A pulley system is 76% efficient. If a 9000 kg box is lifted a distance of 8 m by a force of 700 N, how much rope is pulled from the pulley system?
To find the amount of rope pulled from the pulley system, we first need to determine the work done on the box, taking into account the efficiency of the pulley system.
The work done on an object is given by the equation:
Work = Force x Distance
In this case, the force applied to lift the box is 700 N and the distance it is lifted is 8 m. So, the work done on the box is:
Work = 700 N x 8 m = 5600 N·m
Since the pulley system is 76% efficient, only 76% of the work done on the box is transferred to the box itself. Therefore, the work done by the pulley system is:
Work by pulley system = Efficiency x Work
= 0.76 x 5600 N·m
= 4256 N·m
Now, we can calculate the force exerted by the pulley system using the formula:
Force by pulley system = Work by pulley system / Distance
Given that the force exerted by the pulley system is equal to 4256 N·m and the distance over which it is exerted is what we need to find, let's rearrange the formula:
Distance = Work by pulley system / Force by pulley system
Plugging in the values, we get:
Distance = 4256 N·m / 700 N
≈ 6.08 m
Therefore, approximately 6.08 meters of rope is pulled from the pulley system.