Question

An object with velocity 1.4 m/s i and mass 0.27 kg collides with an object whose...

An object with velocity 1.4 m/s i and mass 0.27 kg collides with an object whose velocity is -2.5 m/s i and whose mass is 0.12 kg. The motion takes place in one dimension. (a) What are the final velocities of the objects if the collision is elastic? b.) What is the total initial kinetic energy in the collision?

Homework Answers

Answer #1

ELASTIC COLLISION ONE DIMENSIONAL


m1 = 0.27 kg                   m2 = 0.12 kg


speeds before collision


u1 = 1.4i                     u2 = -2.5i m/s

speeds after collision


v1 = ?                         v2 = ?


initial momentum before collision


Pi = m1*u1 + m2*u2

after collision final momentum

Pf = m1*v1 + m2*v2

from moentum conservation


total momentum is conserved

Pf = Pi


m1*u1 + m2*u2 = m1*v1 + m2*v2 .....(1)


from energy conservation


total kinetic energy before collision = total kinetic energy after collision


KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2


KEf =   0.5*m1*v1^2 + 0.5*m2*v2^2


KEi = KEf


0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2 .....(2)

solving 1&2


we get

v1 = [ ((m1-m2)*u1) + (2*m2*u2) ] /(m1+m2)

a)


v1 = ( ((0.27-0.12)*1.4) - (2*0.12*2.5) ) /(0.27+0.12)

v1 = -1 i m/s

v2 = ( ((m2-m1)*u2) + (2*m1*u1) ) /(m1+m2)

v2 = ( 0-((0.12-0.27)*2.5) + (2*0.27*1.4) ) /(0.27+0.12)


v2 = 2.9 i m/s


b)


KE = 0.5*m1*u1^2 + 0.5*m2*u2^2 = (0.5*0.27*1.4^2) +(0.5*0.12*2.5^2) = 0.6396 J

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