Asked by JasonJones 3 years ago

A skier of mass 70 kg is pulled up a slope by a motor driven cable. (a) How much work is required to pull him 60 m up a $30^o$ slope (assumed frictionless) at a constant speed of 2.0 m/s? (b) What power must a motor have to perform this task?

A skier

JasonJones

Answered by lancer 3 years ago

a) Work done by the is the force in the cable multiplied by the distance that it pulls the skier.

The tension in the cable is:

$ T=mg \sin \theta $

and the work done is

$ W=Td = mgd \sin \theta = (70 \, kg)(9.8\, m/s^2)(60\,m)\sin\,30^o=2.1 \times 10^4 \, J $

Hence the work required to pull the skier up the slope is 21000 Joules

b)

The power of the motor to pull the skier is,

$ P=\frac{W}{t}=\frac{Td}{t}=Tv=mgv \sin\,\theta $

$ P=(70\,kg)(9.8\,m/s^2)(\sin\,30^o)(2.0\,m/s)=686 W $

Hence the average power given by the motor is 686 Watts.

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Asked: 3 years ago