- #1

Northbysouth

- 249

- 2

## Homework Statement

Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 66° if θ'= 2.22 rad/sec and θ"= 4.475 rad/sec

^{2}

I have attached an image of the question.

## Homework Equations

a

_{n}= v

^{2}/r = rθ

^{2}= vθ'

a

_{t}= v' = rθ'

## The Attempt at a Solution

I've managed to calculate e

_{n}and e

_{t}correctly

a

_{t}= (4.2 ft)(4.475 rad/sec

^{2}) = 18.795 ft/sec

^{2}

a

_{t}= 18.795ft/sec

^{2}

For a

_{n}I calculated velocity first:

v = rθ' = (4.2ft)(2.22 rad/sec)

v = 9.324 ft/sec

Hence a

_{n}= (9.324 ft/sec)(2.22 rad/sec)

a

_{n}= 20.69928 ft/sec

^{2}

Unfortunately, I'm now having difficulty with finding the velocity in terms of i and j.

I had thought that I could use geometry to do it:

a

_{t}cos(90-66) = -17.77 i

a

_{t}sin(90-66) = 7.644 j

But the system says it's wrong. Help is greatly appreciated.