Question

A skier of mass 60 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 75 m up a 30° slope (assumed frictionless) at a constant speed of 2.4 m/s? kJ (b) What power (expressed in hp) must a motor have to perform this task?

Answer 1

Answer:

Explanation:

Given

mass of skier=60 kg

distance traveled by skier=75 m

inclination$(\theta )=30^{\circ}$

speed (v)=2.4 m/s

as the skier is moving up with a constant velocity therefore net force is zero

$F_{net}=0$

Force applied by cable$=mg\sin \theta$

$F=60\times 9.8\times \sin (30)=294 N$

work done$=F\cdot x$

$W=294\cdot 75=22.125 J$

(b)Power$=F\cdot v$

$P=294\cdot 2.4=705.6 W\approx 0.946 hp$