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March 1, 2015

March 1, 2015

Posted by **jason** on Sunday, December 21, 2008 at 3:05am.

Calculate the maximum height of ball 1 from and ground and the rebound height of ball 2.

- Physics -
**drwls**, Sunday, December 21, 2008 at 7:40amI would calculate the kinetic energy of ball 2 just before and after it hits the ground, using energy considerations.

Just before impact, ball 2 (M) and ball 1 (m) have acquired kinetic energy

(1/2)mV^2 + (1/2)MV^2

= M g*0.74 m - m g*0.74 mg

Solve for V of both balls, and the kinetic energy of ball 2.

(1/2)(m + M)V^2 = 0.74 (M-m)g

V^2 = [(M-m)/(M+m)]g*1.48 = 12.38 m^2/s^2

V = 3.52 m/s

= After impact, ball 2 will have 70% of the pre-impact kinetic energy, and its velocity will be V' = sqrt(0.7)V= 0.8367V = 2.94 m/s

Right after ball 2's impact, Ball 1 will continue to rise for a while because it suffered no impact and maintained its velocity V when ball 2 hits the ground. There will be no tension in the string while ball 2 and ba1l 1 both rise.

Ball 1 rises a distance H1 given by

M g H1 = (1/2) M V'^2 = (1/2)M(0.7)V^2

H1 = (0.7)V^2/(2g) = 0.35 V^2/g

When ball 1 hits the ground, ball 2 has already risen from 0.74 to 0.74 + 0.88 = 1.62 m above the ground. It will rise an additional distance until its kinetic energy (1/2) mV^2(at impact)is converted to potential energy

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