Circular Motion, an object attached by a string to a motor

[SDTK]

Homework Statement

A pendulum traveling at constant speed along a circular path
Determine the angle that the string makes with the vertical.

T[/B]he length of the string was measured to be 60 cm.
The period was measured to be 1.41 s
The frequency was found to be 0.709


2. Homework Equations
Is it possible to find the radius with only the Period T and frequency f?

3. The Attempt at a Solution
I believe that it should be possible to use the period and frequency to find the velocity, and from there the radius. Once I have the radius, I can find the angle.

Using:
v = 2(pi)r / T, v = 2 (pi)fr,
v = (2 x pi x radius)/period, v = 2 x pi x frequency x radius

a = v^2/r = (2(pi)f)^2r =(2(pi)/T)^2 r
a = velocity squared / radius = (2 x pi x frequency) squared x radius
= ((2 x pi) / T))squared x radius

I have tried solving for "r" and substituting the solution in order to find velocity, ... but I end up circling back the an equation with both the two unknown variables that I am trying to find, v and r.

with advanced thanks for any advise,
D.T.

 

[Doc Al]

How about drawing a free body diagram of the pendulum? Identify all forces acting and apply Newton's 2nd law.

 

[gneill]

Referring to the thread title, I'm not seeing where the motor comes in...

 

[Doc Al]

Referring to the thread title, I'm not seeing where the motor comes in...

I'm guessing the string of the pendulum is tied to some spinning axis--driven by the motor.

 

[gneill]

I'm guessing the string of the pendulum is tied to some spinning axis--driven by the motor.

Ah. Alrighty then.

 

[SDTK]

Air resistance is not considered

I understand that that force (net) = ma = (mv^2)/r
and that mass "cancels out" so Force(net) = a = v^2 / r.

Velocity is not known. Neither is the radius, or angle

(the length of the string providing the tension, the period and the frequency are known.)

I thought that I could solve for velocity, and from velocity, solve for radius, ... but am now wondering if there is enough info to so do

 

[Doc Al]

Apply Newton's 2nd law to vertical and horizontal force components separately.

 

[SDTK]

Apply Newton's 2nd law to vertical and horizontal force components separately.

thank you