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physics Physics For High Schools (KS4)

Solved problems for the chapter:

Potential Energy

View the theory »

Vertical Motion under Gravity for KS4

1. Free fall acceleration

2. Description of free fall motion

2.1. Instantaneous/Final falling velocity

2.2. Height of fall

2.3. Time of fall

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:potential_energy/5102/

Example 1.

An archer fires an arrow weighing 22 g vertically upwards. As it moves upwards, the arrow's potential energy increases by 4.4 J. How fast is the arrow as it flies away from the bow? Air resistance can be ignored.

Example 2.

Which of the following objects possess potential energy?

A bag lying on the floor.
An apple hanging on a branch.
Pencil in a student's raised hand.
An airplane flying on the runway.
A bee flying through the air.

How did the objects listed below get their potential energy?

A child on a tree.
Skier at the top of the ski slope.
Box on top of a cupboard.
A ball high in the air.
A mountaineer at the top of a mountain.

On one side of an overhanging swing, 3 meters from the axle, sits a girl Nina weighing 21 kg. On the other side, her sister Jane with a mass of 30 kg occupies the same position. Due to her weight, Jane drops 70 cm to the ground with a swing in a slow squat, and her sister lifts the swing into the air. By how much does each of them increase or decrease in potential energy?

A child weighing 45 kg climbed to the top of a slide 1.8 m high. Calculate the potential energy of the child at the top of the slide.

A pot has a mass of 80 dag and is placed on a window sill that is 1.1 m high. Mom moves the pot to a cupboard that is 1.7 m high. Calculate the change in potential energy of the pot.

How high do we have to lift an iron ball weighing 4.8 kg to increase its potential energy by 36 J?

A crane lifts a load from the ground to a terrace, which is at a height of 7.5 m. Calculate the mass of the load if the potential energy of the load on the terrace is 28.5 kJ.

A mountaineer descends from the top of a mountain to a hut. Together with the backpack, the mountaineer weighs 95 kg. Calculate the change in potential energy of the mountaineer if the top of the mountain and the hut are 2864 m and 2401 m respectively to the sea level.

10.

A man weighing 73 kg rises from a supine position in which he has his centre of gravity at a height of 10 cm to an upright position where his centre of gravity is at a height of 1.1 m. By how much does his potential energy increase?

11.

A miner descends down the shaft into the mine. The weight of the miner together with the equipment is 85 kg. By how many kJ does the potential energy of the miner change when the miner descends to a depth of 380 m below the surface? Does the potential energy increase or decrease?

12.

A high-rise has a ground floor and 14 floors. Each floor has a height of 2.8 m. To which level does a man with a mass of 86 kg have to climb in order to have approximately the same potential energy as a car with a mass of 1200 kg in a parking house at a height of 2.6 m? In this task, the height of the car is measured from the ground of the ground floor of the tower.

13.

A wooden cube with a volume of is raised from the ground by , and an aluminum cube is raised from the ground by . The specific weight of the wood from which the wooden cube is made is , and the specific weight of aluminum is .

Calculate the weight of the wooden cube.
Calculate the potential energy of the wooden cube.
What is the mass of the aluminum cube if the cubes have the same potential energy with respect to the ground?

14.

An apple weighing 23 dag hangs on a tree at a height of 3.3 m. Another apple with a mass of 24 dag is at a height of 3.2 m. Which apple has the highest potential energy?

15.

One day, a father weighing 80 kg and a mother weighing 65 kg go to the mountains. Together they arrive at a hut, which is at an altitude of 640 m. The father decides to rest, so he puts down his backpack and lies down on a lounger. The mother walks to a vantage point, which lies 45 m above the hut and is 100 m away from the hut.

Calculate the potential energy of the father on the lounger.
Calculate the potential energy of the mother at the vantage point.
What is the mass of the mother's backpack for the mother with her backpack at the vantage point and the father on the lounger to have the same potential energy when viewed from sea level?

16.

We have six identical wooden shelves with a length of 50 cm, a width of 10 cm and a height of 4 cm. All shelves initially lie on the floor, on the largest surface. The density of the wood from which the shelves are made is .

The six shelves are stacked on top of each other so that they all lie on the largest surface. Calculate the change in potential energy for the top shelf.
Calculate the change in potential energy for all six shelves together. Note that at the beginning of the observation all the shelves lie on the floor, and at the end they are stacked on top of each other.

17.

A jumper weighing 60 kg and tied to an elastic rope, jumps from a bridge that is 40 m high above a river. The length of the rope is 30 m. When jumping, the rope is stretched for 10 m so that the jumper stops just above the river surface.

What is his potential energy before the jump?
What are his potential and kinetic energies when he falls through the length of the rope?
What is the elastic energy of the rope when the jumper is at its lowest point?

18.

A stone falls from a height, h. Just before it hits the ground, it reaches a final speed of . Calculate the height, h from which it fell.

19.

A body falls towards the Earth's surface. Which of the following statement is true about the gravitational potential energy and the kinetic energy of the body?

The gravitational potential energy increases and the kinetic energy also increases.
The gravitational potential energy increases while the kinetic energy decreases.
The gravitational potential energy decreases and the kinetic energy also decreases.
The gravitational potential energy decreases while the kinetic energy increases.