How Do You Calculate Spring Length and Ball Speed in Circular Motion?

[mathzing]

Hi, i am kind of at a loss here. I can't seem to figure out this problem, not sure if i am doing it right or not. All help is greatly appreciated.

A ball of mass 4kg is suspended on a light spring with a constant of 850n/m. the ball is spun in a circular orbit at a constant speed so the string makes an angle of 22 degrees from the vertical. find the length of the spring and the speed of the ball.

Here is what i believe the diagram would look like.

http://img212.imageshack.us/my.php?image=22me2.png

alright so here is what i did right/wrong.

fg=mg
= 4(9.8)
fg =39.2N

fg=fspring
mg=kxcos22
39.2=850xcos22
x=aprox 5cmthe length of the spring is 5cm . That sounds pretty wrong...hope in right :D

ok onto the speed.

fc=(mv^2)/r
T=39.2/cos22=42.3

tsin22=fc
42.3sin22=(m(v^2))/r
42.3sin22=(4(v^2))/5sin22
v=2.7m/s

speed = 2.7m/s

so did i do anything wrong..?

 

[Doc Al]

alright so here is what i did right/wrong.

fg=mg
= 4(9.8)
fg =39.2N

fg=fspring
mg=kxcos22
39.2=850xcos22
x=aprox 5cm


the length of the spring is 5cm . That sounds pretty wrong...hope in right :D

You calculated the amount the spring stretches, but that's not its length.

 

[mathzing]

Hmm, i could be wrong, but i think my teacher intended it as a stretching question. Just incase, how do i find the length, iv never had any lessons relating to the actual length? is my speed correct, or will it need editing?

 

[Doc Al]

Generally a spring has some non-zero unstretched length. But if your teacher wanted you to assume that the spring has an unstretched length of zero, then your method is fine. (I didn't check your arithmetic.)

(You would need additional information to find the unstretched length of the spring.)

 

[mathzing]

yeah that explains it, then he wanted us to find the amount it stretched by, how about the speed of the object, is that correct?

 

[Doc Al]

yeah that explains it, then he wanted us to find the amount it stretched by, how about the speed of the object, is that correct?

Yes, your method--for both parts--is correct (assuming, as I said, the unstretched length of the spring is 0).

In the first part, you clearly are finding the amount the spring stretches. But when you use that to find the radius for computing the centripetal force, that's when you are assuming the unstretched length is zero. (Say the unstretched length were 10 cm instead of 0. Then you would find its stretched length to be 10 + 5 = 15 cm. Which would give you a completely different speed. Make sense?)

 

[mathzing]

yup :D thanks