Question

A mine car, whose mass is 440kg, rolls at a speed of 0.50m/s on ahorizontal track, as the drawing shows. A 150kg chunk of coalhas a speed of 0.80m/s when it leaves the chute. Determinethe velocity of the car/coal system after the coal has come to restin the car.

Answer 1

Answer: 0.56 m/s

Explanation:

hello, there is 25° inclination angle for the chute in the drawing. Thankfully, I know this problem. The conservation of momentum.

so there are X and Y components for the momentum in this problem. The Y component is not conserved as when the coal gets in the cart, the normal force exerted by the surface reduces it to 0.

Now, the X component is definitely conserved here.

so you have the momentum of the cart which is 440*0.5 added to the momentum of the chunk which is 150*0.8*cos(25°), that is the momentum before the coupling between the objects. Afterwards both objects will have the same velocity, so we write the equation like this:

$440*0.5 + 150*0.8*cos(25) = 440*v_{final} + 150*v_{final} \\ => 220+120*cos(25) = (440+150)v_{final} => v_{final} = \frac{220+120*cos(25)}{590} = 0.56 m/s$