Answer to Question #162402 in Physics for Andu

Question

3. The cart with a mass of 4kg and a speed of 3m / s, hits a second cart with a mass of 2kg, which is at rest.
Find the size and speed direction of the second wheelchair after hitting the first wheelchair. Friction is not taken into account.

Answer 1

From the law of conservation of momentum we have:

$$m_1u_1=m_1v_1+m_2v_2.$$

Since collision is perfectly elastic, kinetic energy is conserved and we can write:

$$\dfrac{1}{2}m_1u_1^2=\dfrac{1}{2}m_1v_1^2+\dfrac{1}{2}m_2v_2^2.$$

This formula gives us an additional relationship between velocities. Therefore, with the help of these two formulas we can find the velocity of the second cart after the collision:

$$v_2=\dfrac{2m_1}{(m_1+m_2)}u_1,$$ $$v_2=\dfrac{2\cdot4\ kg}{(4\ kg+2\ kg)}\cdot3\ \dfrac{m}{s}=4\ \dfrac{m}{s}.$$

The sign plus means that the second cart moves to the right.