Question

On an air track, a 400.5 g glider moving to the right at 2.30 m/s collides elastically with a 500.0 g glider moving in the opposite direction at 2.95 m/s . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Elastic collision on an air track. Part A Find the velocity of first glider after the collision.

Answer 1

Answer:

3.53 m/s towards the left

Explanation:

$m_1$ = Mass of first glider = 400.5 g

$m_2$ = Mass of Second glider = 500 g

$u_1$ = Initial Velocity of first object = 2.3 m/s

$u_2$ = Initial Velocity of second object = -2.95 m/s

As momentum and Energy is conserved

$m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}$

${\tfrac {1}{2}}m_{1}u_{1}^{2}+{\tfrac {1}{2}}m_{2}u_{2}^{2}={\tfrac {1}{2}}m_{1}v_{1}^{2}+{\tfrac {1}{2}}m_{2}v_{2}^{2}$

From the two equations we get

$v_{1}=\frac{m_1-m_2}{m_1+m_2}u_{1}+\frac{2m_2}{m_1+m_2}u_2\\\Rightarrow v_1=\frac{0.4005-0.5}{0.4005+0.5}\times 2.3+\frac{2\times 0.5}{0.4005+0.5}\times -2.95\\\Rightarrow v_1=-3.53\ m/s$

The velocity of first glider after collision is 3.53 m/s towards the left