Question

If a body of mass 5kg moving with velocity 5m/s collides with target body of same mass at rest then velocity of (incident) body after colision is

Answer 1

Given :

A body of mass 5kg moving with velocity 5m/s collides with another body of same mass at rest.

To Find :

Velocity of second body after collision.

Solution :

❖ In an elastic collision, the kinetic energy conservation holds only after the collision is over. It does not hold during the short duration of actual collision.

» In 1D collision, velocities of second object after the collision is given by

$\dag\:\underline{\boxed{\bf{\orange{ v_2=\dfrac{2m_1}{m_1+m_2}u_1+\dfrac{m_2-m_1}{m_1+m_2}u_2}}}}$

By substituting the given values;

$\sf:\implies\:v_2=\dfrac{2m}{m+m}u_1+\dfrac{m-m}{m+m}u_2$

$\sf:\implies\:v_2=\dfrac{2m}{2m}u_1+0$

$\sf:\implies\:v_2=u_1$

$:\implies\:\underline{\boxed{\bf{\green{v_2=5\:ms^{-1}}}}}$

Knowledge BoosteR :

• When two equal masses suffer a glancing collision with one of them at rest, after the collision, the two masses move at right angles to each other.
• At the time of collision, the two colliding objects are deformed and may be momentarily at rest with respect to each other.

Answer 2

Given :

A body of mass 5kg moving with velocity 5m/s collides with another body of same mass at rest.

To Find :

Velocity of second body after collision.

Solution :

❖ In an elastic collision, the kinetic energy conservation holds only after the collision is over. It does not hold during the short duration of actual collision.

» In 1D collision, velocities of second object after the collision is given by

$\dag\:\underline{\boxed{\bf{\orange{ v_2=\dfrac{2m_1}{m_1+m_2}u_1+\dfrac{m_2-m_1}{m_1+m_2}u_2}}}}$

By substituting the given values;

$\sf:\implies\:v_2=\dfrac{2m}{m+m}u_1+\dfrac{m-m}{m+m}u_2$

$\sf:\implies\:v_2=\dfrac{2m}{2m}u_1+0$

$\sf:\implies\:v_2=u_1$

$:\implies\:\underline{\boxed{\bf{\green{v_2=5\:ms^{-1}}}}}$

Knowledge BoosteR :

When two equal masses suffer a glancing collision with one of them at rest, after the collision, the two masses move at right angles to each other.

At the time of collision, the two colliding objects are deformed and may be momentarily at rest with respect to each other.