You are moving into an apartment and take the elevator to the 6th floor. Suppose your weight is 640 N and that of your belongings is 940 N. (a) Determine the work done by the elevator in lifting you and your belongings up to the 6th floor (15.2 m) at a constant velocity. (b) How much work does the elevator do on you alone (without belongings) on the downward trip, which is also made at a constant velocity?
To determine the work done by the elevator in lifting you and your belongings up to the 6th floor, we need to calculate the net force acting on the system and multiply it by the displacement.
(a) Work done by the elevator on you and your belongings:
1. First, calculate the total weight of the system by adding your weight and the weight of your belongings: 640 N + 940 N = 1580 N.
2. Since the elevator is moving at a constant velocity, the net force acting on the system must be zero. This means that the upward force exerted by the elevator is equal in magnitude but opposite in direction to the downward force of gravity.
3. The net force acting on the system is the difference between the force exerted by the elevator and the force of gravity: 1580 N - 1580 N = 0 N.
4. The work done by the elevator is given by the equation: Work = Force × Displacement × cos(θ), where θ is the angle between the force and the displacement (which is 0 degrees since the force and displacement are in the same direction).
5. With a constant velocity, the displacement of the elevator is the distance it travels, which is 15.2 m.
6. Since the net force is 0 N, the work done by the elevator is also 0 J. This means that no energy is transferred to the system during this process.
(b) Work done by the elevator on you alone (without belongings) during the downward trip:
1. With only your weight acting as the force, the total weight is 640 N.
2. Similar to the upward trip, the net force acting on the system is zero because the downward force by the elevator cancels out the force of gravity.
3. The net force is 0 N, so the work done by the elevator is also 0 J.
Therefore, in both cases, when the elevator moves at a constant velocity, no work is done by the elevator on you or your belongings.