Write Vector Expression in n-t and x-y coordinates of Acceleration

[Northbysouth]

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/sec²

I have attached an image of the question.

Homework Equations

a_n = v²/r = rθ² = 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/sec²) = 18.795 ft/sec²

a_t = 18.795ft/sec²

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/sec²

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_tcos(90-66) = -17.77 i
a_tsin(90-66) = 7.644 j

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

 

[cosmic dust]

Why don't you try to express e_n and e_t in terms of e_x and e_y ? Doing that, you can find the total acceleration, a = a_n + a_n , in terms of its projections on x and y axis.* e _i is the unit vector in the direction of the subscript "i".

 

[SammyS]

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/sec²

I have attached an image of the question.

Homework Equations

a_n = v²/r = rθ² = 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/sec²) = 18.795 ft/sec²

a_t = 18.795ft/sec²

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/sec²

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_tcos(90-66) = -17.77 i
a_tsin(90-66) = 7.644 j

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

Both n and t components contribute to each of the i and j components.

 

[Northbysouth]

@SammyS: You were right. To find the i component I did the following:

-a_tcos(24) -a_ncos(66) = -25.589i

For j:

a_tsin(24) - a_nsin(66) = -11.265 j

Thanks everyone.