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GCSE Questions: Moments and Centre of Gravity

Q2.The diagram shows a small mobile crane that is used on a building site.

The distance, d, is measured to the front of the cab.

The table below shows information from the crane driver's handbook.

Load/kN Maximum safe distance 'd' /m
10 6.0
15 4.0
24 2.5
40 1.5
60 1.0

 

(a) What is the relationship between the load and the maximum safe distance?

The load forms a clockwise moment - you therefore have to multiply the load by the distance to calculate that moment.

The cab itself will make an anticlockwise moment. As long as the cab is making a bigger moment than the load the crane will not topple over.

The data is showing the limit at which the load can be safely placed... each line of data gives the same moment...

Any two from:

inversely proportional as the load gets bigger

the (maximum safe) distance gets less

load × distance = 60 (kN m)

(2 marks)

(b) The crane driver studies the handbook and comes to the conclusion that a load of 30 kN would be safe at a distance, d, of 2.0 metres.

Is the driver correct?

Explain your answer.

Yes, because the moment produced by the load is 30 × 2 = 60 kNm and that won't make the crane topple over.

The examiners accepted for (1 mark) a correct but insufficiently explained response such as 'Yes because it's safe' For (2 marks) they expected a correct response which was sufficiently explained such as 'Yes, because 60 (kNm) at 1 metre is safe and 30 (kNm) is half the load at twice the distance

They gave no marks for just 'yes' or yes with an incorrect explanation such as 'yes, because 30 is between 24 and 40 and 2 is between 2.5 and 1.5'

They did not accept 'the crane/ cable may break' or other dangers

(2 marks)

(c) What is the danger if the driver does not follow the safety instructions?

The crane will topple over.

(1 mark)

(d) How should the data in the table have been obtained?

A: average results from an opinion poll of mobile crane drivers

B: copied from a handbook for a similar crane

C: results of experiments on a model mobile crane

D: results of experiments on this mobile crane

(1 mark)

(Total 6 marks)