   Chapter 5, Problem 83AP

Chapter
Section
Textbook Problem

A loaded ore car has a mass of 9.50 × 102 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0° above the horizontal. The car accelerates uniformly to a speed of 2.20 m/s in 12.0 s and then continues at constant speed, (a) What power must the winch motor provide when the car is moving at constant speed? (b) What maximum power must the motor provide? (c) What total energy transfers out of the motor by work by the time the car moves off the end of the track, which is of length 1 250 m?

(a)

To determine
The power provided by the winch motor when the car is moving at constant speed.

Explanation

Given Info:

The mass of the car is 9.50×102kg .

The inclination of the shaft with the horizontal is 30.0° .

The car accelerates to a speed of 2.0m/s in 12.0s and then proceeds at constant speed.

When the car is moving at constant speed, the tension of the cable is,

F=mgsinθ       (I)

Formula to calculate the power input is,

P=Fv       (II)

• F is the tension on the cable
• v is the speed of the car

Substitute equation (I) in (II),

P=mgvsinθ

Substitute 9.50×102kg for m, 9.8m/s2 for g, 2

(b)

To determine
The power provided by the motor.

(c)

To determine
The total energy transfers out of the motor by work when the car moves off the end of the track.

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