Principle of Moments (Cambridge (CIE) A Level Physics)

A uniform beam of weight 40 N is 5 m long and is supported by a pivot situated 2 m from one end.

When a load of weight W is hung from that end, the beam is in equilibrium as shown in the diagram.

What is the value of W?

A. 10 N               

B. 50 N               

C. 25 N               

D. 30 N

Answer:

Step 1: List the known quantities

• Weight acting on beam, W_B = 40 N

• Weight acting on mass = W

• Length of beam = 5 m

• Distance to pivot (from end of beam), d_W = 2 m

Step 2: Recall the principle of moments

clockwise moments = anticlockwise moments

Step 3: Calculate the clockwise moment

• Because the beam is uniform, the force of weight acting upon it will be exerted from its centre of gravity

• This will be the middle of the beam

(from the end of the beam)

• The pivot is 2 m from the end of the beam

• Therefore, the force acts at a distance of 2.5 − 2 = 0.5 m from the pivot

Step 4: Calculate the anticlockwise moment

Step 5: Equate the clockwise and anticlockwise moments to calculate

• Therefore, the answer is A

Make sure that all the distances are in the same units and you’re considering the correct forces as clockwise or anticlockwise, as seen in the diagram below