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Chapter 6: Problem 18

An elevator of mass \(m\) rises a vertical distance \(h\) with upward acceleration equal to one-tenth \(g .\) Find an expression for the work the elevator cable does on the elevator.

Short Answer

Expert verified
The work done by the elevator cable on the elevator is given by \(W = m(g+a)h\).

Step by step solution

01

Determine the Gravitational Force

Calculate the gravitational force acting on the elevator. This is given by \(F_g = mg\), where \(g\) is gravitational acceleration.
02

Determine the Net Force

Find the net force required to accelerate the elevator upwards. This net force is the result of the gravitational force and the force from the moving elevator. From Newton's second law, this force can be calculated with \(F_{net} = m(g+a)\), where \(a\) is one-tenth of \(g\).
03

Calculate the Work Done

Finally, calculate the work done by the cable on the elevator. The work done by a force is calculated as \(W = Fd\), where \(F\) is the force and \(d\) is the distance. In this case, the force is \(F_{net}\) and the distance is \(h\). Thus, the work done by the cable is \(W = m(g+a)h\).

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