A train consisting of a locomotive, three passenger cars, and a caboose are coas

Question

A train consisting of a locomotive, three passenger cars, and a caboose are coasting along a straight track at 75 m/s. Each car, including the locomotive, has the same mass of 1500-kg. Ignore any masses of people or objects on the train. The caboose has a safe full of gold which some thieves want to steal. Their plan is to detonate some TNT between the caboose and the rest of the train to free the caboose and bring it to rest on the tracks.

TNT, when detonated, will release 4,184 J for every gram present. How many grams will the thieves need to pull off their scheme and stop the caboose?

Notes

The answer is 1.2 kg of TNT.

You will need to consider both momentum and energy to solve this problem.

Think carefully about how to divide the train into two objects.

Explanation / Answer

Conserving momentum of the system :

(3*1500 + 1500)*75 + 1500*75 = 1500*0 + (4*1500)*v

So, v = (5/4)*75 = 93.8 m/s

Now, conserving energy,

0.5*(5*1500)*75^2 = 0.5*(1500)*0^2 + 0.5*(4*1500)*(93.8)^2 + X

here X = energy released

So, X = 5.3*10^6 J

Now, 1 g of TNT = 4184 J

So, mass required = 5.3*10^6/4184 = 1266 g = 1.266 kg

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.