A particle of mass m moving with speed u collides perfectly inelastically with another particle of mass 2m at rest - Physics - Work Energy and Power

Question

A particle of mass m moving with speed u collides perfectly
inelastically with another particle of mass 2m at rest find loss of
kinetic energy of system in the collisions

Teja Teppala · Accepted Answer

Dear Student,

Let the first particle be of mass mA=m and initial speed vA=u
Let the first particle be of mass mB=2m and initial speed vB=0
It is given that the first particle collides perfectly inelastically with the second particle
⇒They stick together
Let their combined mass be msys=(m+2m)=3m; and their final velocity be vsys
Now, from the law of conservation of momentum,initial momentum of the system = final momentum of the system
⇒mAvA+mBvB=msysvsys⇒(m·u) + (2m·0)=3m·vsys⇒mu=3m·vsys⇒vsys=m3m·u⇒vsys=u3
The initial kinetic energy = 12mAvA2 + 12mBvB2⇒Initial K
E
 = 12m·u2 + 12(2m)·02 = 12mu2 The final kinetic energy = 12msysvsys2⇒Final K
E
 =12(3m)·u32=12·3mu29=16mu2⇒Fractional loss in K
E = Initial K E  - Final K E
Initial K E
×100 =12mu2 -16mu212mu2 ×100⇒=13mu2 12mu2 ×100⇒=23×100⇒≃67%

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A particle of mass m moving with speed u collides perfectly inelastically with another particle of mass 2m at rest .find loss of kinetic energy of system in the collisions