First slide

Types of collision

Question

A particle of mass m moving in the X direction with speed 2v is hit by another particle of mass 2m moving in the Y direction with speed v. If the collision is perfectly inelastic, the percentage loss of energy during the collision is close to

Moderate

A

56 %
B

62 %
C

44 %
D

50 %

Solution

Applying conservation of momentum m2v $\hat{i}$ +2mv $\hat{j}$ = 3m $\overset{⇀}{v}'$
final velocity $|\vec{v'}|$ = $\frac{2 \sqrt{2}}{3} v$
final kinetic energy = $\frac{1}{2} 3 m {(\frac{2 \sqrt{2}}{3} v)}^{2} = \frac{4}{3} m v^{2}$
initial kinetic energy = $\frac{1}{2} m {(2 v)}^{2} + \frac{1}{2} (2 m) v^{2} = 3 m v^{2}$
% loss of energy = $\frac{i n i t i a l k i n e t i c e n e g y - f i n a l k i n e t i c e n e r g y}{i n i t i a l k i n e t i c e n e r g y} x 100$ = 56 %

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