(a) State the conditions for the equilibrium of a rigid body acted upon by parallel forces
(b)(i) Describe an experiment, using the principle of moments, to determine the mass of a metre rule
(ii) State two precautions necessary to ensure accurate results.
(c) A bullet of mass 120g is fired horizontally into a fixed wooden block with a speed of 20ms\(^{-1}\). The bullet is brought to rest in the block in 0.1s by a constant resistance. Calculate the:
(i) magnitude of the resistance;
(ii) distance moved by the bullet in the wood.
Explanation
(a) - Sum of forces in one direction is equal to the sum of forces in opposite direction. - Sum of anti-clockwise moments about a point is equal to the sum of clockwise moment about the same point.
(b) Diagram:
Method: Suspend the metre rule on a knife edge. Adjust its position until it balances horizontally. Note the balance point G. Then suspend a mass M on one side of the rule. Adjust the rule until it balances horizontally again. Read and record X and Y as in the diagram above. According to the principle of moment:
Mgx = Mgy
m = \(\frac{Mgy}{gx} = \frac{My}{x}\)
m = mass of rule
Precautions
- Avoid drought
- Avoid parallax in reading the metre rile
(c)(i) Deceleration a = \(\frac{u - v}{t} = \frac{20 - 0}{0.1}\) = 200ms
Resistance = ma = 0.12 x 200 = 24N
(ii) Distance, s \(\frac{u^2 - v^2}{2a} = \frac{20^2 - O^2}{2 \times 200} = \frac{400}{400}\)
= 1.0m