Notes Ask Your T A 8.8-kg box is being lifted by means of a light rope that is t

Question

Notes Ask Your T A 8.8-kg box is being lifted by means of a light rope that is threaded through a single, light, frictionless pulley that is attached to the ceiling. If the box is being lifted at a constant speed of 2.0 m/s, what is the power delivered by the person pulling on the rope? 0.1725 kw (b) If the box is lifted, at constant acceleration, from rest on the 02669 x w floor to a height of 1.3 m above the floor in 0.42 s, what power is average power is delivered by the person puling on the rope? The work done is the force times the displacement and the average power is the ratio of the work done to the time required. Find the force acting on the box by applying Newton's second lew ation of the box by using a constant celeraton equation. and the

Explanation / Answer

a)

For constant velocity

Force = Weight = 8.8 kg * 9.8 m/s^2 = 86.24 N

Work = 86.24 N * 2 m = 172.48 J every second because that is how far the box goes every second

So we also have 172.48 J / s = 172.48 Watts divide by 1000 = 0.17248 kW

b)

Now we add acceleration to the force

distance = 0.5 * at^2

1.3 m = 0.5 *a*0.42s^2

1.3 m = 0.5 * 0.1764*a
a = 1.3 / 0.088 = 14.77 m/s^2

F = MA
F = 8.8 kg * 14.77 = 130 N PLUS gravity

Force total = 130 + 86.24 = 216.24 N

Work = 216.24 N * 1.3 m = 281.112 N*m = 281.112 J in 0.42 s

281.112/0.42 = 669.31 Watt / 1000 = 0.669 kW

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