# Levers and pulleys multiply force but not energy

### Demonstration

Machines let us move a large force using a small one, but they do not multiply energy.

This demonstration provides an excellent introduction to the principle of conservation of energy.

#### Apparatus and materials

Masses, 1/2 kg, 4

Plank, wooden (2 m to 3 m x 15 cm x 2 cm)

Brick or block of wood as fulcrum

Pulley, single

Pulley, double

Cord

Assorted masses to balance

Metre rule

Retort stand and boss

Nail, 15 cm

Forcemeter, reading up to 10 N

#### Health & Safety and Technical notes

Although the plank is not very heavy, it is safer to move it with one person at each end.

#### Procedure

a Set up a large see-saw on a bench, using the wooden plank and a brick or wood block as the fulcrum. Balance loads in the ratio 10:1 on the two sides of the see-saw. You will need to practise this in advance, as the loads, required to move the see-saw easily will depend upon the friction in the fulcrum you use.

Use the metre rule to measure how far each load moves vertically when you tilt the see-saw. At this ratio you should find that the small load moves 10 times as far as the large load. You can now calculate the energy transferred (force x distance moved vertically) by each of the weights. As the teaching note describes, the point is to compare them.

b Set up the pulley system as shown in the diagram. Attach the forcemeter to the free end of the cord and a 1/2 kg load to the lower pulley. Pull on the cord with the forcemeter. Measure how far the load rises, and how far the forcemeter end of the cord travels, for the same pull. Note the force measured by the forcemeter when you pull just hard enough to get the load rising.

#### Teaching notes

1 When the loads on the see-saw are balanced, the small load can just move the larger one. You are magnifying force. Do the calculations of force x vertical distance to show students that the energy transferred by both loads is the same. You are not magnifying energy.

2 The pulley system in the diagram has a mechanical advantage (MA) of 3, but you can use any system with a MA greater than 1.

As before, you need to measure the distance moved by the load (the 1/2 kg mass) and the effort (the end of the cord tied to the forcemeter). Use the force measured by the forcemeter, and the force exerted by the load, because of gravity (for a 1/2 kg load, this is about 5N). Show students the calculations to demonstrate again that although the force has been magnified (from effort to load), the energy transferred (force x distance) by both the load and the forcemeter are roughly the same.

3 Because of friction, any measurements you make here will not be very accurate. Use the calculations to make the qualitative point that energy is not gained in the process.

The purpose of these demonstrations is:

• to stress the use of machines as force multipliers
• to examine machines from the energy aspect
• to show that machines do not multiply energy.

4 Machines are energy transmitters and force multipliers but not energy multipliers. The output energy transferred is never greater than the input value. As you reduce friction, you approach the ideal case where the two lots of energy transfer are equal. As you increase friction, the output falls further below the input, and the machine will get hot. The amount of thermal energy gained accounts for the difference.

5 This is a denial of the perpetual motion machine - every machine that attempts to put out a greater, or even the same, amount of energy than it takes in fails to do so.

This experiment was safety-checked in December 2005