GCSE Questions: Moments and Centre of Gravity

Q3.

(a) The diagram shows a child's mobile. The mobile hangs from point P on the ceiling of the child's bedroom.

(i) Mark the position of the centre of mass of the mobile by drawing a letter X on a sketch of the diagram. Do this so that the centre of the X marks the centre of mass of the mobile.

• Most of the mass of the mobile comes from the aeroplanes.
• The centre of gravity will therefore lie on the horizontal plane of the aeroplanes.
• The centre of X should be directly below P and in between the model aeroplanes

(1 mark)

(ii) Explain why you have chosen this position for your letter X.

The centre of mass is (vertically) below the point of suspension and the centre of mass is in the middle of the aeroplanes (or level with the aeroplanes)

(2 marks)

(b) The diagram shows a device which helps to prevent a ladder from falling over.

• The 'base' of a simple ladder tilted against a wall would be the red rectangle indicated on the floor of the diagram.
• The danger of a ladder toppling comes about because most of the mass comes from the person on the ladder. As the person climbs the ladder the centre of mass of the 'ladder system' gets higher. As long as the person centres him/herself carefully over the red rectangle area indicated in the diagram it will not topple as the centre of mass will not be outside the base. But if the person leans over to one side (perhaps to paint or clean a window) the centre of mass will be outside the base and the ladder will topple sideways. If you were cleaning an upstairs window you would therefore have to reposition your ladder several times in order to safely clean the whole window.
• The device in the question widens the base steadily as required – a maximum widening occurs below the part of the ladder that is high up. The higher the person climbs the easier it would be for the system to become unstable (you would need to be tilted by a smaller angle for your mass to be outside the base as you climbed higher – so you need more intervention to make it safe). Therefore using this device you would be able to safely lean to the side without making the ladder topple – so with it you would need to only put the ladder up to a window once and you would then be able to lean out to clean a wider expanse of window.

Use the term 'centre of mass' to explain why the ladder, in the situation shown, is unlikely to topple over. You may sketch a diagram to illustrate your explanation.

The centre of mass of the worker and the ladder (and device) can be represented by a line of action of their weight.

This will act vertically down and is inside the base so there will not be a (resultant) moment

it will (only) topple over if the line of action of the weight produced by the centre of mass is outside the base

(3 marks)

(Total 6 marks)