A 50 g bullet moving with a velocity of 10 ms^-1 gets embeded into a 950 g stationary body. Th

A 50 g bullet moving with a velocity of 10 ms^-1 gets...

Key Concepts

Conservation of Momentum

In any collision, especially when external forces are negligible, the total momentum of the system remains constant. This principle helps in determining the final velocity of the combined masses after a collision occurs, regardless of whether the collision is elastic or inelastic.

Perfectly Inelastic Collision

A perfectly inelastic collision is one in which the colliding objects stick together after impact and move as a single object. In such collisions, while momentum is conserved, some of the initial kinetic energy is transformed into other forms of energy such as heat, sound, or deformation energy.

Kinetic Energy Loss in Inelastic Collisions

In inelastic collisions, the kinetic energy after the collision is less than the kinetic energy before the collision. The loss of kinetic energy is not recovered in the motion of the objects; instead, it is dissipated as other forms of energy, marking the intrinsic inefficiency of energy transfer in such collision processes.

Transcript

00:01 In this question we have given that a fifty gram bullet moving with a velocity of ten meter per second got embedded into a nine fifty gram stationary body then we have to find the loss in kinetic energy of the system that this is the body which is initially in rest and let the mass of this body is m two and its velocity is initial velocity is u two and there is a bullet here whose mass is m1 and let's its initial velocity is u1 now after the collision both the system will move with the velocity let this is v and there is a bullet in this body so we can so first time calculating the final velocity of the system so we can say that given data for this question is that is mass of blate m1 is 50 gram we have given its initial speed that is u1 is 10 meter per second.

01:15 We have given the mass of the body that is m2 is 950 gram and we have given its initial speed u2 that is 0 because it is initially in stationary now we can say that according to conservation of momentum that is the initial momentum of the system before the collision which is m1 u1 plus m2 u2 that is equals to final momentum that is m1 plus m2 into v so we can say this is 50 into 10 plus this is 0 because initially rest that is equals to this is 50 plus 950 into v so from here we can see that the final velocity v is meter per second now we can say that the initial kinetic energy that is e1 is equals to this is half m1 u1 square plus half m2 u2 square so this is half into masses 50th into 10 to the power minus 3 this is in kilogram into 10 square plus this is 0 and this will comes out 2 .5 jule this is the initial kinetic energy of the system and we can say that the final kinetic energy of the system is that is e2 is half into total mass that is m m1 plus m2 into final velocity square this is half into this is 50 plus 950 into 10 to the power minus 3 into this is 0 .5 square and this will comes out 0 .1 to 5 jule so we can say that the percentage loss in kinetic energy will be so percentage loss in kinetic energy is given by this is e1 minus e2 e1 into 100 this is 2 .5 minus 0 .125 upon 2 .5 into 100 and that is equal to 95%...

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