3. (a) calculate the work done on a 1500-kg elevator car by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 n. (b) what is the work done on the elevator car by the gravitational force in this process? (c) what is the total work done on the elevator car?



Answer :

(a) Work done on the car by its cable will be 5.92 * [tex]10^{5}[/tex] J.

(b) Work done on the car by the gravitational force will be -5.92 * [tex]10^{5}[/tex] J.

(c) Total work done on the car will be 0 J.

Work done is the product of force and displacement.

  • Mathematically, Work-done = W = Force * Distance

Mass of the car = m = 1500 kg

Distance lifted by the cable = d = 40 m

Frictional force experienced by the car = Fs = 100 N

(a) According to the Newton's second law of motion

F = Fcable - mg - Fs = ma

Fcable = mg + Fs

Work done by the same force = W1

W1 = Fcable * d

W1 = (mg + Fs) * d

W1 = (1500*9.8 + 100) * 40

W1 = 592600

W1 = 5.92 * [tex]10^{5}[/tex] J

(b) Work done by the gravitational force = W2 = mg * d

W2 = 1500*(-9.8)*40

Since the acceleration is acting downwards 'g' will be considered with a negative sign.

W2 = -5.88 * [tex]10^{5}[/tex] J

(c) The total work done on the lift is the work done by the net force exerted on the car during this process:

W3 = Fnet * d

Fnet =  -5.88 * [tex]10^{5}[/tex] J +  5.92 * [tex]10^{5}[/tex] J

Fnet = 0

W3 = 0 * 40

W3 = 0 J

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