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Calculate the work done on a 1,438-kg elevator car by its cable to lift it 50 m at constant speed, assuming friction averages 115 N.

Give your answer in kilojoules.

Answer :

The work done by the cable on a 1,438-kg elevator to lift it 50 m at constant speed, while overcoming a frictional force of 115 N, is 710.37 kJ.

To calculate the work done on a 1,438-kg elevator car by its cable to lift it 50 m at constant speed, while overcoming friction, we use the following information:

  • Elevator mass (m) = 1,438 kg
  • Distance lifted (d) = 50 m
  • Friction force (f) = 115 N
  • Acceleration due to gravity (g) = 9.8 m/s2

The force exerted by the cable must counteract both the gravitational force and the frictional force. The gravitational force is

Fg = m x g,

and the total force (Ftotal) the cable must exert is

Fg + f.

Calculate Gravitational Force:

Fg = mg

= 1,438 kg x 9.8 m/s2

= 14,092.4 N

Total Force:

Ftotal = Fg + f

= 14,092.4 N + 115 N

= 14,207.4 N

Work Done by the Cable:

W = Ftotal x d

= 14,207.4 N x 50 m

= 710,370 J

Now, converting joules to kilojoules:

W = 710,370 J

(1 kJ / 1,000 J)

= 710.37 kJ

Therefore, the work done by the cable to lift the elevator car 50 m, overcoming friction, is 710.37 kJ.

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Rewritten by : Barada