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Exam 11: Collisions

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Question 1

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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.

E) A) and B)
F) C) and D)

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Question 2

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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.

E) A) and C)
F) B) and D)

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Question 3

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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

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

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

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 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

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

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

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

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

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

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

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 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

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

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 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 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

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