# Calibrate a forcemeter by pulling a trolley

##### Demonstration

You can use the formula F = ma to calibrate a forcemeter without using gravity. It is difficult to do with precision.

#### Apparatus and materials

Lightweight forcemeter, 0-10 N, with scale markings concealed by paper (this is to be written on)

Dynamics trolley

Runway

Stopclock

Balance, 5 kg

String

#### Health & Safety and Technical notes

A trolley runway requires two persons to carry it and set it up on the bench.

Ensure that a string is tied across the bottom of the runway to prevent the trolley falling onto anyone.

It is important that the balance is lightweight, so that it does not add to the mass. It is also better if the balance is not too precise.

#### Procedure

a Set up a runway that is compensated for the effect of friction, as described in the experiment Compensating for friction

b Load the trolley, so that its total mass is a whole number of kilograms. Check this by putting the trolley and load on the balance. c Attach the forcemeter to the trolley by a length of string.

d With the forcemeter, apply a force to the trolley to accelerate it from rest. e Measure the time, t, for the motion over a measured distance, x

f Use the formula x = 1/2 at2 to calculate the acceleration, a

g Use F = ma, where m is the measured mass, to find force F in absolute units.

h Mark the paper over the forcemeter scale with this force. For the forcemeter, you also know where to mark zero.

Assume that the meter acts in a 'linear' way. That is, that equal changes in force are represented on the scale by equal distances.

i Make a complete scale for the forcemeter, on the paper.

j Compare this with the scale provided by the forcemeter manufacturer.

#### Teaching notes

1 Newton's laws of motion define the concept of force. A scale of forces in newtons is essentially derived from measurements of mass and acceleration.

2 Students often suppose that the manufacturer has access to some unknown means of providing a scale of absolute reliability. They may have little awareness that calibration is an important process of inherent uncertainty, however it is done. Invite them to discuss which is more reliable, the scale made by themselves or by the manufacturer.

3 It is essential to keep the logic straight: force is calculated from Newton's second law once the acceleration produced by the forcemeter has been found experimentally.

This experiment was safety-checked in March 2005