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Chapter 11: Problem 3

A \(10 \mathrm{~kg}\) box is lifted \(2 \mathrm{~m}\) off the floor and placed on a frictionless horizontal conveyor to take it \(30 \mathrm{~m}\) across a warehouse. At the end of the conveyor, it is lowered \(1 \mathrm{~m}\) where it ends up on a shelf. How much net gravitational potential energy was given to the box from the start to the end of the process?

Short Answer

Expert verified
Answer: The net gravitational potential energy given to the box throughout the process is -98.1 J.

Step by step solution

01

Determine the initial and final heights

Initially, the box is lifted 2 meters off the floor, so the initial height (h1) is 2 meters. After moving horizontally and lowered 1 meter, the final height (h2) of the box would be 1 meter (since it was lowered from the 2 meters initial height).
02

Calculate the change in gravitational potential energy

The change in gravitational potential energy (ΔPE) can be calculated using the formula: ΔPE = m * g * (h2 - h1) where m is the mass of the object (10 kg), g is the acceleration due to gravity (9.81 m/s²), h1 is the initial height (2 m), and h2 is the final height (1 m).
03

Solve for the net gravitational potential energy

Plugging the values into the formula, we get: ΔPE = 10 kg * 9.81 m/s² * (1 m - 2 m) ΔPE = 10 kg * 9.81 m/s² * (-1 m) ΔPE = -98.1 J The net gravitational potential energy given to the box is -98.1 J, which indicates a loss of potential energy as it is lowered to a final height of 1 meter.

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