A 8800 kg railroad car is rolling at 2.4 m/s when a 3100 kg load of gravel is suddenly dropped in. What is the car's speed (in m/s) just after the gravel is loaded?
how do I relate these, I am confused.
To relate the initial speed of the railroad car to its speed after the load of gravel is dropped, you can use the principle of conservation of momentum. The total momentum before the gravel is loaded is equal to the total momentum after the gravel is loaded.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is equal to the mass (m) multiplied by the velocity (v), represented as p = m * v.
Before the load of gravel is dropped, the momentum of the system (railroad car + gravel) is given by:
Initial momentum = (mass of railroad car) * (initial velocity of railroad car)
After the gravel is loaded, the momentum of the system is given by:
Final momentum = (mass of railroad car + mass of gravel) * (final velocity of the system)
Since the total momentum before and after loading the gravel should be the same (as no external forces are acting on the system), we can set up the equation:
Initial momentum = Final momentum
(8800 kg * 2.4 m/s) = (8800 kg + 3100 kg) * (final velocity of the system)
Simplifying the equation:
21120 kg·m/s = 11900 kg * (final velocity of the system)
To find the final velocity of the system (car + gravel), divide both sides of the equation by 11900 kg:
(final velocity of the system) = 21120 kg·m/s / 11900 kg
Calculating the final velocity:
(final velocity of the system) ≈ 1.776 m/s
Therefore, the car's speed just after the gravel is loaded is approximately 1.776 m/s.
To solve this problem, we can use the principle of conservation of momentum. The momentum before the gravel is loaded is equal to the momentum after the gravel is loaded.
The momentum of an object is given by the equation:
momentum = mass × velocity
Before the gravel is loaded, the momentum of the railroad car is:
momentum_before = mass_car × velocity_car
After the gravel is loaded, the momentum of the railroad car and the gravel is:
momentum_after = (mass_car + mass_gravel) × velocity_after
We know the mass of the car (8800 kg), the mass of the gravel (3100 kg), and the initial velocity of the car (2.4 m/s).
Since momentum before = momentum after, we can set up an equation to solve for the velocity_after:
mass_car × velocity_car = (mass_car + mass_gravel) × velocity_after
Plug in the values:
8800 kg × 2.4 m/s = (8800 kg + 3100 kg) × velocity_after
Now we can solve for the velocity_after:
8800 kg × 2.4 m/s = 11900 kg × velocity_after
21120 kg·m/s = 11900 kg × velocity_after
velocity_after = 21120 kg·m/s / 11900 kg
Therefore, the car's speed just after the gravel is loaded is approximately 1.775 m/s.