PHYS 121

Consider two vectors along the x axis, one with x component Ax = 4 m and the other with x component Bx = -6 m. What is A+B?

A+B = -2m⋅ι

Consider two vectors along the x axis, one with x component Ax = 4 m and the other with x component Bx = -6 m. What is A-B?

A-B = 10m⋅ι

What is the difference between scientific laws and scientific theories?

Laws describe what happens under certain circumstances; theories explain why things happen as they do.

A woman stands at the edge of a cliff, holding one ball in each hand. At time t0, she throws one ball straight up with speed v0 and the other straight down, also with speed v0. Which ball has the greater acceleration at the instant of release?

Neither; the accelerations of both balls are the same.

A woman stands at the edge of a cliff, holding one ball in each hand. At time t0, she throws one ball straight up with speed v0 and the other straight down, also with speed v0. Which ball hits the ground with greater speed?

Neither; the balls hit the ground with the same speed.

A woman stands at the edge of a cliff, holding one ball in each hand. At time t0, she throws one ball straight up with speed v0 and the other straight down, also with speed v0. Which ball has the greater speed at the instant of release?

Neither; the speeds are the same.

A car collides with a telephone pole. Do the car and the pole form an isolated system?

No

A car collides with a telephone pole. Does the car alone form an isolated system?

No

An observer in the Earth reference frame observes cart A and cart B moving toward each other with the same speed until they collide and come to rest. Consider this event as seen by observer A moving along with cart A. Assume that this observer matches cart A's initial velocity but does not collide with cart B (that is, observer A continues along at the same velocity that cart A had initially). Would the observer in the Earth reference frame and observer A obtain the same value for the final velocity of cart B after the collision?

No

An observer in the Earth reference frame observes cart A and cart B moving toward each other with the same speed until they collide and come to rest. Consider this event as seen by observer A moving along with cart A. Assume that this observer matches cart A's initial velocity but does not collide with cart B (that is, observer A continues along at the same velocity that cart A had initially). Would the observer in the Earth reference frame and observer A obtain the same value for the initial velocity of cart A?

No

Can two cars traveling in opposite directions on a highway have the same velocity?

No

If one end ball of a Newton's cradle is pulled back and let go, would it be a violation of conservation of momentum if two balls at the other end bounced up at half the first ball's speed?

No

You drop your keys in a high-speed elevator going up at a constant speed. Do the keys accelerate faster toward the elevator floor than they would if the elevator were not moving?

No

A moving object collides with an object at rest. The objects do not interact with any other objects. Ignore any effects due to friction. Is it possible for both objects to be at rest after the collision?

No. Since the system that consists of two objects is isolated, its total momentum should be conserved. The initial momentum is obviously not zero, so it is not possible for both objects to be at rest after the collision.

Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed v1=v and has inertia m1=2m. Object 2 moves with speed v2=sqrt2v and has inertia m2=m. Which object has the larger magnitude of its momentum?

Object 1 has the greater magnitude of its momentum.

Does a zero-kinetic energy reference frame always exist, never exist, or sometimes exist?

Sometimes. If all parts of the system have the same velocity, then there is a reference frame in which they are all at rest and have zero kinetic energy. However, if parts of a system have different velocities, then there is no reference frame that could be moving along with all the parts of the system. In this case all (or most) pieces of the system will have some non-zero velocity in all reference frames. Therefore there will be non-zero kinetic energy in all reference frames.

Which has greater inertia: a 1-quart milk carton filled with feathers or the same carton filled with buckshot?

The carton filled with buckshot has the greater inertia.

A small bullet is fired into a large piece of wood. After the bullet penetrates the wood, the assembly moves as one unit along a low-friction track in the direction of travel of the bullet. Is the combined kinetic energy of the bullet and the wood after the bullet is stuck in the wood greater than, equal to, or less than the initial kinetic energy of the bullet?

The combined energy is less than the initial kinetic energy of the bullet.

A small bullet is fired into a large piece of wood. After the bullet penetrates the wood, the assembly moves as one unit along a low-friction track in the direction of travel of the bullet. After the bullet is stuck in the piece of wood, is the momentum of the wood (not including the bullet; assuming the piece of wood was initially at rest) greater than, equal to, or less than the initial momentum of the bullet?

The momentum of the wood is less than the initial momentum of the bullet.

Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed v1=v and has inertia m1=2m. Object 2 moves with speed v2=sqrt2v and has inertia m2=m. Which object has the larger kinetic energy?

The objects have the same kinetic energy.

Suppose you have an isolated system in which two objects about to collide have equal and opposite momenta. If the collision is totally inelastic, what can you say about the motion after the collision?

The objects will stop moving.

In a collision experiment, the ratio of the velocity change between two carts of equal inertia is found to equal 1. What happens to this ratio if the inertia of each cart is doubled, and the same initial velocities are used?

The ratio of velocity changes remains one.

In a collision experiment, the ratio of the velocity change between two carts of equal inertia is found to equal 1. What happens to this ratio if the original value of inertia is used, and the initial velocities of the carts are doubled?

The ratio of velocity changes remains one.

Suppose that you toss a rock upward so that it rises and then falls back to the earth. If the acceleration due to gravity is 9.8 m/s2, what is the rock's acceleration at the instant that it reaches the top of its trajectory (where its velocity is momentarily zero)? Assume that air resistance is negligible.

