Ball on a string rotational motion(easy for a pro)

[synergix]

Homework Statement

A ball(mass 0.500kg) is tied to the end of a string length= 1.02m. The ball is swung in a vertical circle, with speed decreasing on the way up and increasing on the way down. the ball is being swung in a counter clockwise direction. the speed of the ball is 6.0m/s at the middle of the swing(point B) 4.0m/s at the top of the swing(point C) then back down to 6.0m/s at the other middle of the swing(point D) and then 7.5m/s at the bottom of the swing(Point A). these points would all be at 90^. to each other with the first middle point being on the right the second middle point being on the left as the ball is being swung counterclockwise.

Calculate the Value in N of the net force at point c. What law are you using?

The Attempt at a Solution

My problem is I am not sure whether there will be tangential acceleration acting at this point or merely the two side points so I cannot calculate my force yet. I know that there is the force of gravity acting But I am not certain if there will be tangential acceleration. PLEASE HELP I know it is probably pretty obvious but I can't say for sure if their was or not. originally I was certain their was tangential accel = V²/r but my classmate tried to convince me their would not be and now I am really not sure.

 

[Delphi51]

Oh, it is quite a complicated little problem all right!
You should work out the centripetal force required at the top and the gravitational force that is providing part of it. Fg is not sufficient to hold the ball in circular motion so the string must be pulled with some additional force to top that up the the value of Fc. This extra string force is what you are trying to find.

 

[synergix]

Fc= 0.500kg(4.0m/s^2/1.02m)

Fg=0.500kg(9.81m/s^2)

Am I to find the force of tension? Fg= Ft+Fc sooo Ft= Fg-Fc

That makes sense is that what you mean?

 

[Delphi51]

I would say Fc = Ft + Fg so Ft = Fc - Fg. This applies only at the top of the trajectory.

 

[synergix]

Ahh yes of course thank you.

 

[willem2]

Oh, it is quite a complicated little problem all right!
You should work out the centripetal force required at the top and the gravitational force that is providing part of it. Fg is not sufficient to hold the ball in circular motion so the string must be pulled with some additional force to top that up the the value of Fc. This extra string force is what you are trying to find.

What was asked is the force at the point at the top of the swing. This can be found with
F=ma. There's no tangential acceleration at this point. (because all the forces are in the direction of the center of the circle), so the only acceleration is the centripetal acceleration.