Inelastic collision. Two objects (M1=2 g ; M2=5 g) possess velocities 𝐯1=10 𝐱̂ cm / s and 𝐯2=3

step 1 So in this case, M1 is 2 gram and M2 is 5 gram. In velocity, initial, V1 is 10x kept, and V2 is

Inelastic collision. Two objects (M1=2 g ; M2=5 g) possess...

Inelastic collision. Two objects $\left(M_{1}=2 \mathrm{~g} ; \mathrm{M}_{2}=5 \mathrm{~g}\right)$ possess velocities $\mathbf{v}_{1}=10 \hat{\mathbf{x}} \mathrm{cm} / \mathrm{s}$ and $\mathbf{v}_{2}=3 \hat{\mathbf{x}}+5 \hat{y} \mathrm{~cm} / \mathrm{s}$ just prior to a collision during which they become permanently attached to each other. (a) What is their final velocity? (b) What fraction of the initial kinetic energy is lost in the collision?

Inelastic collision. Two objects $\left(M_{1}=2 \mathrm{~g} ; \mathrm{M}_{2}=5 \mathrm{~g}\right)$ possess velocities $\mathbf{v}_{1}=10 \hat{\mathbf{x}} \mathrm{cm} / \mathrm{s}$ and $\mathbf{v}_{2}=3 \hat{\mathbf{x}}+5 \hat{y} \mathrm{~cm} / \mathrm{s}$ just
prior to a collision during which they become permanently attached to each other.
(a) What is their final velocity?
(b) What fraction of the initial kinetic energy is lost in the collision?

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Key Concepts

Kinetic Energy Loss

In perfectly inelastic collisions, while momentum is conserved, a portion of the kinetic energy is not conserved and is lost due to factors such as deformation, sound, and heat. Calculating the fraction of kinetic energy lost involves comparing the total kinetic energy before and after the collision.

Vector Addition of Velocities/Momenta

In problems involving collisions, velocities and momenta are vector quantities. This means that their components along each axis have to be added separately, allowing the determination of the final velocity vector after the collision by summing the momenta of the individual objects.

Inelastic Collision

An inelastic collision is a type of collision in which the colliding objects stick together after impact. In such collisions, while momentum is conserved, kinetic energy is not conserved because some of it is transformed into other forms of energy like heat or sound.

Conservation of Momentum

This principle states that the total momentum before the collision is equal to the total momentum after the collision, provided no external forces act on the system. In collisions involving vector quantities, both magnitude and direction must be considered in the momentum calculations.

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