(a) State the conditions for the equilibrium of a rigid body acted upon by parallel...
(a) State the conditions for the equilibrium of a rigid body acted upon by parallel forces.
(b)(i) Describe an experiment to determine the mass of a metre rule using the principle of moments.
(ii) State two precautions necessary to obtain accurate results in the experiment described in (b)(i) above.
(c) A bullet of mass 120 g is fired horizontally into a fixed wooden block with a speed of 20 ms\(^{-1}\). If 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) — The sum of clockwise moments about any point is equal to the sum of anticlockwise moments about the same point
— The sum of the forces in one recticn is equal to the sum of the forces in the opposite direction.
b)
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Method: Suspend the metre rule on a thread loop from clamp. Adjust its position until the metre rule balances horizontally and obtain its centre of gravity G. Suspend known mass M at a point on one side of the rule and just the position of the loop until the rule balances horizontally. Read and record the distances y and x in the diagram above. sing the principle of moments Mgx = Mgy
m = \(\frac{My}{x}\)
Therefore the mass M of the metre rule is calculated.
ii) Precautions:
— Firmly fixed the loop
— Avoid draught
— Avoid parallax when reading metre rule.
.
c)(i) Declaration a = \(\frac{v - u}{t} = \frac{0 — 20}{0.1} = — 200m/s^2\)
Resistance F = Ma = 0.12 x 200 = 24N
ii) Distance S = \(\frac{v^2 - u^2}{2a} = \frac{0^2 - 20^0}{2 \times 200}\)
= \(\frac{400}{400} = 1.0m\)