2.1 Forces and their interactions — Practise with help

Work each problem first. Open a hint only if you are stuck, and the full working only to check.

Warm-up: remember

Calculate the energy in the kinetic store of an object of mass 2.0 kg moving at 3.0 m/s.
A spring is stretched. Name the store that increases.

Answers

$E_k = \tfrac{1}{2}mv^2 = 0.5 \times 2.0 \times 3.0^2 = 9.0\,\text{J}$ .
The elastic potential store.

If question 1 went wrong, look again at Section 1.1 and the equation $E_k = \tfrac{1}{2}mv^2$ .

Practise with help

1. A climber has a mass of 65 kg. Take $g = 9.8\,\text{N/kg}$ . Calculate the weight of the climber.

Hint

Weight is a force, so it is measured in newtons. The equation that links mass and weight has $g$ in it.

Next step

Write $W = mg$ , then put in $m = 65\,\text{kg}$ and $g = 9.8\,\text{N/kg}$ .

Full working

\begin{aligned} W &= m g \\ &= 65 \times 9.8 \\ &= 637\,\text{N} \\ &= 640\,\text{N} \quad (2\ \text{significant figures}) \end{aligned}

2. A force of 185 N acts to the right and a force of 120 N acts to the left. Calculate the resultant force.

Hint

The two forces act along the same straight line, but in opposite directions.

Next step

Subtract the smaller force from the larger force. The resultant points in the direction of the larger force.

Full working

185 - 120 = 65\,\text{N}

The resultant force is 65 N to the right, the direction of the larger force.

3. A car travels along a straight road at a constant speed. Describe the forces acting on the car, and explain why the resultant force is zero.

Hint

Draw the car on its own and put an arrow on it for every force. Include the weight and the force from the road.

Next step

A constant speed means the forces along the road balance. Name the forward force from the engine and the backward force from air resistance.

Full working

The car has its weight acting downwards, and a normal contact force from the road acting upwards. These two forces are equal and opposite, so they balance. Along the road, the forward force from the engine balances the backward force from air resistance and friction. Every force is balanced, so the resultant force is zero, and the car keeps a constant speed. This answer is a model answer for you to compare with your own wording.

4. A force of 80 N acts at $25^\circ$ to the horizontal. Resolve the force into a horizontal component and a vertical component.

Hint

The horizontal component uses the cosine of the angle. The vertical component uses the sine.

Next step

Work out $80 \cos 25^\circ$ and $80 \sin 25^\circ$ . Check that the two components are both smaller than 80 N.

Full working

\begin{aligned} F_{\text{horizontal}} &= 80 \cos 25^\circ = 72.5\,\text{N} \\ F_{\text{vertical}} &= 80 \sin 25^\circ = 33.8\,\text{N} \end{aligned}

5. Two forces of 25 N and 40 N act on a box in the same direction. Calculate the resultant force, and state its direction.

Hint

The forces point the same way, so one force adds to the other.

Next step

Add 25 N and 40 N.

Full working

25 + 40 = 65\,\text{N}

The resultant force is 65 N in the direction of the two forces.