Forces and elasticity
Changing shape
To stretch, bend or compress (squash) an object, you need . Stretching a spring needs one force pulling down and another holding it at the top.
- the object goes back to its original shape and length when the forces are removed. A spring stretched gently does this.
- the object doesn't go back to its original shape. A spring stretched too far stays longer.
Key terms
Hooke's law: F = ke
The of a spring is to the force on it, as long as the is not passed. You must recall this equation:
, or F = ke
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | newtons (N) |
| Spring constant | k | newtons per metre (N/m) |
| Extension | e | metres (m) |
A stiffer spring has a bigger spring constant. The same rule works for compression.
Example: a spring with k = 25 N/m has a 2 N force on it. Find the extension.
- Rearrange: e = F ÷ k
- e = 2 ÷ 25
- e = 0.08 m (8 cm)
Common mistake
Extension is how much longer the spring gets, not its total length. Subtract the original length.
Key terms
Force–extension graphs and stored energy
A graph of (up the side) against (along the bottom) for a spring:
- is a straight line through the origin at first, showing extension is directly proportional to force
- has a equal to the , k
- curves once the limit of proportionality is passed, as the spring stretches more for each extra newton
Stretching a spring does on it, which is stored in its store. If it isn't inelastically deformed, the work done equals the energy stored. This equation is on the equation sheet:
Eₑ = ½ke²
Example: a spring with k = 200 N/m is stretched by 0.1 m.
- Eₑ = ½ke² = 0.5 × 200 × 0.1²
- Eₑ = 1 J
On the straight part of the graph, the area under the line also equals the energy stored.
Required practical 6: force and extension
- Hang a spring from a clamp stand, with a metre ruler clamped beside it.
- Record the position of the bottom of the spring with no masses on it.
- Hang a mass holder on the spring and add masses one at a time (100 g has a weight of 0.98 N).
- After each one, record the new position and work out the from the start.
- Plot force against extension.
- the force (weight) on the spring.
- the extension.
- use the same spring throughout.
Hazard: masses can fall, so clamp the stand to the bench and keep your feet clear. Wear eye protection in case the spring snaps.
Improving accuracy: read the ruler at eye level, using a pointer fixed to the spring, and wait for the spring to stop bouncing.