Question

A block of mass $0.50kg$ is moving with a speed of $2.00ms$ on a smooth surface. It strikes another mass of $1.00kg$ and then they move together as a single body. The energy loss during the collision is

• A. $0.67J$
• B. $0.34J$
• C. $0.16J$
• D. $1.00J$

Answer 1

The correct option is A $0.67J$

Momentum is conserved in horizontal direction during a collision.

Let the final velocity attained by the combined mass be $v$

Thus Initial momentum= Final momentum

$⟹m_1{v}_1+m_2{v}_2=(m_1+m_2)v$

$⟹v=\frac{\left(0.5\right)\left(2\right)+\left(1\right)\left(0\right)}{1.5}=\frac{2}{3}m/s$

Thus energy lost=$\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2-\frac{1}{2}(m_1+m_2)v^2$

$=\frac{1}{2}\left(0.5\right)(2{)}^2+0-\frac{1}{2}(1.5\left)\right(\frac{2}{3}{)}^2$

$=0.67J$