If the hook has a 1,000 N load, what is the force in rope attached to the motor at W?
The correct answer and explanation is:
To determine the force in the rope attached to the motor at W, the key concept is to consider the system’s mechanical advantage and the way forces are distributed across various components.
If the system is a simple pulley system, the force in the rope at W can be calculated using the principles of equilibrium and the force transmission in the rope. The rope carries the load applied by the hook, and its tension is distributed throughout the system.
In a single-pulley setup, assuming that the pulley does not add any friction or resistance, the force in the rope at W is essentially equal to the load. This means the force at W is 1,000 N. However, if there are multiple pulleys or the system has a mechanical advantage, then the force at W will differ depending on the number of supporting strands of rope.
For example, in a system with a block and tackle setup, the number of ropes sharing the load determines how the force is divided. If there are 2 ropes supporting the load, the force at W would be halved (i.e., 500 N). If there are 4 ropes, the force at W would be one-quarter of the load (i.e., 250 N).
The general relationship is that the more ropes you have, the less force is needed at the motor to lift the load. This is the concept of mechanical advantage, where a smaller force can be applied to move a larger load over a larger distance.
To summarize, without knowing the exact configuration of the pulley system, the force in the rope at W can either be equal to the load or divided by the number of supporting ropes, depending on the system’s design. If the system has no mechanical advantage, the force at W is 1,000 N. If it does, it will be less.