Chapter 2: Forces and their interactions
The chapter problem: the bike-hire workshop
A bike-hire workshop beside a river looks after a fleet of cargo bikes. The mechanics check the same things on every bike: the suspension, the tyres, the brakes and the gears.
These are the facts to use all the way through the chapter.
- The bike and its rider together have a mass of 110 kg.
- The front suspension spring compresses by 0.020 m when the front wheel pushes up with a force of 600 N.
- The front tyre carries a force of 540 N. Its contact patch with the road has an area of 12 cm².
- Pushing the bike up the workshop ramp takes a force of 150 N along the ramp. The ramp is 8.0 m long.
- The brake lever is 0.090 m from its pivot. The brake cable is 0.030 m from the pivot. A hand pulls the lever with a force of 60 N.
By the end of the chapter you will work out the weight of the loaded bike, the spring constant of the front spring, the energy the spring stores, the work done pushing the bike up the ramp, the pressure in the front tyre and the moment on the brake lever. You will also decide whether the lever makes the brakes work better.
First contact: no working yet. Estimate. The bike and rider have a mass of 110 kg. Without a calculator, is their weight closer to 100 N, 1000 N or 10 000 N? Write your estimate down.
If you are not sure where to start
Weight is a force. On the Earth, each kilogram has a weight of about 10 N. So 110 kg has a weight of about 1100 N, which is closer to 1000 N.
By the end of this chapter
You will be able to:
- name contact and non-contact forces, and represent a force as a vector;
- calculate the weight of an object from its mass;
- find the resultant of two forces acting in a straight line;
- describe elastic and inelastic deformation;
- use the force-extension relationship, and calculate the energy stored in a spring;
- calculate the work done when a force moves an object;
- calculate pressure from force and area, and explain atmospheric pressure;
- calculate the moment of a force, and use balanced moments;
- explain how levers and gears transmit the turning effect of a force.
Two further skills are for Higher tier only: drawing free body diagrams and resolving a force into two components, and using the pressure at a depth in a fluid.
Where it is used
Every tool you pick up uses these ideas. So does every bridge, crane, tyre and tap. Engineers choose the shape and the size of a part so that the forces, the pressure and the turning effects all stay safe.
Your turn to connect it
Where in your own day do you push, pull or turn something? Write two examples. One should be a time you used a tool to make a job easier, and one should be a force you felt for yourself.