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Sagot :
The question is incomplete. Here is the complete question.
Suppose the mass of a loaded elevator is 1600 kg.
(a) What force, in Newtons, must be supplied by the elveator's cable to produce an acceleration of 0.745 m/s² upwards against a 185N frictional force?
(b) How much work, in joules, is done by the cable in lifting the elevator 21m?
(c) What is the final speed, in meters per second, of the elevator if it starts from rest?
(d) How much work, in kilojoules, went into thermal energy produced by friction?
Answer: (a) F = 1377 N
(b) W = 28917 J
(c) v = 5.6 m/s
(d) W = 3.885 kJ
Explanation:
(a) According to Newton's Second Law: [tex]F_{net}=m.a[/tex], in which, [tex]F_{net}[/tex] is the vetorial sum of all the forces in a system and its unit is [F] = kg.m/s² or newton (N).
In the elevator's case, and assuming going upwards is positive:
[tex]F-F_{f}=m.a[/tex]
F - 185 = 1600(0.745)
F = 1377 N
For an elevator to produce an acceleration of 0.745m/s² upwards, the cables have to supply a force of 1377 newtons.
(b) Work is the energy transferred to an object while is being moved. It is calculated as: W = F.s. Its unit is [W] = N.m or Joule (J)
In the elevator's cable:
W = 1377.21
W = 28917 J
The work done by the elevator's cable is W = 28917 joules.
(c) Acceleration is variation in velocity along time. Since we know the displacement of the elevator:
[tex]v^{2}=v_{0}^{2}+2a\Delta x[/tex]
where:
v₀ is initial velocity, which is this case v₀=0 because it starts from rest;
a is acceleration;
Δx is the displacement
Replacing values:
[tex]v^{2}=2(0.745)(21)[/tex]
[tex]v=\sqrt{31.29}[/tex]
v = 5.6 m/s
Final speed of the elevator is 5.6 m/s.
(d) [tex]W=F_{f}.s[/tex]
W = 185(21)
W = 3885 J
Work transferred into thermal energy because of friction is W = 3.885 kJ.
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