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Solved problems for the chapter:

Work and Energy

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Work for KS4

1. Calculation of work performed

1.1. Work of a force acting in the direction of motion of a body

1.2. Work of a force acting in the opposite direction to the motion of a body

1.3. Work of a force acting at an angle to the direction of motion of a body

2. Work and energy

3. Forum

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Unit conversion

1. Meaning of unit conversion

2. SI prefixes

3. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:work_and_energy/5107/

Example 1.

A formula 1 driver wants to accelerate his car so that its kinetic energy will increase by 1.5 MJ. At least how long does he have to accelerate to do this if the engine is running at 750 kW?

Example 2.

A cyclist rides his bike down a slope. At the highest point of the slope, he has potential energy equal to 3.6 kJ. As he wants to further increase its speed, he drives by pedaling while driving. How much work does he have to do in driving to have kinetic energy that is 5.7 kJ higher at the lowest point than he had at the top of the slope?

It takes a crane 18 seconds to lift a load to a certain height. Calculate the change in potential energy of the load if the crane lifted the load with a power of 25 kW.

A parachutist descends evenly towards the ground from a height of 800 m. The mass of the parachute is 65 kg. How much work does the force of air resistance do on the parachute?

An electric car of mass 256 g accelerates from rest to a speed of 9 in 4 s.

By how much does the car's kinetic energy increase during acceleration?
What is the average power of the car's engine?

A paper plate is lifted off the ground so that its potential energy relative to the ground is 180 mJ. When the plate is dropped, an air resistance force acts on it during the fall, which inhibits its movement. During the fall, the resistance force performs 140 mJ of work. Calculate the kinetic energy of the plate just before it falls to the ground.

A child stands on the balcony and drops a stone to fall freely. His friend stands under the balcony and catches the stone. In doing so, the stone acts on his arm with force and performs 8.8 J of work. The mass of the stone is 160 g, and the friend catches it at a height of 120 cm from the ground. Air resistance can be ignored. At what height does the child drop the stone?

An elevator can lift a load of 1.4 t through a height of 12 m.

By how much, in kJ, does the potential energy of the load increase during lifting?
How long does the elevator lift the load when operating at an average power of 4.2 kW?

A car drives up a slope. At the bottom of the slope, its kinetic energy is equal to 245 kJ, and at the top of the slope, its kinetic energy is equal to 192 kJ. While driving uphill, its potential energy increases by 136 kJ.

What is the change in the car's kinetic energy?
Does the car receive or transmit work while driving?
Calculate the work that the car exchanges with its surroundings while driving uphill.

10.

A car with a mass of 1.4 t descends a slope. At the top of the slope, the car's speed is 18 km / h. It drops by 12 m while driving downhill and has a speed of 54 km / h at the end. Calculate the work that the car exchanges with its surroundings while driving downhill. We ignore air resistance.

11.

A child pushes a car up the slide. Initially, the kinetic energy of the car is 3.8 J. As the child moves up the slide, the car's potential energy increases by 2.5 J. How much kinetic energy does the car have at the top of the slide? The frictional forces in this task can be neglected.

12.

A trolley weighs 200 g. It is pushed along the horizontal ground to a slope. Just before it starts to climb, it has a speed of 18 km / h. As it is driven up the slope,the speed decreases. Frictional forces performing 1.2 J of work act on the trolley during the ascent.

Draw a sketch and describe the energy changes of the trolley during the ascent.
By how much does the kinetic energy of the trolley change during the ascent (from the moment it starts to climb to the moment it reaches its highest position)?
Calculate the change in potential energy of the trolley during the ascent.
How high does the trolley climb?

13.

A skier weighing 80 kg descends a gentle slope. He drives during the descent so that at the moment he descends 8.3 m lower, he has a speed of 14 m / s. How much work does the skier do while driving?

14.

A small metal plate weighing 84 g is placed on an icy slope. The plate is stationary at first. By how much does the potential energy of the plate have to be reduced in order to have a speed of 6.2 m / s in the end.

15.

A child weighs 50 kg together with a sled. He drives the sled towards a slope 1.5 m high. What is the minimum kinetic energy the child must have at the base of the slope to reach the top of the slope without propulsion?

16.

A skier weighing 84 kg descends a steep slope. He does not stop or brake during the descent. How many meters must he descend to have a velocity of 72 km / h in the end if he does not have kinetic energy at the beginning?

17.

A child weighing 40 kg slides down the slide. At the top of the slide, the child has a height of 1.9 m, and at the bottom of the slide, his height is 30 cm. During the descent on the slide, the frictional force does 180 J of work. Calculate the change in the child's kinetic energy during the descent down the slide.

18.

A wooden board lies on the floor, on the largest surface. Its length is 100 cm, width 50 cm, and height 8.0 cm. The density of the wood from which the board is made is . We do not lift the board, but just tip it from the largest surface (the lying position) to the smallest surface (in an upright position). What is the least amount of work we have to do?

19.

A worker pushes a cart weighing 15 kg up a slope. The cart moves straight evenly, and the braking forces are neglected. The worker pushes with a force of 107 N, which is parallel to the direction of movement of the cart, and in doing so performs 375 J of work.

Force applied on the cart and the height change

How far does the cart travel?
Calculate the height change of the cart.

20.

A rider weighs 80 kg together with a bike. While driving, he sees an obstacle in front of him, so he applies the brakes quickly. He brakes with a constant force of 200 N and stops after covering a distance of 8 m. Calculate the speed the cyclist had when he started to apply the brake.

21.

A student kicks a slipper weighing 80 g to slide on the floor perpendicular to a wall. The slipper is subjected to a constant frictional force of 0.24 N. When it is 1.5 m away from the wall, it has a speed of .

What is the kinetic energy of the slipper when it is 1.5 m away from the wall?
How much work is done by the frictional force over the 1.5 m distance?
At what speed does the slipper collide with the wall?

22.

A mass is lifted from rest on the ground to Y. There is no air resistance.

is the increase in gravitational energy of the mass. is the kinetic energy of the mass at Y. Which expression is equal to the mechanical work done on the mass?

23.

A box of mass slides down a slope of length against a frictional force . It descends a vertical height .

As the box slides down the slope, it loses gravitational potential energy and it does work against the friction. Which row gives the loss in gravitational potential energy and the work done against friction?

	loss in gravitational potential energy	work done against friction
A
B
C
D

24.

A horizontal force pulls a box along a horizontal surface. The box gains of kinetic energy and of thermal energy is produced by the friction between the box and the surface. How much work is done by the force?

25.

A car of mass is moving at . The engine does work on the car and the speed increases to . How much work is done by the engine to increase the speed of the car?