Conical Pendulum: Period and Tension Calculation

[tachu101]

Homework Statement

Conical Pendulum Question

Mass (m) is attached to the ceiling by a String of Length (s)
The string makes an angle of ($$\theta$$) with the vertical

Compute the Period of Revolution and the Tension in the string?

Mass of Bob (m) -- 4.35kg
Length of String (s) -- 5.50 meters
$$\theta$$ -- 64 degrees

Homework Equations

1/2(mv^2)$$/$$radius -- Centripetal Force

W= mg -- weight

Not sure what else I need

The Attempt at a Solution

I think that the tension in the string would be

Tcos($$\theta$$)=mg ---- T=(mg)$$/$$cos($$\theta$$)

So

(4.35)(9.81)$$/$$cos(64)= ---- 97.35 NI have no idea how to get the period though, but I think it has to do with

Tsin$$\theta$$= 1/2(mv^2)$$/$$radius

 

[Doc Al]

So far, so good.

Once you find the speed you can use that to find the period. What's the radius of the bob's path?

 

[tachu101]

I think that the radius would be

string length --- (s) sin (Theta) --- so 5.5sin(64)= 4.94m

I am not sure the equation to find the period though?

I have radius, string length, tension in string, and mass of the Bob.

 

[Doc Al]

I think that the radius would be

string length --- (s) sin (Theta) --- so 5.5sin(64)= 4.94m

Good.

I am not sure the equation to find the period though?

The period is just the time the bob takes to make one complete revolution. Find the speed (and figure out the distance).

 

[tachu101]

Would I find the speed by using Tsin(theta)= (1/2)(mv^2)/radius ----

97.35 sin (64) = (1/2)(4.35)(v^2)/(4.94) ----- velocity = 14.097 m/sec ?so the distance would be (2)(radius)(pi)= (2)(4.94)(pi)= 31.03m

I am stuck now on how to find the period. Is there a certain equation that is used to find the period, we just started this topic?

 

[Doc Al]

Is there a certain equation that is used to find the period, we just started this topic?

How about distance = speed x time?

 

[tachu101]

So (2)(pi)(r)=(velocity)(time)

thus

31.03m=(14.1m/sec)(t) ---- so ---- period= 2.2 sec?

 

[Doc Al]

Sure. It's just the time required for one revolution. You have the distance and the speed--that's all there is to it.

 

[tachu101]

thank you so much for the help, I am going to go back and check all of my work.