2.2 Forces and elasticity — 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 weight of a bag of mass 4.0 kg. Take $g = 9.8\,\text{N/kg}$ .
Give one example of a contact force, and one example of a non-contact force.

Answers

$W = mg = 4.0 \times 9.8 = 39.2\,\text{N}$ , so $39\,\text{N}$ to 2 significant figures.
A contact force is friction, tension, air resistance or the normal contact force. A non-contact force is the gravitational force, the electrostatic force or the magnetic force.

If question 1 went wrong, return to Section 2.1 and the equation $W = mg$ .

Practise with help

1. A spring has a spring constant of 150 N/m. It is stretched by 0.24 m. Calculate the force applied to the spring.

Hint

The force, the spring constant and the extension are linked by one equation.

Next step

Write $F = ke$ , then put in $k = 150\,\text{N/m}$ and $e = 0.24\,\text{m}$ .

Full working

\begin{aligned} F &= k e \\ &= 150 \times 0.24 \\ &= 36\,\text{N} \end{aligned}

2. A force of 30 N stretches a spring by 0.12 m. Calculate the spring constant.

Hint

You need the spring constant on its own, so rearrange $F = ke$ .

Next step

Divide the force by the extension: $k = \dfrac{F}{e}$ .

Full working

\begin{aligned} k &= \frac{F}{e} \\ &= \frac{30}{0.12} \\ &= 250\,\text{N/m} \end{aligned}

3. A spring has a spring constant of 350 N/m. It is stretched by 0.20 m. Calculate the energy stored in the elastic potential store.

Hint

The extension is squared in the energy equation. Work out the square first.

Next step

Write $E_e = \tfrac{1}{2}ke^2$ , then replace $e^2$ with $0.20^2 = 0.040$ .

Full working

\begin{aligned} E_e &= \tfrac{1}{2} k e^2 \\ &= 0.5 \times 350 \times 0.20^2 \\ &= 0.5 \times 350 \times 0.040 \\ &= 7.0\,\text{J} \end{aligned}

4. A spring is stretched a little and springs back when it is released. A second spring is stretched too far and stays longer. Describe the difference between the two changes, and name each one.

Hint

Compare what happens to each spring after the force is removed.

Next step

Say which spring returns to its original length and which one does not.

Full working

The first spring returns to its original length when the force is removed, so its change is elastic deformation. The second spring stays longer, so its change is inelastic deformation. This answer is a model answer for you to compare with your own wording.

5. A force is added to a spring and the extension is measured. The results are shown in the table. The graph of force against extension is a straight line through the origin. Calculate the spring constant from the gradient.

Force (N)	Extension (m)
0.0	0.00
20.0	0.10
40.0	0.20
60.0	0.30

Hint

The gradient of a straight-line graph is the change in the vertical value divided by the change in the horizontal value.

Next step

Choose the largest pair of values, such as 60.0 N and 0.30 m. Divide the force by the extension.

Full working

k = \frac{60.0}{0.30} = 200\,\text{N/m}

The gradient of a force-extension graph is the spring constant.