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- anonymous

A wooden plank is inclined at and angle of 23 degrees above the horizontal. A 2.0 kg box attached to a rope is is pulled up the incline. The coefficient of kinetic friction between the box and the wooden plank is 0.15.
What does the tension in the rope is the box moves up the incline at a constant velocity?

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- anonymous

- chestercat

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- TuringTest

here's a basic diagram|dw:1329436877812:dw|

- anonymous

Got it............. Im having problems knowing what the tension it is referring to actually is...

- TuringTest

...now let's do a little trig|dw:1329436980919:dw|we can use the force of gravity into the surface to find N, which we can use to find friction. we then have\[T-f-F_g\sin\theta=0\]along the direction of the incline, which we can use to find T.
got it from here?

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- anonymous

What equation is T-f-Fgsin\[T-f-Fgsin \theta=0?\]

- anonymous

Would T be the applied force?

- TuringTest

yes, T is the applied force (tension)
I got that equation by just summing all the forces along the direction of the ramp, which we know sum to 0 because the object is moving at a constant velocity.

- anonymous

I got the X component to be 7.8 and The normal force to be 18.4. Now, Im not sure what to do because the applied force would be 7.8 and it is not the right answer.

- TuringTest

\[\sum F=T-F_g\sin\theta-f=0\]\[T=F_g\sin\theta+f=mg\sin\theta+\mu N=mg(\sin\theta+\mu \cos\theta)\]\[=2(9.8)[\sin(23^{\circ})+0.15\cos(23^{\circ})]\approx10.36\text{N}\]

- anonymous

Oh! Thanks so much!!! I didnt learn that equation yet in school so I was very confused... But I will ask my teacher tomorrow!

- TuringTest

welcome, good luck!

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