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Applications of Integration

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(1) The acceleration due to gravity near the surface of Mars is 3.72ms^-2. A rock is thrown straight up from the surface with an initial velocity of 23ms^-2. How high does it go? (Note: gravitational acceleration acts downwards so is negative).

(2) A 30m uniform chain (mass 25kg) is hanging from the roof of a factory. What work is done to wind the chain up onto a drum?

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Solution Summary

We solve two problems in Newtonian mechanics, one involving throwing a ball on Mars and one involving computing the work required to lift a chain.

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(1) By conservation of energy, we have:

1/2 m v_0^2 = mgh,

where m is the mass of the rock, g = 3.72 m/s^2 is the acceleration due to gravity on the surface of Mars, and
v_0 =23 m/s is the initial speed of the rock. Solving for h, we obtain:

h = ...

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