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Old Dec 1st 2009, 11:57 PM   #1
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Rotation and Torque

A catapult made with a rod of negligible mass that is 3.00m long has a mass of 60.0 kg 0.14m from the pivot point on one side and a 0.120 kg mass 2.86m on the other side. I need to find the speed that the 0.120 kg mass achieves (largest speed) once the rod is released. I am unsure of where to begin, I have found the inertia for both masses and can put them into the equation:

K = 1/2 I w^2

But then I have two unknowns ( w and K ) and I am confused on what to do from there, or even if I have done anything right up to that point.

The inertias I got were 7.8 kgm^2 for the larger mass and 0.343 kgm^2 for the smaller mass (just in case that data turns out to be relevant).

Thank you for any help in advance, it is greatly appreciated and thank you for your time.
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Old Dec 3rd 2009, 11:46 AM   #2
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Rotation and Torque

AmyBee,

You could try an energy based approach. Assume that the catapult is on a level. The bottom pivot loses 60*0.14*g (82.4J) of potential energy, the stone gains 0.12*2.86*g (3.3J) of potential energy. Therefor assuming a 100% efficiency of energy transfer, 79.1J of potential energy gets transfered into the kinetic energy of the object. 0.5*0.12*v^2.

Therefor v should equal 36.29 m/s or almost 130 km/h.

Note that the largest speed might not necesserily give the furtherest range (approx 28m).
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