A skier is pulled by a tow rope up a frictionless ski slope that makes an angle

Question

A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 13° with the horizontal. The rope moves parallel to the slope with a constant speed of 0.85 m/s. The force of the rope does 890 J of work on the skier as the skier moves a distance of 3.7 m up the incline. (a) If the rope moved with a constant speed of 2.2 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 3.7 m up the incline? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 0.85 m/s and (c) 2.2 m/s?

Explanation / Answer

here,

theta = 13 degree

speed of rope , u0= 0.85 m/s

work done , w = 890 J

distnace , s = 3.7 m

(a)

work would the force of the rope do on the skier as the skier moved a distance of 3.7 m up the incline is remains the same , as the velocity of the skier is constant or there is no accelration

work would the force of the rope do on the skier as the skier moved is 890 J

(b)

let the tension in the rope be t

t * d = W

t * 3.7 = 890

t = 240.54 N

when v = 0.85 m/s

the rate of the force of the rope doing work on the skier, P = t *v

P = 240.54 * 0.85

P = 204.46 W

the rate of the force of the rope doing work on the skier is 204.46 N

(c)

let the tension in the rope be t

t * d = W

t * 3.7 = 890

t = 240.54 N

when v = 2.2 m/s

the rate of the force of the rope doing work on the skier, P = t *v

P = 240.54 * 2.2

P = 529.19 W

the rate of the force of the rope doing work on the skier is 529.19 N

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