Solve Centripetal Motion Problem: Find Tension & Acceleration

[rickylin89]

I have a problem that I've tried to figure out, but I can't figure it out.

Here it is:

You whirl a ball of mass 0.40 kg on a string of length 0.90 m. At the point shown the angle of the string from the vertical is 30 degrees and the ball has a speed of 3.5 m/s.

a) Make a free body diagram of the ball.
b) Find the tension in the string.
c) What is the acceleration of the ball, tangential and radial components?
c) Now consider the ball at the top of the circle. What is the smallest speed of the ball so that the ball continues in a circle?

Any help with this problem would be greatly appreciated!

 

[rickylin89]

I have a homework problem that I've tried to figure out, but I can't figure it out.

Here it is:

You whirl a ball of mass 0.40 kg on a string of length 0.90 m. At the point shown the angle of the string from the vertical is 30 degrees and the ball has a speed of 3.5 m/s.

a) Make a free body diagram of the ball.
b) Find the tension in the string.
c) What is the acceleration of the ball, tangential and radial components?
c) Now consider the ball at the top of the circle. What is the smallest speed of the ball so that the ball continues in a circle?

Any help with this problem would be greatly appreciated!

 

[tiny-tim]

Hi rickylin89!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

(and please don't double-post )

 

[rickylin89]

Honestly, I really don't know how to start this problem. Any help would b great.

 

[Dr.D]

Draw a free body diagram and write the equations of motion. If you are familiar with them, us the polar coordinate form for the equations of motion; it will make things easiest.

 

[rickylin89]

I'm not sure if I have the right free body diagram. I figured there was a down force of gravity, an up force of net force, and then I don't know what other forces there are.

 

[Dr.D]

Where does this "up force" come from? The only forces you can include have to come from somewhere!

What direction is the force in the string?

 

[rickylin89]

I think there is a tension that is 60 degrees to the left of the down force of mg. Is that righ?

 

[Dr.D]

What matters is that the tension in the strings is ALONG the strong.

 

[rickylin89]

I don't really understand what you mean.

 

[rickylin89]

The tension is along the string, but I was referring to the free body diagram and the fact that the tension is mgsin(60). Is that right?

 

[Dr.D]

No, that is really not correct. Just call the tension T for right now, but recognize that it acts along the string. The apply Newton's second law, with the proper acceleration of the mass and the correct force sums along the string and perpendicular to the string.