Question

A mine car (mass=420 kg) rolls at a speed of 0.50 m/s on a horizontal track, as the drawing shows. A 250-kg chunk of coal has a speed of 0.85 m/s when it leaves the chute. Determine the speed of the car–coal system after the coal has come to rest in the car.

250 kg 25.0° 0.85 m/s 420 kg 0.50 m/s

Answer 1

here,

the mass of car ,m1 = 420 kg

initial speed of car 1 , u1 = 0.5 m/s

the mass of chunk , m2 = 250 kg

speed of coal , u2 = 0.85 m/s

let the speed of the car–coal system after the coal has come to rest in the car be v

using conservation of momentum

m1 * u1 + m2 * u2 * cos(theta) = (m1 + m2) * v

420 * 0.5 + 250 * 0.85 * cos(25) = (420 + 250) * v

solving for v

v = 0.6 m/s

the speed of the car–coal system after the coal has come to rest in the car is 0.6 m/s