Answer to Question #198858 in Physics for Loc

Question

A man of mass m₁= 70.0 kg is skating at v1= 8.00 m/s behind his wife of mass m₂= 50.0 kg, who is skating at v₂=4.00 m/s. Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. (a) Sketch the problem with before - and - after diagrams, representing the skaters as blocks. (b) Is the collision best described as elastic, inelastic, or perfectly inelastic? Why? (c) Write the general equation for conservation of momentum in terms of m₁, v₁, m₂, v₂, and final velocity vf . (d) Solve the momentum equation for v_f

Answer 1

(a) Let's draw before- and after diagrams:

(b) Collision is perfectly inelastic, because it occurs when the maximum amount of kinetic energy of a system is lost. As a result, there is a zero coefficient of restitution and colliding bodies stick together.

(c) From the lwa of conservation of momentum, we have:

$$m_1v_1+m_2v_2=(m_1+m_2)v_f.$$

(d)

$$v_f=\dfrac{m_1v_1+m_2v_2}{m_1+m_2},$$ $$v_f=\dfrac{70\ kg\cdot8\ \dfrac{m}{s}+50\ kg\cdot4\ \dfrac{m}{s}}{70\ kg+50\ kg}=6.3\ \dfrac{m}{s}.$$