# Acceleration of chairlift [closed]

So I'm struggling with this question, and am wondering if anyone can give me the right direction to go. For the sake of not cheating, I've changed the figures etc. I just need help on the approach. I can do similar questions on a horizontal plane, but I'm stuck now the acceleration isn't perpendicular to gravity. Edit: realized I gave the wrong description/ sketch for the angle I have

A person is being lifted up a slope with an incline from horizontal of 6 deg on a ski chairlift. The winch pulling the chairlift accelerates the chairlift up the slope, which results in the person and seat tilting back with an angle of 9 degrees from what would be perpendicular to motion. What is the acceleration of the winch? Treat the cable connecting the chairlift to the winch-cable as weightless, ie the person & chairlift act as a pendulum.

## closed as off-topic by Brandon Enright, Kyle Kanos, John Rennie, Valter Moretti, Qmechanic♦Mar 26 '14 at 18:54

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• The approach is nearly identical to doing this on a horizontal plane. The only added difficulty is that you'll have to decompose more vectors into components. I always recommend choosing your two coordinate axes to be parallel and perpendicular to the direction of acceleration. – BMS Mar 25 '14 at 20:27

Lets do a Free Body Diagram of the lift (NOTE: Always do A FBD first).

What are the forces acting on the lift?

$$\sum \vec{F} = \begin{pmatrix} -T \sin\psi \\ T \cos\psi - W \end{pmatrix}$$

What is the acceleration on the lift?

$$\vec{a} = \begin{pmatrix} -a \cos \theta, a \sin \theta \end{pmatrix}$$

Combine them with $\sum \vec{F} = m \vec{a}$ and solve for $T$ and $\psi$.

You do know the direction of the tension force, the force of gravity and the direction of the resultant force, so well as the magnitude of the force of gravity. You can create some goniometric equations with that.