Force on an object in circular motion

[BuBbLeS01]

Homework Statement

A hammer thrower whirls a 18.2 kg iron ball on the end of a 1.2 m string at 1.0 revolutions per second in a horizontal circle. Calculate the force in the string.

Homework Equations

F=m(v^2/r)

The Attempt at a Solution

I am not sure how to do this...
I set up a table of forces in the x and y direction...
x = T & centripetal force
y = W
I am not even sure I am starting off right.

 

[G01]

What type of force is acting through the string? (i.e. What type of motion is it causing?)

 

[Proggle]

Since the circle is horizontal, you know that F=m(v^2/r) will be equal to the tension in the string.

Can you obtain that value from the known information?

 

[BuBbLeS01]

No I need to get the revolutions/sec in radians/sec

 

[BuBbLeS01]

So I multiplied 1 rev/sec by 2pi to get the velocity...
F= 18.2 kg(2pi^2/1.2) = 598.76 N
That seems high?

 

[G01]

Ok, you have the velocity in radians per second, so you have the angular velocity. The formula you are using assumes that the velocity is in meters per second. So, you'll either have to convert or use the version of the formula where the angular velocity is involved. Do you know this form of the centripetal force formula?

 

[Proggle]

Hmm, still missing something.

The velocity in your formula needs units of m/s, not radian/s. You're almost there, can you change it to that?

 

[BuBbLeS01]

I think the formula is v= wr to get it into m/s so that would be 598.76rad/s * 1.2 m = 718.51 m/s

 

[G01]

I think the formula is v= wr to get it into m/s so that would be 598.76rad/s * 1.2 m = 718.51 m/s

This is not correct.

Check you math when computing the angular frequency.

Remember:

$$\omega = 2 \pi f$$

 

[BuBbLeS01]

ok if I am doing this right I am getting a huge number of 7818780.67 N

 

[BuBbLeS01]

I think I did something wrong maybe its supposed to be...
w=2pi * f = 6.28 rad/s
v=wr
6.28 rad/s * 1.2 m = 7.54 m/s

 

[G01]

I think I did something wrong maybe its supposed to be...
w=2pi * f = 6.28 rad/s
v=wr
6.28 rad/s * 1.2 m = 7.54 m/s

Yes this is correct. Sorry, I apparently didn't notice the error either.

 

[BuBbLeS01]

thanks!

 

[G01]

thanks!

No problem!