Question

A 4.45 g object moving to the right at 18.6 cm/s makes an elastic head-on collision with an 8.9 g object that is initially at rest.
18.6 cm/s
4.45 g
8.9 g
Find the velocity of the first object immediately after the collision. The acceleration of gravity is 9.8 m/s 2 . Answer in units of cm/s.

Answer 1

Answer:

v₁f = -6.2 cm/s

Explanation:

• Assuming no external forces acting during the collision, total momentum must be conserved, as follows:

        $m_{1} *v_{1o} = m_{1}* v_{1f} + m_{2}* v_{2f}$

• As the collision is elastic, total kinetic energy must be conserved also:

       $\frac{1}{2}*m_{1}*v_{1o}^{2} = \frac{1}{2}*m_{1}*v_{1f} ^{2} + \frac{1}2}*m_{2}*v_{2f}^{2}$

• From the givens, we know that m₂ = 2* m₁
• Replacing in the above equations, rearranging both sides and simplifying, we can find the following expression for v₁f:

       $v_{1f} = \frac{-m_{1} }{3*m_{1}} *v_{1o} =\frac{-v_{1o}}{3} = -\frac{18.6 cm/s}{3} = -6.2 cm/s$

• v₁f = -6.2 cm/s (which means that it bounces back after the collision).