Centripetal force of a block on a string

[physics10]

I am really in a jam, I have no idea if I solved this correctly or not, it is due Monday morning 8:00am /eastern time.

Here is the question:
A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 28m/s, the block hangs vertically down. But when the van maintains the same speed around an unbanked curve (radius=150m), the block swings toward the outside of the curve. Then the string makes an theta with the vertical. Find theta.

This is what I got, I don't know if I am doing it correctly or not.

The sum of Fy=0
ncos theta=mg
theta=tan^-1 (28m/s)^2/(150m)*(9.80m/s)= theta=28 degrees

Please help if you can, you can e-mail me if you like at jc_ro2003@yahoo.com

 

[andrewchang]

Your calculations are correct.

 

[Fermat]

I don't know how you derived it, but your expression,

$$\tan\theta = \frac{v^2}{rg}$$

is correct, and so is the 28 degrees.

 

[gunblaze]

The Centripetal force on the van is the 'force' that is causing the ball to swing outwards. By solving the centripetal force of the van, u will be able to get the magnitude of the 'force' that is acting on the ball. By combining with the vertical unchanging force on the ball, gravity (9.81m/s^2), and using tan, u shld be able to the solve.. But i guess u noe that.. Haha:)

 

[physics10]

thanks

thank you guys for all your help, I am a new member to this site and you guys have been great.