Conical Pendulum Homework: Determine Force, Find Radial Acceleration

[sailsinthesun]

Homework Statement

Consider a conical pendulum with a 81.0 kg bob on a 10.0 m wire making an angle of theta= 2.00° with the vertical.

(a) Determine the horizontal and vertical components of the force exerted by the wire on the pendulum.
(b) What is the radial acceleration of the bob?

Homework Equations

F=ma
a=v^2/r

The Attempt at a Solution

(a)After drawing the FBD for the wire and resolving the vectors, I get the horizontal force to be Fsin(theta) and the vertical to be Fcos(theta). Fcos(th)=mg so F=mg/cos(th). Then Fsin(th)=27.7484N and Fcos(th)=794.61N.

I'm pretty sure I did these correctly, but I'm not sure how to get the second part.
(b)I calculated the radius using r=10sin(2deg). Here is where I'm lost. I know a=v^2/r, and I have r, but need to find v. Any help or hints?

 

[Dick]

If you have the horizontal force, then you know the horizontal acceleration from F=ma. That 'a' is the same 'a' as in a=v^2/r.

 

[Moetasim]

Great job on calculating the horizontal and vertical components of the force exerted by the wire on the pendulum. Your approach seems correct and your calculations are consistent with the given information. For the second part, you are on the right track. As you mentioned, the equation for radial acceleration is a=v^2/r. In this case, v represents the tangential velocity of the bob, which can be found using the equation v=ωr, where ω is the angular velocity. To find ω, you can use the equation ω=√(g/L), where L is the length of the wire (10 m in this case). Once you have calculated ω, you can plug it into the equation for v and then use that value to calculate the radial acceleration. I hope this helps. Keep up the good work!