Principle of Moments (CIE AS 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

$\mathrm{clockwise} \mathrm{moment} = W_{B}d$

$\mathrm{clockwise} \mathrm{moment} = 40 \times 0.5$

$\mathrm{clockwise} \mathrm{moment} = 20 \mathrm{N} \mathrm{m}$

Step 4: Calculate the anticlockwise moment

$\mathrm{anticlockwise} \mathrm{moment} = W{d}_W$

$\mathrm{anticlockwise} \mathrm{moment} = W \times 2 = 2W$

Step 5: Equate the clockwise and anticlockwise moments to calculate

$\mathrm{clockwise} \mathrm{moment} = \mathrm{anticlockwise} \mathrm{moment}$

$20 = 2W$

$W = \frac{20}{2} = 10 \mathrm{N}$

• Therefore, the answer is A