2.1 Forces and their interactions — Practise

Work through these on your own. Keep your working neat: the method matters as much as the answer.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

A pupil has a mass of 55 kg. Take $g = 9.8\,\text{N/kg}$ . Calculate the weight of the pupil.
An apple has a mass of 0.20 kg. Take $g = 9.8\,\text{N/kg}$ . Calculate the weight of the apple.
A box is pushed to the right with a force of 320 N. A friction force of 180 N acts to the left. Calculate the resultant force on the box, and give its direction.
Two people push a car in the same direction. One pushes with a force of 400 N and the other pushes with 350 N. Calculate the resultant force on the car.
Two teams pull on a rope in opposite directions. Each team pulls with a force of 1200 N. Calculate the resultant force on the rope.
A box of tools has a mass of 5.0 kg. On the Moon, $g = 1.6\,\text{N/kg}$ . Calculate the weight of the box on the Moon.
A crate has a mass of 40 kg. Take $g = 9.8\,\text{N/kg}$ . Calculate the weight of the crate.
Classify each of these forces as a contact force or a non-contact force: friction, the magnetic force, tension, the gravitational force.
A book rests on a table. Name the force the table exerts on the book, and the force the book exerts on the table. Explain why these two forces form an interaction pair.
A pupil says that their weight is 50 kg. Explain what is wrong with this statement.
H A force of 40 N acts at $35^\circ$ to the horizontal. Resolve the force into a horizontal component and a vertical component. Give each component to 3 significant figures.
H Two forces act at right angles. One force is 60 N and the other is 80 N. Calculate the magnitude and the direction of the resultant force.

Answers and concise solutions

1. Weight of the pupil

Answer: $W = mg = 55 \times 9.8 = 539\,\text{N}$ , so $540\,\text{N}$ to 2 significant figures.

2. Weight of the apple

Answer: $W = mg = 0.20 \times 9.8 = 1.96\,\text{N}$ , so $2.0\,\text{N}$ to 2 significant figures.

3. Resultant force on the box

Answer: The two forces act in opposite directions, so subtract: $320 - 180 = 140\,\text{N}$ to the right.

4. Resultant force on the car

Answer: The forces act in the same direction, so add: $400 + 350 = 750\,\text{N}$ in the direction of the push.

5. Resultant force on the rope

Answer: The forces are equal and opposite, so the resultant force is $0\,\text{N}$ . The forces are balanced.

6. Weight of the box on the Moon

Answer: $W = mg = 5.0 \times 1.6 = 8.0\,\text{N}$ . The mass is the same on the Earth, but the weight is smaller because $g$ is smaller.

7. Weight of the crate

Answer: $W = mg = 40 \times 9.8 = 392\,\text{N}$ , so $390\,\text{N}$ to 2 significant figures.

8. Contact and non-contact forces

Friction and tension are contact forces, because the objects touch.
The magnetic force and the gravitational force are non-contact forces, because the objects do not touch.

9. The interaction pair

The table pushes up on the book with a normal contact force.
The book pushes down on the table with a normal contact force of the same size.
The two forces are an interaction pair, because they come from the interaction between the book and the table, and each object feels one force.

10. What is wrong with the statement

The kilogram is the unit of mass, not of weight.
Weight is a force, so it is measured in newtons.
A correct statement is that the pupil has a mass of 50 kg and a weight of about 490 N on the Earth, because $W = mg = 50 \times 9.8$ .

11. The two components

Answer: Horizontal component $= 40\cos 35^\circ = 32.8\,\text{N}$ . Vertical component $= 40\sin 35^\circ = 22.9\,\text{N}$ .

12. The resultant force

Answer: Magnitude $= \sqrt{60^2 + 80^2} = 100\,\text{N}$ . Direction $= 53.1^\circ$ from the 60 N force, found from $\tan\theta = 80/60$ .