5.2 Energy: GPE & KE

A uniform solid cuboid of concrete of dimensions 0.50m × 1.20m × 0.40m and weight 4000 N rests on a flat surface with the 1.20 m edge vertical as shown in diagram 1.

What is the minimum energy required to roll the cuboid through 90° to the position shown in diagram 2 with the 0.50 m edge vertical?

A steel sphere is dropped vertically onto a horizontal metal plate. The sphere hits the plate with a speed u, leaves it at a speed v, and rebounds vertically to half of its original height.

 Which expression gives the value of   ?

A ball released from a height h₀ above a horizontal surface rebounds to a height h₁ after one bounce. The graph that relates h₀ to h₁ is shown below.

If the ball (of mass m) was dropped from an initial height h and made three bounces, the kinetic energy of the ball immediately after the third impact with the surface was

An object of mass m passes a point X with a velocity v and slides up a frictionless incline to stop at point Y which is at a height h above X

A second object of mass ½ m passes X with a velocity of ½ v. To what height will it rise?

The diagram shows two bodies X and Y connected by a light cord passing over a light, free-running pulley. X starts from rest and moves on a smooth plane inclined at 30° to the horizontal.

What will be the total kinetic energy of the system when X has travelled 2.0 m along the plane?

A 4 kg ball and a 3 kg block of wood were placed in an arrangement as shown below. When the ball was released, it fell through a distance of 5 m, pulling the block of wood up the ramp.

If the pulleys were well oiled and the surface of the ramp exerts a frictional force of 2 N, what is the final speed of the sphere after falling through the 5 m?

A block of mass 12 kg is released from rest and it slides down a 30° frictionless incline plane. It is stopped by a spring with a spring constant k as shown below.

The initial distance between the point of release and the uncompressed spring is 3.0 m. After the block comes to rest momentarily, the spring is compressed by 1.3 m.

 What is the value of k?

A falling mass pulls a trolley from rest on a horizontal table. Given that:

The mass of the trolley = 1.5 kg

The mass of the falling mass = 0.5 kg

The distance the mass falls through = 1.0 m

Frictional force from the table = 0.8 N

The distance the trolley moves = 1.2 m

What is the maximum kinetic energy of the trolley?

A solid rubber ball has a diameter of 8.0 cm. It is released from rest with the top of the ball 80 cm above a horizontal surface. It falls vertically and then bounces back up so that the maximum height reached by the top of the ball is 45 cm, as shown.

If the kinetic energy of the ball is 0.75 J just before it strikes the surface, what is its kinetic energy just after it leaves the surface?

A body travelling with a speed of 20 has kinetic energy E_k 

If the speed of the body is increased to 80    what is its kinetic energy?

The diagram shows a lift system in which the elevator (mass m₁) is partly counterbalanced by a heavy weight (mass m₂)

At what rate does the motor provide energy to the system when the elevator is rising at a steady speed v ? (g = acceleration of free fall)

A block of mass 2.0 kg is released from rest on a slope. It travels 7.0 m down the slope and falls a vertical distance of 3.0 m

 The block experiences a frictional force parallel to the slope of 5.0 N.

What is the speed of the block after falling this distance?

The diagram shows two identical vessels X and Y connected by a short pipe with a tap.

Initially, X is filled with water of mass m to a depth h, and Y is empty.

 When the tap is opened, water flows from X to Y until the depths of water in both vessels are equal.

 How much potntial energy is lost by the water during this process? (g = acceleration of free fall)

A concrete cube of side 0.60 m and uniform density 2.0 × 10³ kg m^–3 is lifted 5.0 m vertically by a crane.

 What is the change in potential energy of the cube?

A steel ball is falling at constant speed in oil.

Which graph shows the variation with time of the gravitational potential energy E_p and the kinetic energy E_k of the ball ?

Car X is travelling at half the speed of car Y. Car X has twice the mass of car Y.

 Which statement is correct?

A truck of mass 500 kg moves from rest at the top of a section of track 400 m long and 30 m high, as shown.

 The frictional force acting on the truck is 250 N throughout its journey

What is the final speed of the truck?