# Cable car system : Tension in the pull cable

1. May 14, 2014

### Curieuse

1. The problem statement, all variables and given/known data

Figure shows a section of a cable car system. The maximum permissible mass of each car with occupants is 2800 kg. The cars, riding on a support cable are pulled by a second cable attached to the support tower on each car. Assume that the cables are taut and inclined at θ= 35°. What is the difference in tension between adjacent sections of pull cable if the cars are at the maximum permissible mass and are being accelerated up the incline at .81 m/s2.

2. Relevant equations

FNET=ma

3. The attempt at a solution

From figure,

T2 = T1 +Mg sin θ
T1 = Mg sin θ
Thus, T2 = 2 Mg sin θ

And Tn = n Mg sin θ

Thus, T5 - T2 = (5-2) Mg sin θ = 3*9.8*2800*sin(35°)= 47216.8 N

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2. May 14, 2014

### BvU

I read the exercise somewhat differently: adjacent sections of pull cable means you have to take e.g. T2 - T1, not T5 -T2 as you seem to be doing. Then: the pull cable is the one that provides the acceleration, so I would expect the acceleration should appear somewhere in the answer, isn't it ?

3. May 14, 2014

### Curieuse

Oh of course! I thought the same about the T2-T1 thing and then saw this
and redid it.
But yeah! The acceleration is in the answer, It skipped my mind soo bad when I redid it with the section things and all.
So the free body diagram goes to this,
and so the equation for Tn = n(ma+mg sinθ)
And T5-T3= 2(2800)(.80+9.8 sin(35°))
For Tn-Tn-1 = 2800(.80+9.8 sin(35°))

So, i guess we could answer both! But also refer to the question,
Figure shows a section of a cable car system. The maximum permissible mass of each car with occupants is 2800 kg. The cars, riding on a support cable are pulled by a second cable attached to the support tower on each car. Assume that the cables are taut and inclined at θ= 35°. What is the difference in tension between adjacent sections of pull cable if the cars are at the maximum permissible mass and are being accelerated up the incline at .81 m/s2.

But then, there's be a chance to get at the implied meaning if someone has a solution manual of some sort to the Fundamentals of Physics- 8th edition extended by Halliday, Resnick and Walker..o have had it in class or something.. I guess there's no better way to know it than that!

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4. May 14, 2014

### BvU

I see. This has nothing to do with physics any more. It is clear you completely understand the situation. The formulation of the exercise is confusing, not intentionally, I suppose, but they could have written "tension between adjacent sections of three cars each" to keep it clear...

They mention an acceleration of .81 m/s2. Is there a reason you write 0.80 ?

5. May 15, 2014

### Curieuse

No! It has to be .81! Clearly saturated with the problem i am now! :tongue2: