A collar of mass 10 kg is released from rest at point B, 4 m below the point A…

Q: A collar of mass 10 kg is released from rest at point B, 4 m below the point A. the spring constant of spring is 100 N/m and natural length of spring is 3 m. Find work done by friction.

Numerical

(a) –100 J

(b) –200 J

(c) –300 J

(d) –400 J

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Ans: (b)
Sol: Gain in Gravitational P.E of collar = Loss in P.E of Spring + Work done against friction

$\displaystyle m g h = \frac{1}{2} K x^2 + W_f $

$\displaystyle W_f = m g h – \frac{1}{2} K x^2 $

$\displaystyle W_f = 10 \times 10 \times 4 – \frac{1}{2} \times 100 \times 2^2 $

$\displaystyle W_f = 200 J $

Work done by friction = – 200 J