Question

Number 1. Part b: what are the final kinetic energy of the system

Answer 1

Given that there is a cart of mass, m = 0.12 kg moving with initial speed of, u1 = 0.45 m/s and it collides with another cart of mass, m = 0.12 kg with initial speed, u2 = 0 m/s

We have to find the initial and final kinetic energy.

(a) Initial kinetic energy,

`\begin{gathered} K\mathrm{}E.1=(1)/(2)mv^2 \\ =(1)/(2)*0.12*(0.45)^2 \\ =0.012\text{ J} \end{gathered}`

According to the conservation of linear momentum,

`mu1+mu2=2mv`

Here, v is the final speed.

`\begin{gathered} 0.12*0.45=2*0.12* v \\ v=(0.45)/(2) \\ =0.225\text{ m/s} \end{gathered}`

Here, the final speed is 0.225 m/s.

(b) The formula to find kinetic energy is

`K\mathrm{}E\mathrm{}=(1)/(2)(2m)v^2`

Substituting the values, we get

`\begin{gathered} K\mathrm{}E\mathrm{}=0.12*(0.225)^2 \\ =6.075*10^(-3)\text{ J} \end{gathered}`

Hence the kinetic energy is 6.075 x 10^(-3) J.