# Working against a band brake

##### Demonstration

Using a band or friction brake and wheel to show the transfer of work into thermal energy.

#### Apparatus and materials

Demonstration forcemeters, 0-20N, 2

Wheel with band brake

Stopwatch

Rod and two bosses

Retort stands, 2

#### Health & Safety and Technical notes

You can improvise the wheel with band brake if you have a belt-driven table or disc. Slip off the belt and substitute a webbing belt or length of thick string. Alternatively, a bicycle ergometer could be used.

#### Procedure

a Secure the belt firmly at the ends of the two spring balances, which you have supported from above. Adjust the belt tension by raising or lowering the support so that both forcemeters read about half full scale.

b Turn the wheel by hand at a steady rate for at least 30 seconds and record the 'steady' readings of the two forcemeters. Note the time taken to turn the wheel and count the number of turns taken.

#### Teaching notes

1 As the wheel is turned, the chemical store (food and oxygen) in the operator’s muscles is transferred to the band brake so warming it up and increasing its thermal energy.

2 If you want to calculate the energy transferred, the logic is quite tricky, but explained as follows.

Read the forces F1 and F2 from the spring balances while allowing the wheel to slip past the fixed belt, as in diagram I. This is equivalent to diagram II in which the spring balances are replaced by two loads suspended by pulleys with the tension in each side of the belt being F1 and F2 as before. Now the belt does not slip but rather the loads move. Finally this arrangement can be transformed into diagram III, in which one end of the belt is fixed to the wheel and the other carries a load equal to the difference between F1 and F2. As the band brake is turned the belt does not slip but the load rises.

The energy transferred to the system, E= (F1 – F2) x distance moved.
So the energy transferred to band brake is
E = (F1 - F2) x (circumference of wheel) x (number of turns)

This energy increases the thermal energy of the band brake and so its temperature rises.

This experiment was safety-checked in November 2005