Suppose that instead of steel balls we use puttyballs. They will collide inelast

Question

Suppose that instead of steel balls we use puttyballs. They will collide inelastically and remain stuck togetherafter the collision. How high will the balls rise after thecollision?
Two identical steel balls, each of mass 2.1 kg,are suspended from strings of length 27 cm so that they touch whenin their equilibrium position. We pull one of the balls back untilits string makes an angle q = 27 degree with the vertical and let it go. It collides elastically with theother ball. How high will the other ball rise? Suppose that instead of steel balls we use puttyballs. They will collide inelastically and remain stuck togetherafter the collision. How high will the balls rise after thecollision?

Explanation / Answer

from energy conservation, PE of left ball = mgl(1- cos) = PE of left ball beforecollision = (1/2)mv2 v = 2gl(1-cos) >>> compute this withl=.27, =270 after the elastic collision, both momentum and KE areconserved, so mv = mu + mV >>> u = velocity of left ball aftercollision, V= velocity of right bll after collision v - u = V (1/2)mv2 = (1/2)mu2 +(1/2)mV2 v2 - u2 = V2 =(v-u)2 v+u = v-u so u = 0 >>> after the collision, the first ballstops and the second ball gets the same velocity v. So the secondball will rise to the same initial height, i.e., to angle270. If the collision were inelastic, the enrgy conservation doesnot hold and the momentum conservation becomes mv = 2mu (because the 2 balls stick together). so u= v/2 if the 2 balls go up to angle (to the right), 2mgl(1-cos) = (1/2)(2m)u2 Now you can compute . hope this helps! Now you can compute . hope this helps!

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