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In the pulley system shown, all the pulleys are massless and frictionless and the rope is of negligible mass, Aristotle wanted to raise the 262-newton weight to a height of 3.00 meters. (a) Find the magnitude of force F he needed to pull on the rope to move the weight upward with a constant velocity. (b) What was the mechanical advantage of the pulley system? (c) How far did he have to move his end of the rope? (d) How much work did he do? (e) How much work was done on the weight?

Respuesta :

The pulley is a simple machine that reduces the effort required to perform

work.

The correct responses are;

  • (a) 131 N
  • (b) M.A. is 2
  • (c) 6 m.
  • (d) 786 J
  • (e) 786 J

Reasons:

The probable diagram of the pulley in the question, obtained from a similar

question posted online is attached.

The attached weight to the pulley, [tex]F_W[/tex] = 262 Newton

Height to which the weight is to be raised, h = 3.00 m

(a) The magnitude of the force needed to pull on the rope to move the

weight  upwards with a constant velocity is given as follows;

Force to pull rope, F = Tension in the rope, T

The weight is shared equally by the two parts of the rope holding the

pulley attached to the weight.

[tex]F_W[/tex] = 2 × T

Therefore;

262 N = 2 × T

T = 262 N ÷ 2 = 131 N

  • The force for pulling the rope at constant velocity, F = T = 131 N

(b) The mechanical advantage of a simple pulley system is given by the

number of ropes that are supporting the weight (load).

The number of ropes supporting the weight = 2 ropes

Therefore;

  • The mechanical advantage of the pulley system, M.A. = 2

(c) Raising the weight 3 meters, is such that the length of the two sides of

the rope holding the pulley attached to the weight are reduced by 3

meters relative to top pulley, therefore;

Change in length of rope attached to the weight = The distance the end of the rope is moved

Change in length of the rope attached to the weight = 2 × 3 m = 6 m

Therefore;

  • The distance rope is moved at the rope end, d = 6 meters

(d) Work done, W = Force of pulling, F × Distance of pulling, d

Therefore;

  • The work done in pulling, W = 131 N × 6 m = 786 J

(e) Work done on weight, W = Force applied to weight, [tex]\mathbf{F_W}[/tex] × Distance moved by weight, h

Therefore;

  • W = 262 N × 3.00 meters = 786 Joules

Learn more about pulleys here:

https://brainly.com/question/492803

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