball makes with the wall is $\theta$ , the angle the final velocity vector makes with the same plane is

A) < $\theta$
B) = $\theta$
C) > $\theta$
D) unknown; insufficient information is given for an unambiguous answer.