3.2 Forces, acceleration and Newton's laws of motion — 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 car of mass 1400 kg accelerates at 2.0 m/s². Calculate the resultant force.
A resultant force of 150 N gives an object an acceleration of 5.0 m/s². Calculate the mass of the object.
A resultant force of 350 N acts on a trolley of mass 70 kg. Calculate the acceleration.
A car of mass 1200 kg accelerates at 7.0 m/s². Calculate the resultant force on the car.
A lorry of mass 30000 kg accelerates at 3.5 m/s². Calculate the resultant force on the lorry.
A book rests on a table without moving. Name the two forces acting on the book, and explain why the resultant force is zero.
A rocket pushes hot gas downwards out of its engine. Use Newton's third law to explain why the rocket moves upwards.
The chapter problem asks for the acceleration of the bus and the resultant force on it. Say which equation you would use for each step, and name the quantities you need.
H Explain what is meant by inertial mass, and why an object with a larger inertial mass is harder to stop.
A resultant force of 900 N acts on a car of mass 1500 kg. Calculate the acceleration.
A resultant force of 6.0 N acts on a ball of mass 0.50 kg. Calculate the acceleration.

Answers and concise solutions

1. Resultant force on the car

Answer: $F = ma = 1400 \times 2.0 = 2800\,\text{N} = 2.8 \times 10^3\,\text{N}$ .

2. Mass of the object

Answer: $m = \dfrac{F}{a} = \dfrac{150}{5.0} = 30\,\text{kg} = 3.0 \times 10^1\,\text{kg}$ .

3. Acceleration of the trolley

Answer: $a = \dfrac{F}{m} = \dfrac{350}{70} = 5.0\,\text{m/s}^2$ .

4. Resultant force on the car

Answer: $F = ma = 1200 \times 7.0 = 8400\,\text{N} = 8.4 \times 10^3\,\text{N}$ .

5. Resultant force on the lorry

Answer: $F = ma = 30000 \times 3.5 = 105000\,\text{N}$ , so $1.1 \times 10^5\,\text{N}$ to 2 significant figures.

6. The two forces on the book

The weight of the book pulls downwards, and the normal contact force from the table pushes upwards.
The two forces are equal in size and opposite in direction, so they balance and the resultant force is zero. Newton's first law then says the book stays at rest.

7. The force that moves the rocket

The rocket pushes the gas downwards.
By Newton's third law the gas pushes the rocket upwards with an equal force in the opposite direction, and this upward force moves the rocket.

8. Choosing the equation for each step

For the acceleration, use $a = \dfrac{\Delta v}{t}$ . I need the change in velocity and the time taken.
For the resultant force, use $F = ma$ . I need the mass of the bus and the acceleration I have just found.

9. Inertial mass

Inertial mass is a measure of how difficult it is to change the velocity of an object, defined as the ratio of the force acting on the object to the acceleration it produces.
A larger inertial mass means a larger force is needed for the same acceleration, so a heavier object is harder to start moving and harder to stop.

10. Acceleration of the car

Answer: $a = \dfrac{F}{m} = \dfrac{900}{1500} = 0.60\,\text{m/s}^2$ .

11. Acceleration of the ball

Answer: $a = \dfrac{F}{m} = \dfrac{6.0}{0.50} = 12\,\text{m/s}^2$ .