Find the minimum initial height of the roller coaster if the roller coaster is to complete the diameter loop.

A crate, starting from rest, is pulled across a floor with a constant horizontal force of . For the first the floor is frictionless and for the next the coefficient of friction is . What is the final speed of the crate?

A child descends a slide high and reaches the bottom with a speed of . How much thermal energy due to friction was generated in this process?

A runner arrives at the bottom of a hill. He runs up the hill with a constant acceleration until he reaches the top, then runs at a steady pace along the top of the hill. When are the kinetic and potential energies of this man at their greatest?

Two balls are thrown off a building with the same speed. One is thrown straight up, and one at a angle. Which statement is true if air resistance is ignored?

A skier starts at the top of a hill with of energy. Assuming energy is conserved, what is her final kinetic energy?

A skier starts at the top of a hill with of potential energy. At the bottom of the hill, she has only of kinetic energy. Assuming that at the top of the hill she has only potential energy and at the bottom she has only kinetic energy, what can we conclude?

Computational

A ball is dropped from above the ground. Assuming gravity is , what is its final velocity?

Mike jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle). He falls for before the bungee cord begins to stretch. Mike's mass is and we assume the cord obeys Hooke’s law. The constant is . If we neglect air resistance, what is the distance below the bridge Mike’s foot will be before coming to a stop. Ignore the mass of the cord and treat Mike as a particle.

A projectile is fired at an upward angle of from the top of a cliff with a speed of . What will be its speed when it strikes the ground below? (Use conservation of energy to solve this problem)