Question

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 60m up a 30 degree slope (assumed frictionless) at a constant speed of 2.0 m/s ?(b) What power must a motor have to perform this task?

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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 60m up a 30 degree slope (assumed frictionless) at a constant speed of 2.0 m/s ?(b) What power must a motor have to perform this task?

2021-02-13

Mass of skier (m)=70 kg
Applied Force (F)=$$\displaystyle{m}{g}{\sin{{30}}}={345.35}\ {N}$$
Let the work-done (W) be required to pull him d=60m up a 30
slope (assumed frictionless)
$$\displaystyle{W}={m}{g}{\sin{{30}}}\cdot{d}$$
$$W=20.6\ kJ$$
(b) The constant speed (v)=2.0 m/s
The power of motor $$\displaystyle{\left({P}\right)}={F}\cdot{v}$$
P=686.70W