# Pendulum in an accelerated frame

tjackson3

## Homework Statement

Granted, I may be thinking too much into this.

You are sitting in a jet airplane as it accelerates at a constant rate down the
runway. Being a good physics student you hold the string of a small pendulum of length
l = 0.75m and mass m = 1 kg. You then measure the angle between the string and a
vertical line and $\theta = 37^{\circ}$. Assume $\sin\ 37 = 3/5; \cos\37 = 4/5; \tan\ 37 = 3/4$, and take $g = 10 m/s^2$

a.) What is the magnitude of the acceleration of the plane?
b.) What is the tension on the string?

## Homework Equations

Nonrelativistic coordinate transformation: $x' = x - vt$

## The Attempt at a Solution

There are a couple of ways I can see doing this, but I think both show that I don't completely understand what's going on. My first thought was that the net acceleration is zero, meaning that $a = g\cos\theta = 8 m/s^2$. This would make the tension $\sqrt{m^2g^2 + mg^2\cos^2\theta} = \sqrt{100 + 100.5625} = \sqrt{200.5625}$ but I don't think that's correct.

Alternatively, it could involve circular motion, although I have no idea what to plug in for the velocity in the centripetal force equation.

Thanks for the help!