This is a reverse collision, and momentum is still conserved. The original momentum is zero.

Momentum is conserved in any collision, but kinetic energy is only conserved in elastic collisions. So, an inelastic collision has conservation of momentum, but not conservation of kinetic energy.

In an inelastic collision, kinetic energy is not conserved. In an elastic collision, kinetic energy is conserved and there is no transfer of energy to the surroundings.

Momentum is conserved regardless of the type of collision. All of the given quantities are conserved during an elastic collision.

Work is determined using the equation . Here,  is the force applied, is the displacement of the object, and  is the angle of the force relative to the movement of the object. Since gravity is acting on the box, we can solve for the force of gravity causing the movement of the box. Note that in this case refers to the angle between gravity and the box's path; thus, the angle will be 60^o, rather than 30^o.

Notice how the work done by gravity is equal to the potential energy of the box at the top of the ramp. This is because mechanical energy is conserved in the system; thus, we can set the two equations equal to each other.

Work is represented by the product of force and displacement:

We are given the force on the box and the distance it travels. Use these values to calculate the work done.

Note that the mass of the box for this problem is irrelevant. There is no vertical displacement, so the force of gravity does not come into play. The only force that matters in this question is the "pushing force."

Work is generally considered a path function. This means that the amount of work depends on the path taken.

Work in a gravitational field, however, is not a path function; it is a state function. This means that work is independent of the path taken in a gravitational field. This occurs because the force due to gravity acts only in one direction (downwards); therefore, the work performed with or against gravity will only depend on the vertical distance travelled.

In this question both students lift the boulder along the same vertical distance (a distance of ). Student Z might have travelled a larger total distance by using the inclined plane, but the smaller  compensates for the larger distance in the work formula.

The work done is equal to the gravitational potential energy of the block after it has been lifted.

The gravitational potential energy is calculated using the following formula:

We are given the mass and the change in height, and we know the acceleration due to gravity. Using these values, we can solve for the change in potential energy by multiplication.

The work done by any force that is perpendicular to the displacement is equal to zero. Since the block is moving horizontally, the net force in the vertical direction will be equal to zero; therefore, work done by either gravity or the normal force will be equal to zero.

Work is given by , the dot product of force and displacement. Since the dot product only sees the components of vectors which are parallel to each other, the dot product of two perpendicular vectors is 0. Force is directed radially inward, while displacement is directed tangent to the circumference. At any point along this object's path, the force is perpendicular to displacement, so  is simply 0.

Remember that the work done by a force on an object is dependent on the angle of the force to the object's displacement. The normal force acts perpendicularly to the ramp, which means it has an angle of 90^o with respect to the box's displacement.

Because , the total work done on the box by the normal force is .