A mountain climber is about to haul up a 30 m length of hanging rope. How much w

Question

A mountain climber is about to haul up a 30 m length of hanging rope. How much work will it take if the rope weighs 0.5 N/m?

The amount of work required is ? J (Type an integer or a decimal & Please show your work).

(Hint: To determine if you are using the correct solution....here is a similar problem with the correct answer, however, no solution was provided: A mountain climber is about to haul up a 90 m length of hanging rope. How much work will it take if the rope weighs 0.75 N/m? The amount of work required is = 3037.5 J)

Explanation / Answer

First, let us determine the function for the force.

Force = (weight) * (length of rope that is still hanging) = 0.5(30 - x)

The limits of integration will be 0 < x < 30. The reason for this is that the mountain climber starts

with 30-m of rope. When he is done hauling in the rope, then there will not be any rope hanging

and force acting upon it.

Now, we will set up the work integral.

work = integral 0 to 30 .5(30-x) dx = 0 to 30 .5 (30x - (x^2 / 2)) = 225 J

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