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Springs that measure force

Forces and motion · level 3, lesson 5 of 6

A question to start

Hang a small weight on a spring, and it stretches. Hang two, and it stretches more. How much more? Could you use this to measure forces?

The idea

Pull on a spring, and it stretches. For most springs, as long as you don't pull too hard:

Twice the force gives twice the stretch. Three times the force, three times the stretch.

This rule was found by Robert Hooke in 1660, and is called Hooke's law. It means a spring can measure forces: mark how far it stretches for 1 N, 2 N, 3 N, and you have a scale.

That is a newton meter, or spring balance: a spring in a tube with a scale of newtons beside it, and a hook at the bottom.

no weight1 N2 N

If you pull too hard, past the spring's elastic limit, it stays stretched when you let go and the rule no longer works. A spring scale must never be overloaded.

Springs are everywhere in machines: in pens, car wheels, mattresses and clocks. The landing legs of many landers have springs or crushable parts inside to soak up the bump of touchdown. A Mars rover is an exception: its wheels hang from levers and joints, the rocker-bogie, with no springs at all, so it rolls slowly and evenly over rocks without bouncing.

Worked examples

1. Reading a spring. A spring stretches 2 cm for each 1 N. A rock makes it stretch 7 cm. The force is \(7 \div 2 = 3.5\) N.

2. Too much? The same spring's elastic limit is at 10 N. A 15 N load would bend it out of shape for good.

Try it

  1. A spring stretches 3 cm with 1 N. How far does it stretch with 4 N?
  2. A spring stretches 5 cm with 2 N. What force stretches it 10 cm?
  3. What is the elastic limit?
  4. What instrument uses a spring to measure force?
Answers
  1. 12 cm.
  2. 4 N.
  3. The largest force a spring can take and still go back to its own length; past it, it stays stretched.
  4. A newton meter (spring balance).

Common mistake

"The spring's length doubles when the force doubles." It is the stretch, the extra length, that doubles. A 10 cm spring that stretches to 12 cm with 1 N is 14 cm long with 2 N, not 24 cm.

Where it leads