A particle moving with a velocity v in +x direction has an inelastic collision with a wall movin

step 1 we have problem number 104 in which there is a particle first of all one figure is being given t

A particle moving with a velocity v in +x direction has an...

A particle moving with a velocity $\mathrm{v}$ in $+\mathrm{x}$ direction has an inelastic collision with a wall moving in opposite direction with a speed $\mathrm{V}$ and coefficient of restitution is e. If the speed of the ball remains same after collision then $\mathrm{V}$ is (modulus value) (a) $\frac{1-\mathrm{e}}{1+\mathrm{e}} \mathrm{v}$ (b) $\frac{1-\mathrm{e}}{1+2 \mathrm{e}} \mathrm{v}$ (c) $\frac{1-e}{1+e} v^{2}$ (d) $\frac{1-2 e}{1+e} v$

A particle moving with a velocity $\mathrm{v}$ in $+\mathrm{x}$ direction has an inelastic collision with a wall moving in opposite direction with a speed $\mathrm{V}$ and coefficient of restitution is e. If the speed of the ball remains same after collision then $\mathrm{V}$ is (modulus value)
(a) $\frac{1-\mathrm{e}}{1+\mathrm{e}} \mathrm{v}$
(b) $\frac{1-\mathrm{e}}{1+2 \mathrm{e}} \mathrm{v}$
(c) $\frac{1-e}{1+e} v^{2}$
(d) $\frac{1-2 e}{1+e} v$

Key Concepts

Reference Frame Transformation

Transforming to a different inertial frame, such as shifting to the reference frame of a moving wall, allows for easier application of conservation laws and collision principles. This technique helps isolate the intrinsic characteristics of the collision, such as the effects due solely to the coefficient of restitution, independent of the overall motion of the system.

Coefficient of Restitution

This is a measure of how 'bouncy' a collision is, defined as the ratio of the relative speed after collision to the relative speed before collision along the line of impact. It quantifies the elasticity of the collision, with a value of 1 representing a perfectly elastic collision (no kinetic energy lost) and a value less than 1 indicating an inelastic collision (with loss of kinetic energy).

Relative Velocity in Collisions

In collision analysis, using the concept of relative velocity helps simplify the problem by considering the velocities of objects with respect to one another. This is particularly useful when one of the objects is moving since the collision’s behavior can be effectively analyzed by shifting to a frame where one object is momentarily at rest.

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