Question

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?

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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