The rock has a downward acceleration of 9.8 m/s2.

You hit a pitched baseball with a bat. In which reference frame is the translational (nonconvertible) kinetic energy greater: the reference frame in which the bat is at rest immediately before the collision or the reference frame in which the ball is at rest immediately before the collision?

The translational kinetic energy is greater in the reference frame in which the ball is at rest. The translational kinetic energy is greater in the reference frame in which the center of mass is moving the most quickly. Because the bat has so much more inertia than the ball, most of the inertia of the system moves with the bat. Hence, to the ball, most of the inertia of the system is rushing toward it, meaning that the center of mass is moving very quickly.

A car is traveling north. What is the direction of its acceleration and the direction of its velocity if it is speeding up?

The velocity is north and the acceleration is north.

A car is traveling north. What is the direction of its acceleration and the direction of its velocity if it is slowing down?

The velocity is north, but the acceleration is south.

Two cars collide head-on on a busy street. An observer standing on the street witnesses the accident and calculates how much of the cars' initial kinetic energy went into deforming the cars upon collision, Edef. A police officer was driving next to one of the cars at a matching speed when the cars collided. Would this officer calculate a higher value of Edef, a lower value of Edef, or the same value of Edef if he used the velocities of the cars measured in his reference frame?

This officer would calculate the same value of Edef.

An observer in the Earth reference frame observes cart A and cart B moving toward each other with the same speed until they collide and come to rest. Consider this event as seen by observer A moving along with cart A. Assume that this observer matches cart A's initial velocity but does not collide with cart B (that is, observer A continues along at the same velocity that cart A had initially). Would the observer in the Earth reference frame and observer A obtain the same value for the relative velocity of the two carts after the collision?

Yes

Can two cars traveling in opposite directions on a highway have the same speed?

Yes

If one end ball of a Newton's cradle is pulled back and let go, would it be a violation of conservation of energy if two balls at the other end bounced up at half the first ball's speed?

Yes

You drop your keys in a high-speed elevator going up at a constant speed. Do the keys accelerate faster toward the elevator floor than they would if the elevator were accelerating downward?

Yes

Is it possible for a change of physical state to occur in a closed system?

Yes. Consider a piece of paper burning in a very well-insulated chamber. There are no interactions with anything outside the system and the momentum of the system is constant.

Is it possible for a change of physical state to occur in an isolated system?

Yes. Consider a piece of paper burning in a very well-insulated chamber. There are no interactions with anything outside the system and the momentum of the system is constant.

Can you tell from the coefficient of restitution whether a collision has added kinetic energy to a system, taken some away, or left the system's kinetic energy unchanged?

Yes. If the coefficient of restitution is greater than one, energy has been changed into kinetic energy. If the coefficient of restitution is less than one, then kinetic energy has been changed to some other form of energy. If the coefficient of restitution is equal to one, then the initial and final kinetic energies are identical.

Is it possible for the momentum of a system consisting of two carts on a low-friction track to be zero even if both carts are moving?

Yes. Momentum is a vector. Therefore, the system has zero momentum if two conditions are met: the carts move in opposite directions and the absolute value of the product of inertia and velocity is the same for the two carts.

A car collides with a telephone pole. Do the car, the pole, and Earth form an isolated system?

Yes. The car certainly has a change in momentum and it certainly has contact with other objects (the pole).The car and pole have a combined momentum that definitely changes.Ignoring celestial motion the total momentum of the car-pole-Earth system is the same before and after the crash.

A moving object collides with an object at rest. The objects do not interact with any other objects. Ignore any effects due to friction. Is it possible for just one object to be at rest after the collision? If so, which one?

Yes. The object that is initially moving could stop and impart all of its momentum to the second object initially at rest.

A woman stands at the edge of a cliff, holding one ball in each hand. At time t0, she throws one ball straight up with speed v0 and the other straight down, also with speed v0. If the ball that is thrown downward has an acceleration of magnitude a at the instant of its release (i.e., when there is no longer any force on the ball due to the woman's hand), what is the relationship between a and g, the magnitude of the acceleration of gravity?

a=g

Two identical carts are released from the top of two low-friction inclined tracks. Cart A is on a track inclined at an angle of 30° and cart B is on a track inclined at an angle of 60°. Consider the x component of each cart's acceleration, where the x direction is parallel to the track. If the magnitude of the x component of cart A's acceleration is aAx, which of the following is true about the magnitude of the x component of cart B's acceleration?

aAx < aBx < 2aAx

During two separate collisions, it is known that the magnitude of the impulse delivered to cart A is greater than the impulse delivered to cart B. Is the magnitude of the change in momentum of cart A greater than, less than, or equal to the change in momentum of cart B?

greater than

The SI base unit for mass is the _______.

kilogram

A woman stands at the edge of a cliff, holding one ball in each hand. At time t0, she throws one ball straight up with speed v0 and the other straight down, also with speed v0. Which ball has the greater average speed during the 1-s interval after release (assuming neither hits the ground during that time)?

the ball thrown downward

A 2000-m race is held on a 400-m oval track. From start to finish, what is the displacement of the winner?

Δx= 0 m