What is the tension as a function of theta

[amackeytexas]

Need some help with this answer.
A mass m on the end of a string in length L. At the bottom it is given a push to a speed V. What is the tension as a function of theta, where theta is the angle from the intial position?

 

[Doc Al]

Start by identifying the forces acting on the mass. Then apply Newton's 2nd law, realizing that the mass is centripetally acceleration. Conservation of energy will come in handy as well.

 

[amackeytexas]

Thanks. How close is this? mv^2/L=Tcos theta

 

[Doc Al]

Thanks. How close is this? mv^2/L=Tcos theta

Check it for $\theta = 0$. Does it make sense? (What forces act on the mass at that angle?)

 

[amackeytexas]

forces at that angle are Tsin theta=mg

 

[clive]

Hi makeytexas,

in order to find the corect answer you must take into account the energy's conservation law too:

$$\frac{m v_0^2}{2}=\frac{m v^2}{2}+m g L cos \theta$$

where $$v_0$$ is the initial speed.

The static equilibrium condition along the string direction would be

$$T=mg cos \theta + \frac{m v^2}{L}$$

...

 

[Doc Al]

in order to find the corect answer you must take into account the energy's conservation law too:

$$\frac{m v_0^2}{2}=\frac{m v^2}{2}+m g L cos \theta$$

where $$v_0$$ is the initial speed.

That should be:
$$\frac{m v_0^2}{2}=\frac{m v^2}{2}+m g L (1 - cos \theta)$$

 

[clive]

You're right Doc Al !