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

# 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

365.9k points

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

389.5k points

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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