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?

Respuesta :

Answer:

Explanation:

Given

mass of skier=60 kg

distance traveled by skier=75 m

inclination[tex](\theta )=30^{\circ}[/tex]

speed (v)=2.4 m/s

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

[tex]F_{net}=0[/tex]

Force applied by cable[tex]=mg\sin \theta[/tex]

[tex]F=60\times 9.8\times \sin (30)=294 N[/tex]

work done[tex]=F\cdot x[/tex]

[tex]W=294\cdot 75=22.125 J[/tex]

(b)Power[tex]=F\cdot v[/tex]

[tex]P=294\cdot 2.4=705.6 W\approx 0.946 hp[/tex]