Solve problems involving kinetic energy and gravitational potential energy using 𝐸𝑘 = 1 2 𝑚𝑣2 and ∆𝐸𝑝 = 𝑚𝑔∆ℎ.

A cyclist with a combined mass of 85 kg (including bicycle) is travelling at 12 m s⁻¹ along a level road. The cyclist then ascends a hill and comes to rest at a vertical height of 6.5 m above the starting point. Determine the change in total mechanical energy of the cyclist and bicycle system during the ascent. Show your working.

A pendulum bob of mass 0.50 kg is released from rest at position A, swings down through the lowest point B, and rises to position C where it momentarily comes to rest. The diagram shows the vertical heights of positions A and C above point B. Air resistance causes 0.80 J of energy to be dissipated during the swing from A to C. What is the speed of the bob as it passes through point B?

A student throws a 0.15 kg ball vertically upward from ground level with an initial speed of 18 m/s. At the moment the ball reaches its maximum height, calculate: (a) the maximum height reached by the ball (1 mark) (b) the change in gravitational potential energy from ground level to maximum height (1 mark) (c) verify your answer to part (b) by comparing it to the initial kinetic energy of the ball (1 mark)

A ball of mass 0.25 kg is dropped from rest from a height of 5.0 m. What is the kinetic energy of the ball just before it hits the ground? (Assume no air resistance and g = 10 m s⁻²)