Question

A 3.0-kg mass sliding on a frictionless surface has a velocity of 5.0 m/s east when it undergoes a one-dimensional inelastic collision with a 2.0-kg mass that has an initial velocity of 2.0 m/s west. After the collision the 3.0-kg mass has a velocity of 1.0 m/s east. How much kinetic energy does the two-mass system lose during the collision?

Answer 1

Answer:

24 J

Explanation:

given,

mass of the block 1, M = 3 Kg

initial speed in east direction, u = 5 m/s

mass of the block 2, m = 2 Kg

initial speed in west direction, u' = 2 m/s

final speed of block 1, after collision, V = 1 m/s

Kinetic energy loss during collision = ?

taking east direction positive

using conservation of momentum

M u + m u' = M V + m V'

3 x 5 + 2 x(-2) = 3 x 1 + 2 x V'

2 x V' = 8

 V' = 4 m/s

loss in kinetic energy

=$KE_i - KE_f$

=$(\dfrac{1}{2}Mu^2+\dfrac{1}{2}mu'^2) - (\dfrac{1}{2}MV^2+\dfrac{1}{2}mV'^2)$

=$(\dfrac{1}{2}\times 3 \times 5^2+\dfrac{1}{2}\times 2 \times (-2)^2) - (\dfrac{1}{2}\times 3 \times 1^2+\dfrac{1}{2}\times 2 \times 4^2)$

= 24 J

loss in kinetic energy is equal to 24 J