Answer to Question #182931 in Physics for Andu

Question

15. A sphere with mass m1 = 2kg and moving at a speed of 10m / s hits another sphere with mass m2 = 3kg that is at rest at point A. After hitting the spheres continue to move together and stop at point B.

The coefficient of friction of bodies with horizontal surface AB is 0.1. Calculate:

A) The velocity of the spheres after impact

B) The work of frictional forces

C) The distance AB traversed by spheres until they stop

Answer 1

A) The velocities after impact:

$$m_1v_1=(m_1+m_2)v_2,\\\space\\ v_2=v_1\frac{m_1}{m_1+m_2}=4\text{ m/s}.$$

B) The work of frictional forces was equal to the kinetic energy:

$$W=KE=\frac12 (m_1+m_2)v_2^2=40\text{ J}.$$

C) The force of friction was

$$f=\mu(m_1+m_2)g.$$

The work by frictional forces:

$$W=KE=fd,\\\space\\ d=\frac{W}{f}=\frac{W}{\mu(m_1+m_2)g}=8.2\text{ m}.$$