Answer to Question #167907 in Classical Mechanics for KARREN

Question

A 40t rail car travels at 4km/h and collides with a 100t wagon on the same track, moving in the opposite direction at 1,2km/h

i) Find their velocities immediately after impact, assuming no energy loss [8]

ii) Find the impulse between them [5]

Answer 1

Given,

Mass of the rail car $(m)=40 ton$

Speed of rail car $(u)=4km/h$

Mass of wagon $(M)=100 ton$

Speed o the wagon $(U)=1.2 km/h$

As per the question, both are moving in opposite direction.

Let after the collision, the velocities becomes $v$ and $V$ respectively.

Now, applying the conservation of energy

$mu-MU=mv+MV$

$\Rightarrow 40\times 4-100\times 1.2=40v+100V$

$\Rightarrow 40v+100V=160-120$

$\Rightarrow 40v+100V=40$

$\Rightarrow 2v+5V=2...(i)$

As there is no loss of energy, so total energy always be conserve,

So, the coefficient of elasticity $(e)=1$

$e=\frac{V-v}{u-U}$

$\Rightarrow V-v=4-1.2$

$\Rightarrow V-v=2.8km/h ...(ii)$

From equation (i) and (ii)

$\Rightarrow 7V=5.6+2$

$\Rightarrow V=\frac{7.6}{7}km/hour$

$V=1.08km/hour$

Now, substituting the value of V in equation (ii)

$v=-2.8+1.08$

$=-1.72 km/hour$

here -ive sign indicates that after the collision, both car will move opposite to each other.

ii) Impulse between them = $(mu+mv)+(MU+MV)$

$=40\times 4+40\times 1.72+100\times 1.2+100\times 1.08$

$=160+68.8+120+108$

$=456.8ton-km/hour$