You are moving into an apartment and take the elevator to the 6th floor. Suppose your weight is 790 N and that of your belongings is 1080 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?

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To determine the work done by the elevator in lifting you and your belongings to the 6th floor, you need to calculate the work done against gravity.

(a) The formula to calculate work is:

Work = Force × Distance × Cos(θ)

In this case, the force acting against gravity is the weight of you and your belongings combined. So the force is the sum of your weight and the weight of your belongings:

Force = Weight of You + Weight of Belongings

Plugging in the values:

Force = 790 N + 1080 N = 1870 N

The distance is given as 15.2 m, and since the elevator moves at a constant velocity, the angle (θ) between the force and direction of motion is 0 degrees, so Cos(θ) = 1.

Work = 1870 N × 15.2 m × Cos(0°)

Since Cos(0°) = 1, the formula becomes:

Work = 1870 N × 15.2 m × 1 = 28424 N·m or 28424 Joules (J)

Therefore, the work done by the elevator in lifting you and your belongings to the 6th floor is 28424 J.

(b) On the downward trip, since the velocity is constant, there is no work done by the elevator on you alone. The force of gravity is acting downwards, but since the displacement is in the same direction as the force, the angle between the force and the direction of motion is 0 degrees.

Therefore, using the same formula:

Work = Force × Distance × Cos(θ)

The force acting against gravity is your weight, which is 790 N.

Plugging in the values:

Work = 790 N × 15.2 m × Cos(0°) = 11836 N·m or 11836 J

So, the work done by the elevator on you alone during the downward trip is 11836 J.

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