A mine car, whose mass is 590 kg, rolls at a speed of 0.5 m/s on a horizontal track, as the drawing shows. A 150 kg chunk of coal has a speed of 0.95 m/s when it leaves the chute. Determine the velocity of the car/coal system after the coal has come to rest in the car.
mass of cart (velocity of cart) + mass of car(velocity of car) = (total mass)velocity
solve for "velocity"
To determine the velocity of the car/coal system after the coal has come to rest in the car, we will use the principle of conservation of linear momentum.
The initial momentum of the system is equal to the final momentum of the system.
The total momentum before the coal enters the car is given by:
Initial momentum = (Mass of the mine car) × (Velocity of the mine car)
The total momentum after the coal comes to rest in the car is given by:
Final momentum = (Mass of the mine car + Mass of the coal) × (Final velocity of the system)
Since momentum is conserved, we can equate the initial and final momenta:
(Mass of the mine car) × (Velocity of the mine car) = (Mass of the mine car + Mass of the coal) × (Final velocity of the system)
Substituting the given values:
(590 kg) × (0.5 m/s) = (590 kg + 150 kg) × (Final velocity of the system)
Now, we can solve for the final velocity of the system:
Final velocity of the system = (590 kg × 0.5 m/s) / (590 kg + 150 kg)
Final velocity of the system ≈ 0.3571 m/s
Therefore, the velocity of the car/coal system after the coal has come to rest in the car is approximately 0.3571 m/s.
To determine the velocity of the car/coal system after the coal has come to rest in the car, we can apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it.
The momentum of an object is given by the product of its mass and velocity. In this case, we have two objects: the mine car and the chunk of coal.
Before the coal enters the car, we can write the initial momentum of the system as:
Initial momentum = (mass of car * velocity of car) + (mass of coal * velocity of coal)
After the coal comes to rest in the car, the velocity of the coal becomes zero. Therefore, the final momentum of the system can be written as:
Final momentum = (mass of car * velocity of car) + (mass of coal * 0)
According to the conservation of momentum, since no external forces act on the system, the initial momentum should be equal to the final momentum.
Therefore, we can set up the following equation:
(mass of car * velocity of car) + (mass of coal * velocity of coal) = (mass of car * velocity of car) + (mass of coal * 0)
Simplifying the equation, we get:
(mass of car * velocity of car) = (mass of car * velocity of car)
Since both sides of the equation are equal, this means that the velocity of the car/coal system after the coal has come to rest in the car is equal to the initial velocity of the car, which is 0.5 m/s.