Consider the collision of two balls, one with mass m1 = m and a second with mass
ID: 2019814 • Letter: C
Question
Consider the collision of two balls, one with mass m1 = m and a second with mass m2 = 2m. Initially the lighter ball moves with speed v1i and the second is at rest. The collision all happens in one dimension; along a straight line.a) If the collision between these balls is perfectly inelastic, what is the final speed of the combined object after the collision? in terms of v1i.
b) Imagine the same collision again, this time it happens elastically, with all the kinetic energy conserved. What is the final speed for mass m2?
Explanation / Answer
b)We know that in an elastic collision momentum remains conserved. Let the final velocities of masses m and 2m are V1 and V2 mv1=2mV2 +mV1 That gives v1=V2+V1 Also kinetic energy remain conserved so 0.5mv1^2=0.5mV1^2 + 0.5*2*m*V2^2 That gives v1^2=V1^2 + 2 V2^2 So put the value of v1 fron first equation we wil get V1^2 + V2^2 +2*V1*V2= V1^2 + 2V2^2 That gives V2=2V1 a)In case of inelastic collision momentum remains conserved Let finally both the masses moves with the speed V So mv1=(m+2m)V That gives V=v1/3