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Solved problems for the chapter:

Kinetic Energy

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Kinetic Energy for A-Levels

1. Translational kinetic energy

1.1. Work - Kinetic energy theorem

2. Rotational kinetic energy

2.1. Moment of inertia of a real body

2.2. Kinetic energy of a rolling body

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:kinetic_energy/5047/

Example 1.

The kinetic energy of a body with a mass of is . What is its velocity?

Example 2.

An apple weighing 350 g falls from a tree at a height of 2.8 m. By how much joules does the apple's kinetic energy increase during the fall? Air resistance can be ignored.

Two bodies have the same kinetic energy. The first body has a mass of and a velocity of . The second body weighs . What is the velocity of the second body?

A spherical object has a potential energy of 60 J at altitude . What is its kinetic energy at altitude ?

A body falls freely from a height of 6 m. Its potential energy changes with height, as shown in the graph below. Draw a graph of the kinetic energy against the height of the body.

A body of mass 0.1 kg attached to a pendulum is displaced from its equilibrium position by 4 cm before it is released to freely oscillate. What is the kinetic energy of the mass as it passes through the equilibrium position?

Which of the following objects have kinetic energy?

A student riding a bicycle.
An apple hanging on a branch.
A bus heading towards the station and stops.
An aircraft parked on the runway.
A bee flying through the air.

For the movements listed below, determine whether the kinetic energy of the observed bodies increases or decreases.

A student rides his bike down the slope and does not brake.
An apple is torn off the branch and falls to the ground.
A bus is heading towards the station and stops.
An aircraft takes off on the runway on take-off.
A ball kicked vertically upwards moves towards the highest point.

Calculate the kinetic energy of a 76 kg cyclist riding at a constant speed of .

10.

A 145 tonnes train runs at a speed of . Calculate its kinetic energy.

11.

A car weighs 1.4 tonnes. At what speed must he drive to have a kinetic energy of 280 kJ?

12.

A football player kicks a ball at a speed of . The moment the ball takes off, the kinetic energy of the ball is equal to 3 J. Calculate the mass of the ball.

13.

A father weighs 80 kg and runs at a speed of and the son, weighing 40 kg, runs at a speed of . Which of them has the highest kinetic energy?

14.

A skier weighs 90 kg and has a speed of . As she descends a slope, her speed increases by . By how many kJ does her kinetic energy increase?

15.

A car weighing 800 kg travels at a speed of . It then decelerates uniformly, reducing its speed by every second. Calculate the change in the car's kinetic energy after 8 s of deceleration.

16.

A 600 kg aircraft accelerates in a horizontal direction from a speed of 180 km/h to 216 km/h against air resistance of magnitude 1200 N and covers a distance of 500 m.

Calculate the kinetic energy of the aircraft at the speed of 180 km/h.
What is the change in the kinetic energy of the aircraft during acceleration?
Calculate the average thrust with which the engine acts on the airplane during acceleration.

17.

A boat, together with all equipment and passengers, weighs 350 kg. While the boat is sailing at a speed of , a diver weighing 90 kg jumps into the water and the boat continues to run at a constant speed. By how many kJ does the kinetic energy of the boat change when the diver jumps into the water?

18.

A cube, initially resting on a smooth ice base, is pushed by a boy with a force so that it begins to move with acceleration. When the boy performs 4 J of work, the cube has a velocity of . Calculate the mass of the cube.

19.

A plastic baby truck with its trailer weighs 1.6 kg and runs on batteries by driving steadily at a speed of 9.0 km/h. While driving, a child puts a toy weighing 800 g in the trailer. The speed of the truck does not change.

Calculate the kinetic energy of the empty trailer truck.
Compare the kinetic energy of the empty trailer truck and the kinetic energy of the trailer truck with the toy.
By how much does the kinetic energy of the truck change when the child put the toy in the trailer?
At what speed should the truck drive after having the toy in the trailer in order to have the same kinetic energy as at the beginning?

20.

Which of the following statements about cars are correct? Correct the wrong statements.

If two cars have the same mass and the same speed, they will have the same kinetic energy.
The car with a higher mass certainly has higher kinetic energy.
If a car drives straight uniformly, its kinetic energy cannot change in any way.
When the speed of a car increases while driving at a constant mass, its kinetic energy will also increase.
If two cars have the same kinetic energy and the first has a higher mass than the second, then the second has a lower speed than the first.
The following applies to two cars moving straight at the same speed: A car with twice the mass has twice the kinetic energy.
The following applies to two cars with the same mass moving straight: The car with twice the speed has twice the kinetic energy.

21.

A Formula 1 race car together with the racer weighs 605 kg and drives at a speed of 306 km/h. Calculate the mass of a truck moving at 72 km/h that has the same kinetic energy as the race car.

22.

How fast can a Cheetah, weighing 56 kg, run to have as much kinetic energy as an Elephant, weighing 5.6 tonnes and walking at 9 km/h?

23.

Apple fruit is torn off the branch of a tree and falls to the ground. The apple fruit weighs 175 g and the branch is 3.2 m high. Neglecting air resistance:

does the apple have kinetic energy during the fall?
does the kinetic energy of the apple change during the fall? Clarify the answer.
What is the kinetic energy of the apple just before it falls to the ground?

24.

A car moves along a horizontal road. Its initial kinetic energy is . A constant resistive force of acts on the car. No other horizontal forces act on the car. What is the kinetic energy of the car after it has travelled a distance of ?

25.

A woman of mass has of kinetic energy. What is her speed?

26.

A man jumps from a stationary balloon. After falling several hundred metres, he opens his parachute. At which position is his kinetic energy greatest?

just after he jumps from the balloon
just before he opens his parachute
just after his parachute opens
just before he lands

27.

A gas molecule strikes the wall of a container. The molecule rebounds with the same speed.

What happens to the kinetic energy and what happens to the momentum of the molecule?

	kinetic energy	momentum
A	changes	changes
B	changes	stays the same
C	stays the same	changes
D	stays the same	stays the same

28.

The diagram shows a frictionless pendulum.

The pendulum bob swings from point P through point Q to point R then back to P. At which point is the energy of the pendulum bob greatest?

at point P
at point Q
at point R
it is the same at points P, Q and R

29.

An object of mass is travelling at . How much kinetic energy does the object have?