Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
