Centripetal acceleration and angles

[Bjamin0325]

Homework Statement

A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 34 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 120 m), the block swings toward the outside of the curve. Then the string makes an angle theta with the vertical. Find theta.

Homework Equations

Fc=v^2/r

The Attempt at a Solution

All I could do was get the centripetal force, 34^2/120=9.63333N.

I have no idea where to go from here, and there are no similar problems I can find.

Thanks a million for any help.

 

[andrevdh]

The formula that you give is for the acceleration. So you calculated the centripetal acceleration.

The block will experience two forces - its weight, W, and the tension T in the string. The vertical component of the tension balances the weight of the block while the horizontal component supplies the necessary centripetal force.

 

[m2003]

To find the angle theta, we can use the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the block, v is the velocity, and r is the radius of the curve. We can rearrange this equation to solve for theta: theta = arctan(v^2/gr), where g is the acceleration due to gravity.

In this problem, we know the velocity (34 m/s), the radius (120 m), and the acceleration due to gravity (9.8 m/s^2). Plugging these values into the equation, we get theta = arctan((34 m/s)^2 / (9.8 m/s^2 * 120 m)) = arctan(13.8) = 86.5 degrees.

Therefore, the string makes an angle of 86.5 degrees with the vertical when the van maintains a speed of 34 m/s around the unbanked curve. This angle is larger than 90 degrees because the block is swinging outward due to the centripetal force, creating a larger angle with the vertical.