Answer to Question #102738 in Classical Mechanics for No-am

Question #102738
A 40 tonnes rail car travels at 4km/h collides with a 100 tonnes wagon moving on the same track in the opposite direction at 1.2 km/h. Find their velocities immediately after impact assuming no loss of energy.
1
Expert's answer
2020-02-11T10:09:43-0500

Weight of the rail car "(m_1)" =40tons

Velocity "(u_1)" =4Km/hour

Mass of the wagon"(m_2)" =100 tons

Velocity of wagon"(u_2)" =1.2k/hour

Let the final velocity of the rail wagon("v_1") and the final velocity of wagon ("v_2" )

Now, applying the conservation of the linear momentum.

"m_1u_1+m_2u_2=m_1v_1+m_2v_2"

"40v_1+100v_2=40 \\times4-100\\times1.2"

"\\Rightarrow 40v_1+100v_2=160-120=40"

"\\Rightarrow 2v_1+5v_2=2--------(i)"

The collision is elastic,

So, e=1

"e=\\dfrac{v_2-v_1}{u_1-u_2}"

"\\Rightarrow 1=\\dfrac{v_2-v_1}{4-1.2}"

"v_2-v_1=2.8----(ii)"

From equation (i) and (ii)


"v_1=\\dfrac{-12}{7} km\/hour"


"v_2=\\dfrac{7.6}{7}km\/hour"



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Comments

Assignment Expert
12.02.20, 17:02

Yes, since the collision is elastic, the car and wagon will not merge after impact.

No-am
11.02.20, 19:30

So it would be wrong to assume that the car and the wagon merge after impact?

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