Kinetic and Potential Energy Problem Solving

[Callen9]

Homework Statement

Doing some homework with kinetic energy and potential energy. I came across 3 questions that I am struggling with. Basically we have a mass attached to the end of a string. The string is hanging straight down to start off these questions. The following questions assume that the string never has slack in it!

#1, If the length of the string is 1m, calculate the angle made by the string with the vertical when height=.1m?

#2, If the mass is .06kg, what is the tension on the string when height=.1m?

#3, What is the tension of the string when the ball falls back to its original position from a height .1m?

Homework Equations

Well, I know mgh=1/2mv², the m will cancel out leaving us with, gh=1/2v²

The Attempt at a Solution

For #1, If I draw this out, we will have a shape that looks like a right triangle with the hypotenuse of 1m and the vertical side of 1m-height (.1)=.9m. Using SOHCAHTOA we should get an angle of 25.84 degrees.

For #2, I'm not sure about this one, I think I have to label all the forces acting on the mass and do something from there.

For #3,Shouldn't the tension of the string be the Net Force=ma? The only tension acting on the string in the initial position (which is at 0 degrees) should be just the .6kgx9.8?

 

[ideasrule]

For #1, If I draw this out, we will have a shape that looks like a right triangle with the hypotenuse of 1m and the vertical side of 1m-height (.1)=.9m. Using SOHCAHTOA we should get an angle of 25.84 degrees.

Yup.

For #2, I'm not sure about this one, I think I have to label all the forces acting on the mass and do something from there.

I'm not sure either. If the mass is moving at h=0.1 m, the tension will be higher, because it has to provide the required amount of centripetal acceleration. However, I think the question assumes that the mass starts off at this position, so it isn't moving at this time.

For #3,Shouldn't the tension of the string be the Net Force=ma? The only tension acting on the string in the initial position (which is at 0 degrees) should be just the .6kgx9.8?

Tension also has to provide the centripetal acceleration, so it's going to be more than 0.6kg*9.8 m/s^2.

 

[Callen9]

So I'm guessing for #2, It would be something along the lines of T1+T2=?... most likely the value of centripetal force.

Same for #3 I guess too.