Question

Sphere Σ1 of mass m moves with speed υ and collides centrally and elastically with sphere Σ2 of mass 2m, which moves with speed -υ a) The change of momentum of the system of two spheres due to the impact is equal to ΔΡ = -mu b). The mechanical energy of the system after the impact is less than the mechanical energy of the system before the impact. c). The kinetic energy of the system both before and after the impact is equal with 3/2 mv ^ 2. d) The momentum of the system of the two spheres both before and after the impact is equal to zero. choose the correct answer

Answer 1

Given:

Mass of sphere 1 = m

Speed of sphere 1 = υ

Mass of sphere 2 = 2m

Speed of sphere 2 = -υ

In a system of colliding bodies, the final kinetic energy is less than the initial kinetic energy of the system.

Let's determine the kinetic energy before and after collision using the formula:

`KE=(1)/(2)m_1(v_1)^2+(1)/(2)m_2(v_2)^2_{}`

Thus, we have:

`\begin{gathered} KE=(1)/(2)mu+(1)/(2)\ast2m\ast(-u)^2 \\ \\ KE=(1)/(2)mu^2+m(-u)^2 \\ \\ KE=(1)/(2)mu^2+mu \\ \\ KE=(3)/(2)mv^2 \end{gathered}`

Therefore, the kinetic energy of the system both before and after impact is 3/2 mv².

ANSWER:

c). The kinetic energy of the system both before and after the impact is equal with 3/2 mv².