1intial energy is 1/2 mv2
maximum extension will be wen realtive velocity is 0
so mv'2 +elastic energy=K.E
by montum conservation
mv=2mv'
v'=v/2
hence proved
max. e.p.e=1/4 mv2
a body with a kinetic enrgy K collides elasticaly with another bidy of the same mass kept at rest. find the maximum elastic potential enery of the body during the collision
ans k/2
i am not abel to understand the question at all i mean how come elastic potential comes to play
pls could anyone solve it
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6 Answers
11hey i kknow if it were a spring bu in the question nothing is mentioned absolutely nothing so how can we know how spring comes + in ur diagram the blocks dont collide
1HINT: elastic potential energy will be maximum when velocities of both the bodies are the same(at an instant during the collision)
initial momentum of system = mu
from conservation of linear momentum, when velocities are same and =V
mV+mV=mu or V=u/2
during collision, elastic potential is max when velocities of both particles are same ie when V=u/2
initially we have KE=k=mu2/2
conserving total energy, \frac{(m+m)V^2}{2} + elastic\ potential_{max}=\frac{mu^2}{2}
putting V=u/2 you get the result ie elastic potential=k/2
1oh i didnt realise xyz had posted the same solution before me. varun you can look up HC verma pgs 145-146 for better understanding
3varun ... the balls are like spongy things... when they collide they deform ... and this deformity is stored as potential energy of the ball.....
1yeah varun..i was thinking the same way as iitimcomin is saying..the balls are spongy stuffs.we can assume tiny springs attached to them in all directions and hence proceed with the proof........and collision doesnt necesarily mean that body must have physical contact,it has to do with the impulse.....