A body m, rests on the smooth floor while another body m2 is placed on top. All surfaces are smo

step 1 Problem number 107. 107 in which there is a body M1 which rests on the smooth floor where anothe

A body m, rests on the smooth floor while another body m2 is...

A body $\mathrm{m}$, rests on the smooth floor while another body $\mathrm{m}_{2}$ is placed on top. All surfaces are smooth. If a velocity $\mathrm{v}_{0}$ is given to $\mathrm{m}_{1}$ towards the right, and the collision of $\mathrm{m}_{2}$ with the side of $\mathrm{m}_{1}$ is elastic the time taken for $\mathrm{m}_{2}$ to slide off is $\left(\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}}=\mathrm{k}\right)$ (a) $\left(\frac{2 \mathrm{k}+3}{\mathrm{k}+1}\right)\left(\frac{\mathrm{d}}{\mathrm{v}_{0}}\right)$ (b) $\frac{2 \mathrm{~d}}{\mathrm{v}_{0}}, \frac{1}{\mathrm{k}+1}$ (c) $\frac{3 \mathrm{~d}}{\mathrm{v}_{0}}$ (d) $\frac{1-k}{1+k} \cdot \frac{d}{v_{0}}$

A body $\mathrm{m}$, rests on the smooth floor while another body $\mathrm{m}_{2}$ is placed on top. All surfaces are smooth. If a velocity $\mathrm{v}_{0}$ is given to $\mathrm{m}_{1}$ towards the right, and the collision of $\mathrm{m}_{2}$ with the side of $\mathrm{m}_{1}$ is elastic the time taken for $\mathrm{m}_{2}$ to slide off is $\left(\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}}=\mathrm{k}\right)$
(a) $\left(\frac{2 \mathrm{k}+3}{\mathrm{k}+1}\right)\left(\frac{\mathrm{d}}{\mathrm{v}_{0}}\right)$
(b) $\frac{2 \mathrm{~d}}{\mathrm{v}_{0}}, \frac{1}{\mathrm{k}+1}$
(c) $\frac{3 \mathrm{~d}}{\mathrm{v}_{0}}$
(d) $\frac{1-k}{1+k} \cdot \frac{d}{v_{0}}$

Key Concepts

Elastic Collision

An elastic collision is a type of collision in which both momentum and kinetic energy are conserved. In problems involving elastic collisions, equations are set up to ensure that the total momentum before the collision equals the total momentum after the collision, and similarly for the kinetic energy, allowing for the determination of velocities post-collision.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system with no external forces, the total momentum remains constant regardless of the collision events that occur within the system. This concept is essential in analyzing collision problems, as it provides a relationship between the masses and velocities of the bodies involved before and after the collision.

Relative Motion Analysis

Relative motion analysis involves studying the movement of one body with respect to another. This is important in problems where multiple bodies interact, since the effective velocity as seen from a moving reference frame (such as one of the colliding bodies) is used to determine collision times and paths. This method simplifies the analysis of successive collisions or interactions in the system.

Frictionless Dynamics

In systems where all the contacting surfaces are smooth (frictionless), there is no energy loss due to friction. This simplifies the calculations by ensuring that no energy is dissipated through heat, allowing kinetic energy conservation (in elastic collisions) and momentum conservation to be the key tools for analyzing the motion and interactions of the bodies involved.

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