Question

1. A sphere of mass 25kg
is movie at a speed
of 1.5m/s undergous
collision with another
sphere of mass 50kg moving at 3m/s in the same direction,
find the common velocity
in m/s after collision is completely inelastic and also
find loss in kinetic energy due to collision​

Answer 1

Answer:

Mass 1 (m₁) = 25 kg

Initial Velocity (u₁) = 1.5 m/s

Mass 2 (m₂) = 50 kg

Initial Velocity (u₂) = 3 m/s

Let v₀ be the velocity of the combined mass after an inelastic collision between them.

According to the law of conservation of momentum.

m₁u₁+m₂u₂ = v₀(m₁+m₂)

= (25*1.5) + (50*3) = v₀(25+50)

= 37.5+150 = 75v₀

= 187.5 = 75v₀

= 2.5 m/s = v₀

Initial K.E = K.E of m₁+K.E of m₂

= 1/2m₁u₁² + 1/2m₂u₂²

= [0.5*25*1.5*1.5] + [0.5*50*3*3]

= 28.125 + 225

= 253.125 J

Final K.E = 1/2(m₁+m₂)v₀²

= [0.5*(25+50)*2.5*2.5]

= [0.5*75*2.5*2.5]

= 234.375 J

Loss in K.E = Initial K.E - Final K.E

= 253.125 - 234.375 J

= 18.75 J

I hope this helps.