What is the Length of the Pendulum?

[BoostAdiction]

Homework Statement

Suppose that a simple pendulum consists of a 50.0 g bob at the end of a cord of negligible mass. The angle (theta) between the cord and the vertical is given by: (theta)=(0.01000rad)cos[(5rad/s)t ], where t is time. A. What is the pendulum's length? B. What is the pendulums maximum potential energy? C. What is the maximum tension in the cord?

Homework Equations

PE=mgh
KE=1/2mv^2

The Attempt at a Solution

I got part a. Part b is throwin me off. I know how to find the maximum kinetic energy (KE=5rad/s x .392m x .1 rad) I am confused as to how to find potential, and even more lost on the tension

 

[BoostAdiction]

I have feel like mgh should equal KE because KE is energy in motion and the max potential of a pendulum would mean that its not moving right? As its about to swing the other way?

 

[tiny-tim]

Hi BoostAdiction!

Yes, that 's right … or, to put it in more mathematical language, PE + KE = constant, so PE is maximum when KE is minimum … in this case, when KE = 0!

Hint: tension = radial component of weight minus acceleration … and the acceleration is … ?

 

[BoostAdiction]

Woot! So in this case...PE=KE and KE = 5rad/s x .392m x .1 rad which equals, .196 J meaning PE does as well..Hopefully. I am going to assume the acceleration is... 0.5 rad/s^2?

 

[tiny-tim]

Im going to assume the acceleration is... 0.5 rad/s^2?

Can't work out how you got that … you should be using the formula for radial acceleration in circular motion … and it should depend on the angle.

 

[BoostAdiction]

Just made a guess on it :D. I can't find the radial acceleration in circular motion...all i found was the derivative of omega/derivative of t

 

[tiny-tim]

Have you been taught acceleration = v²/r = ω²r?