A helter-skelter ride has a spiral slide. The top of the slide is \(7\text{ m}\) higher than the bottom. The average frictional resistance is \(50\text{ N}\). A boy of mass \(60\text{ kg}\) slides down, starting from rest. At the bottom he has speed \(10\text{ m s}^{-1}\).

Find the length of the slide.

Enter just the number.

A helter-skelter ride has a vertical drop of \(7\text{ m}\). A boy of mass \(60\text{ kg}\) starts from rest and reaches the bottom with speed \(10\text{ m s}^{-1}\).

Work out the amount of mechanical energy lost.

Enter just the number in joules.

A boy slides down a helter-skelter and some mechanical energy is lost because of friction.

What form of energy has most of this lost mechanical energy been changed into?

A box of mass \(10\text{ kg}\) slides \(3\text{ m}\) down a rough slope inclined at \(30^\circ\) to the horizontal. At the top of the slope its speed is \(3.25\text{ m s}^{-1}\) and at the bottom its speed is \(5\text{ m s}^{-1}\).

Find the coefficient of friction between the box and the slope.

Enter just the number.

A sack of mass \(12\text{ kg}\) slides down a ramp, starting from rest at a height of \(2\text{ m}\) above the ground. It reaches the ground with speed \(6\text{ m s}^{-1}\).

Work out the amount of mechanical energy dissipated.

Enter just the number in joules.

A skydiver of mass \(80\text{ kg}\) falls \(1000\text{ m}\) from rest and then opens the parachute for the remaining \(2000\text{ m}\) of the fall. Air resistance is negligible until the parachute opens. The skydiver is travelling at \(5\text{ m s}^{-1}\) just before hitting the ground.

Find the average resistance force while the parachute is open.

Enter just the number in newtons.

A tile of mass \(1\text{ kg}\) slides \(3\text{ m}\) down a roof inclined at \(20^\circ\) to the horizontal. The tile then falls \(5\text{ m}\) under gravity and hits the ground with speed \(10.5\text{ m s}^{-1}\).

Find the frictional force between the tile and the roof.

Enter just the number in newtons.

A model racing car of mass \(50\text{ g}\) is released from rest at the top of a downward-sloping track. The resistance to the motion of the car is \(0.05\text{ N}\). The car comes to rest on a horizontal piece of track that is \(2\text{ m}\) lower than the top of the track.

Find the distance that the car has travelled.

Enter just the number in metres.

A diver jumps from a board \(10\text{ m}\) above a swimming pool. The diver has initial velocity \(u\text{ m s}^{-1}\) upwards. The horizontal component of motion is negligible. A constant resistance of \(0.5\text{ N kg}^{-1}\) acts on the diver.

Find an expression for the height of the diver above the pool at the highest point of the dive.

A golf ball of mass \(45.9\text{ g}\) is hit from a tee with speed \(50\text{ m s}^{-1}\). The ball lands in a pond \(5\text{ m}\) lower than the tee after travelling along a curved path of length \(160\text{ m}\). The resistance acting on the ball has magnitude \(0.3\text{ N}\).

Find the speed of the ball just before it hits the water.

Enter just the number.

A golf ball of mass \(45.9\text{ g}\) hits the pond with speed \(22.5\text{ m s}^{-1}\). The water immediately absorbs \(8\text{ J}\) of energy from the ball. The ball then sinks vertically and just comes to rest at the bottom. The resistance acting on the ball in the water is \(3\text{ N}\).

Find the depth of the pond.

Enter just the number in metres.

A golf ball of mass \(45.9\text{ g}\) is hit from a tee with speed \(180\text{ km h}^{-1}\). The ball rises to a height of \(20\text{ m}\), having travelled along a curved path of length \(61.875\text{ m}\). At the highest point of its path the ball is travelling at \(144\text{ km h}^{-1}\).

Find the magnitude of the average resistance force acting on the ball.

Enter just the number in newtons.

A golf ball of mass \(45.9\text{ g}\) is hit from a tee with speed \(50\text{ m s}^{-1}\). The average resistance force is \(0.185\text{ N}\). The ball travels a total curved path length of \(61.875+105.8\text{ m}\) and lands on the green, which is \(4\text{ m}\) lower than the tee.

Find the speed of the ball just before it lands on the green.

Enter just the number.

A golf ball of mass \(45.9\text{ g}\) lands on the green with speed \(35\text{ m s}^{-1}\) and is immediately brought to rest.

Find the energy absorbed by the green.

Enter just the number in joules.