Question 1

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

Accepted Answer

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. It is also equal to the average force multiplied by the time interval over which the force is applied. Therefore, knowing the impulse and the total time allows us to calculate the average force acting on the system. Instantaneous force, final momentum, and initial momentum cannot be determined solely from the impulse and total time without additional information.

Question 2

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

Accepted Answer

The area under the force-time curve represents the impulse, which is equal to the change in momentum of the system according to the impulse-momentum theorem.

Question 3

Collisions demand forces that

Accepted Answer

The answer of Collisions demand forces that
...

Question 4

Elastic collisions between two bodies satisfy all of the following except

Accepted Answer

In an elastic collision, while the relative speed of approach equals the relative speed of separation, and both momentum and kinetic energy are conserved, the statement about relative velocity of approach being equal to relative velocity of separation is not always true because it does not account for direction; only the magnitudes (speeds) are guaranteed to be equal.

Question 5

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

Accepted Answer

An impulse changes an object's momentum and can also change its kinetic energy and position as a result of that change in momentum. However, an impulse does not change an object's rest mass (inertia), which is an intrinsic property of the object not affected by external forces.

Question 6

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

Accepted Answer

In an inelastic collision, the total kinetic energy of the colliding bodies is not conserved due to the transformation of some kinetic energy into other forms of energy, such as heat or sound. However, the total momentum of the system and the velocity of the center of mass remain conserved, and the total energy in the universe is conserved but may change forms.

Question 7

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

Accepted Answer

In an isolated, totally elastic two-body collision, both the center-of-mass velocity and the center-of-mass speed remain unchanged. This is because the total momentum of the system (which determines the center-of-mass velocity) is conserved, and the total kinetic energy (which influences the center-of-mass speed) is also conserved in an elastic collision.

Question 8

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)

Accepted Answer

Due to the conservation of momentum and the fact that M > m, it is physically impossible for the smaller mass m to impart to the larger mass M a speed roughly equal to its original speed. The momentum of the system must be conserved, and given the mass disparity, transferring all of m's initial velocity to M would violate this principle.

Question 9

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)

Accepted Answer

In a collision where M > m, the conservation of momentum dictates that the larger mass M cannot reverse its direction while conserving momentum and energy if it is initially moving and collides with a smaller mass m at rest. This is because the momentum of the system must be conserved, and for M to reverse direction, it would require an external force not accounted for in the collision dynamics.

Question 10

A projectile of mass M_phits 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

Accepted Answer

In an inelastic collision, kinetic energy is not conserved, but momentum is. The center-of-mass speed depends only on the total momentum and the total mass, both of which are conserved regardless of whether the collision is elastic or inelastic. Therefore, the center-of-mass speed remains unchanged between elastic and inelastic collisions.

Question 11

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

Accepted Answer

The answer of Two identical masses (one initially at rest)...

Question 12

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

Accepted Answer

The necessity for equal masses, one mass initially at rest, and a perfectly elastic collision are all related to ensuring the specific outcome of the velocity vectors forming a right angle post-collision. The collision being confined to a horizontal plane is not a necessary assumption for the velocity vectors to form a right angle, as this outcome is determined by the masses, initial conditions, and the nature of the collision (elasticity), not the plane in which the collision occurs.

Question 13

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

Accepted Answer

The answer of Let V be the speed of a...

Question 14

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

Accepted Answer

The answer of Before collision, the velocity vectors of two...

Question 15

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

Accepted Answer

In a partially elastic collision where a piece breaks off, the principle of conservation of momentum ensures that the velocity and speed of the center of mass, as well as the total change in momentum, remain unchanged. However, the final velocities of the two main particles and the broken piece are not confined to a single plane due to the three-body interaction, making option C the correct answer.

Question 16

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

Accepted Answer

In a totally inelastic collision, the total kinetic energy before the collision is equal to the total internal energy after the collision. In Case I, the total kinetic energy before the collision is 2(1/2)mv^2 = mv^2. In Case II, the total kinetic energy before the collision is (1/2)mv^2. Therefore, the ratio of the total kinetic energy before collision in the two cases (II to I-that is, TKE_II/TKE_I) is TKE_II/TKE_I = (1/2)mv^2/mv^2 = 1/2.

Question 17

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

Accepted Answer

The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv^2, where m is the mass and v is the velocity of the object. In this case, if the velocity in case II is double that in case I (as implied by the notation suggesting a comparison between two scenarios with different velocities), then the kinetic energy in case II would be (1/2 m(2v)^2) = 2^2 * (1/2 mv^2), which is 4 times the kinetic energy in case I. Therefore, the ratio of the kinetic energy per vehicle in case II to that in case I is 4.

Question 18

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

Accepted Answer

In case II, the potential for damage and harm to the occupants of the vehicle is greater due to the implied increase in risk factors or conditions that could lead to more severe outcomes compared to case I.

Question 19

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

Accepted Answer

The answer of If the previous scenarios were modified solely...

Question 20

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

Accepted Answer

In an ideal collision between a superball and an immovable wall, assuming no energy is lost, the final speed of the ball will be equal to its initial speed, V, but in the opposite direction. This is because the collision is elastic, conserving kinetic energy and momentum, with the wall not moving due to its immovability.

Quiz 11: Collisions

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

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

Collisions demand forces that

Elastic collisions between two bodies satisfy all of the following except

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

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

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

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)

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 projectile of mass M_phits 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

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

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

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

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

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

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

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

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

Quiz 11: Collisions

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

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

Collisions demand forces that

Elastic collisions between two bodies satisfy all of the following except

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

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

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

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)

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 projectile of mass Mp hits a target (initially at rest) of mass Mt. 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

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

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

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

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

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

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

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

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 projectile of mass M_phits 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

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