Help on this would be amazing; centripetal force & projectile motion

[dominus96]

Homework Statement

David used a sling to kill Goliath. The mass of the rock was 2.5 kg and the sling had a length of 1.2 m. If it spun horizontally 2 m above his head 7 times in 3 seconds:

a. What was the launch velocity?

b. What is the centripetal force and tension?

c. How far is David from Goliath?

Homework Equations

Fc=mv^2/r
F=ma
Fc=m4(pi^2)r/t^2

The Attempt at a Solution

I tried setting ma=mv^2/r, but that would only give me the velocity it spins at, not the velocity at which it was launched. And I'm not sure what to do with the 2 m.

Assistance would be great, I've been trying this for 2 hours and still nothing.

 

[qspeechc]

7 times in 3 seconds gives you the angular speed, which will also be the launch speed. We assume it was rotating about David's head at a constant rate.

From the angular speed you have calculated, you can get the centripetal force. This must equal the tension

For c. you need to use the equations of motion, which is where the 2m comes in

 

[dominus96]

Thank you

 

[Saladsamurai]

Thank you

I am a little rusty, but I am quite sure that the launch speed does not equal the angular speed. The rock leaves the sling's cirular path in a direction perpendicular to the string.

Angular speed=\omega launch speed=v_{tangential}

Do you know of a relationship between angular and tangential speed?

Casey

 

[qspeechc]

ah crap, yes, i meant the tangentil speed, lol.

 

[dominus96]

Yes i figured that out, but thanks for the lead. it helps a lot.