Final answer:
In a block and tackle system with 4 pulley wheels and 4 supporting ropes, the amount of rope that needs to be pulled to lift a 250-pound weight 3 feet is 4 feet.
Step-by-step explanation:
To calculate the amount of rope that needs to be pulled in a block and tackle system, we need to consider the mechanical advantage of the system. The mechanical advantage is determined by the number of supporting ropes in the system. In this case, there are 4 pulley wheels and 4 supporting ropes.
Each pulley wheel contributes to the mechanical advantage by reducing the amount of force required to lift the weight. With 4 pulley wheels, the system has a mechanical advantage of 4.
Since the weight being lifted is 250 pounds and the mechanical advantage is 4, the force required to lift the weight is 250/4 = 62.5 pounds. To calculate the length of rope that needs to be pulled, we can use the equation Force x Distance = Work. Rearranging the equation, we have Distance = Work / Force. In this case, Work is the weight being lifted, which is 250 pounds, and Force is 62.5 pounds. So, the distance of rope that needs to be pulled is 250 / 62.5 = 4 feet.