In some of the problems you will combine the two concepts conservation of energy

Question

In some of the problems you will combine the two concepts conservation of energy and conservation of momentum.

1) Two railraod cars start from rest rolling down an inclined track. At the bottom of the track, they collide and couple with a third car. The final speed of the three coupled cars should not exceed 0.73 m/s. What is the maximum height from which the two cars can be released?

(Assume that all three cars have the same mass. Ignore any friction)

2) A railraod car is moving on a level (horizontal) track. It collides and couples with two other cars. Together the three cars should move up an inclined track to a height of 0.053 m and come to rest. What must be the initial speed of the moving car?

(Assume that all three cars have the same mass. Ignore any friction.)

Explanation / Answer

here,

let the mass of cars be m

let the height of the incline be h

let the velocity before the collison of two cars be u

v = 0.73 m/s

using conservation of momentum

2*m*u = ( 2m+m)*v

2*u = 3*0.73

u = 1.095 m/s

using conservation of energy

2m*g*h = 0.5 * 2 * m*u^2

9.8 * h = 0.5 * 1.095^2

h = 0.06 m

the height of the incline is 0.06 m

2.

let the mass of cars be m

let the height of the incline be h

let the velocity before the collison of two cars be u

h = 0.053 m

using conservation of momentum

2*m*u = ( 2m+m)*v

v = 2/3 *u

using conservation of energy

2m*g*h = 0.5 * 2 * m*v^2

9.8 * 0.053 = 0.5 * (2/3 * u)^2

u = 1.53 m/s

the initial speed of the moving car is 1.53 m/s

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