A mountain climber is about to haul up a 50m length of hanging rope. How much work will it take if the rope weighs .624 N/m?

half the weight times the distance

To determine the amount of work required to haul up the hanging rope, we can use the following formula:

Work = Force × Distance

In this scenario, the force exerted on the rope is due to its weight, and the distance is the length of the rope.

First, let's calculate the force exerted by the rope. We can do this by multiplying the weight per unit length by the total length of the rope:

Force = Weight per unit length × Length of the rope

Given that the weight per unit length is 0.624 N/m and the length of the rope is 50 m, we can plug these values into the formula:

Force = 0.624 N/m × 50 m
Force = 31.2 N

Now that we have the force, we can calculate the work using the work formula mentioned earlier:

Work = Force × Distance

In this case, the distance is also the length of the rope, which is 50 m. Plugging in the values:

Work = 31.2 N × 50 m
Work = 1560 J

Therefore, it would take 1560 joules of work to haul up the 50-meter length of hanging rope.