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Work Energy Theorem, Kinetic Energy, and Tension 
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#1
Oct1609, 10:28 PM

P: 36

1. A rescue helicopter lifts a 90 kg person straight up by means of a cable. The person has an upward acceleration of 0.70 m/s2 and is lifted from rest through a distance of 10 m. What is the tension in the cable and how much work is done by the tension in the cable? Use the workenergy theorem to find the final speed of the person as well.
2. Work Energy theorem: Wnet = (1/2 mass velocity final^2)  (1/2 mass velocity initial^2) Tension: T = mass gravity 3. Tension: mass gravity T = 90 kg * 9.8 m/s^2 T = 882 N Which is wrong according to Webassign. WET = Delta K WET = (1/2 mass velocity final^2)  (1/2 mass velocity initial^2) Not sure how to go about solving this part. I guess the masses cancel, but what next? 


#2
Oct1609, 10:35 PM

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PF Gold
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#3
Oct1609, 10:44 PM

P: 36

Ok, so I tried using Newtons Second Law, Force = mass * acceleration, and now I got 63 N, which is apparently still wrong.



#4
Oct1609, 10:48 PM

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Work Energy Theorem, Kinetic Energy, and Tension



#5
Oct1609, 10:58 PM

P: 36

I think I understand, so would the net force be 9.1 m/s^2 * 90 kg which would equal 819 N?



#6
Oct1609, 11:09 PM

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No. Did you draw a free body diagram for the person like I suggested?
T is pulling him upwards. Weight is pulling him downwards. Let's call the magnitude of the weight W. Then the weight is W. To find the net force, add the two forces that are acting on him: T + (W) = T  W = Fnet = +63 N For T  W to be positive, T must be greater than W. In other words, the force pulling him upwards is greater than the force pulling him downwards, so that the force pulling him upwards "wins." This is what we mean when we say that there is a NET upward force on him. "Net" = the direction and magnitude of the end result, after all forces have been considered. T  W = 63 N. You know what W is. 


#7
Oct1609, 11:13 PM

P: 36

W is equal to the weight, which is the gravitational force times the mass, so 9.8 m/s^2 * 90 kg... which is 882 N. Correct?



#8
Oct1609, 11:22 PM

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#9
Oct1609, 11:30 PM

P: 36

So I add 63 N to 882 N to get 819 N? Or is it positive 819 N since it is in the opposite direction of the weight? Or would it be 945 N since that is what 63 N + 882N (the opposite of the weight) equals?



#10
Oct1609, 11:36 PM

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There is only one of those possibilities that makes sense (the third one that you wrote). I am going to tell you the reason for the fourth time: the force pulling him upward has to be larger (in magnitude) than the force pulling him downward in order for him to be moving upward.
One way to think of it: T  W = 63 T  882 = 63 T = 882 + 63 Just think of it in terms of magnitudes (ignoring direction). The *magnitude* of the weight is 882 N, and the magnitude of the tension is 63 N larger than that. 


#11
Oct1609, 11:40 PM

P: 36

So the work done by the tension would be equal to the force times the displacement, or 945 N * 10 m, which would equal 9450 J?



#13
Oct1709, 12:03 AM

P: 36

So then to find the final speed of the person I'm supposed to use the work energy theorem which will help me find the change in kinetic energy which is [ (1/2 mass velocity final^2)  (1/2 mass velocity initial^2) ]?



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