Investigation of the laws of equilibrium for a set of coplanar forces The Professional Development Service for Teachers is funded by the Department of Education and Skills under the National Development Plan T.H.

Apparatus

Method Find the centre of gravity of the metre stick Find the mass and hence the weight of the metre stick Set up the apparatus as in the photo Use a spirit level to ensure the apparatus is horizontal Record each weight with its position (include the weight of the metre stick acting at its centre of gravity.)

Balance the metre stick on a straight sharp edge e.g. a protractor and record its centre of gravity. Here, the centre of gravity is at the 502 mm mark.

Why isn’t the centre of gravity at the 500 mm mark? One of the ends of the metre stick might be slightly damaged. The material from which the metre stick is made might not be uniform.

Find the mass of the metre stick The mass is g What is the weight of the metre stick?

Set up the apparatus

Use a spirit level to check that the metre stick is horizontal

Why does the metre stick have to be horizontal? The weights act vertically downwards. We calculate the moments by multiplying each weight by the perpendicular distance from a reference point. If the metre stick is horizontal, these distances can be read directly. Otherwise, we would have to use trigonometry.

Record the forces and their positions Note that there are five downward forces (including the weight of the metre stick), and two upward forces.

How do these results verify the two laws of equilibrium?

First Law: When a body is in equilibrium, the vector sum of the forces acting on it is zero.

Second Law: When a body is in equilibrium, the sum of the moments about any point is zero.

The sum of the clockwise and the anticlockwise moments, to two significant figures, is zero. This verifies the second law.

Sources of Error Take the readings from the metre stick at eye level to avoid the error of parallax. Replacing the spring-based Newton balances with digital Newton balances would increase the accuracy of the upward force measurements.