A railroad car starts from rest rolling down an inclined track. At the bottom of

Question

A railroad car starts from rest rolling down an inclined track. At the bottom of the track, it collides and couples with two other cars. The final speed of the three coupled cars should not exceed 1.85m/s. What is the maximum height from which the car can be released? (Assume that all three cars have the same mass. Ignore any friction.)

railroad car starts from rest rolling down an inclined track. The bottom of the track, it collides and couples with two other cars, The final speed of the three coupled cars should not exceed 1.85m/s. What is the maximum height from which the car can be released?. (Assume that all three cars have the same mass. Ignore any friction. Start from the basic equations on the formula sheet. Clearly state all known quantities. Then show the individual steps of your work. Always use with numbers. Just the right answer will not give full credit.)

Explanation / Answer

since the collsion is inelastic all the bodies will go together with a common speed given V = 1.85 m/sec

we can conserve momentum just before and just after collision

since the block comes from height H , by conserving energy   we get speed U just before collision = (2gH )^0.5

MU =3MV

H = 1.571 m

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