   Chapter 5, Problem 50P

Chapter
Section
Textbook Problem

Q A skier of mass 70.0 kg is pulled up a slope by a motor-driven cable, (a) How much work is required to pull him 60.0 m up a 30.0° slope (assumed frictionless) at a constant speed of 2.00 m/s? (b) What power (expressed in hp) must a motor have to perform this task?

(a)

To determine
The work required to pull the skier up.

Explanation

Given Info:

The mass of the skier is 70.0kg .

The height to which the skier should be pulled is 60.0m .

The slope of the cable is 30.0° .

The constant speed of the motor is 2.00m/s .

The work done by the non-conservative force is,

Wnc=ΔKE+ΔPE       (I)

• ΔKE is change in kinetic energy
• ΔPE is change in potential energy

The change in kinetic energy is zero because the motor is pulling him up at a constant speed.

Wnc=ΔPE=mgΔh

• Δh is the change in height of the skier

Since, Δh=hsinθ

Wnc=mghsinθ

• m is the mass of skier
• g is acceleration due to gravity
• h is the height to which the skier should be pulled
• θ is the slope of the cable

Substitute 70

(b)

To determine
The power of the motor in hp to perform the task.

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