Question

. Estimates of inertia and forces:

(a) A cabin cruiser of 15 tonnes (1 tonne = 103 kg) drifts in towards a dock at a speed of 0.3 ms-1 after its engines have been stopped. A woman on the dock is able to reach the boat with a boathook when it is 2 m from the dock and thereafter can push with a constant force of 400 N. Can she bring the boat to rest before it hits the dock?

(b) A man of mass 80 kg jumps down on a paved road from a height of 0.5 m. He does not bend his knees on landing so his motion is arrested in about 2 cm. What is average force on his bone structure?

(c) If the man now tries jumping from a height of 1.5 m but does bend his knees on impact so that his centre of gravity descends a further distance h after his feet touch the ground, what must h be so that the average force exerted on him by the impact is only five times his normal weight?

Answer 1

(a)

Yes, she can because the work done on boat by the applied force is sufficient to make the final kinetic energy of boat zero

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(b)

we know

Work done = force * displacement

so,

force = Work done / displacement

force = mgh / d

force = 80 * 9.8 * 0.5 / 0.02

force = 19600 N

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(b)

here, center of gravity moves additional 'h'

so,

Work done = force * displacement

mg * (1.5 + h) = 5 * mg * h

1.5 + h = 5h

1.5 = 5h - h

h = 1.5 / 4

h = 0.375 m