Question

I need help with additional problems 6.1 AA and 6.1 B

Answer 1

Given that the mass of toy car is, m = 1.45 kg and the mass of toy train is, M = 3.85 m/s.

The initial velocity of the toy train is u_t = 2.05 m/s.

The initial velocity of the toy car is u_c = 4.75 m/s

After the collision, the final velocity of the toy car is v_c = 2.05 m/s

(a) The final velocity of the toy train can be obtained using the conservation of momentum,

`\begin{gathered} mu_(_c)+Mu_t_{}=mv_c+Mv_(_t) \\ v_t=(mu_c+Mu_t-mv_c)/(M) \\ =(11.8075)/(3.85) \\ =3.06\text{ m/s} \end{gathered}`

(b) Initial kinetic energy is

`\begin{gathered} KE._i=(1)/(2)m(u_c)^2+(1)/(2)M(u_t)^2 \\ =(1)/(2)1.45(4.75)^2+(1)/(2)3.85(2.05)^2 \\ =24.4476\text{ J} \end{gathered}`

Final kinetic energy is

`\begin{gathered} KE._f=(1)/(2)m(v_c)^2+(1)/(2)M(v_t)^2 \\ =(1)/(2)1.45(2.05)^2+(1)/(2)3.85(3.06)^2 \\ =21.0717\text{ J} \end{gathered}`

Thus, a change in kinetic energy will be

`\begin{gathered} \Delta KE=KE._f-K.E._i \\ =21.06-24.43 \\ =-3.3759\text{ J} \end{gathered}`