A 1.46 × 10
4
kg railroad car moving at 7.05
m/s to the north collides with and sticks toanother railroad car of the same mass that is
moving in the same direction at 1.76 m/s.
What is the velocity of the joined cars after
the collision?
Answer in units of m/s
To find the velocity of the joined cars after the collision, we can use the law of conservation of linear momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the initial momentum before the collision by multiplying the mass of each car by its respective velocity. Then, we can calculate the final momentum by adding up the individual momenta of the joined cars.
Let's denote the mass of each car as m and the velocity of the first car as v1 and the velocity of the second car as v2.
Initial momentum before the collision is given by:
Initial momentum = (mass of first car * velocity of first car) + (mass of second car * velocity of second car)
Plugging in the given values:
Initial momentum = (1.46 × 10^4 kg * 7.05 m/s) + (1.46 × 10^4 kg * 1.76 m/s)
To simplify the calculation, let's factor out the mass:
Initial momentum = (1.46 × 10^4 kg) * (7.05 m/s + 1.76 m/s)
Now, we can calculate the final momentum, which will be the sum of the individual momenta of the joined cars. Since they stick together after the collision, their masses add up, and we can use the combined mass of both cars.
Final momentum after the collision = (combined mass of both cars) * (final velocity)
Finally, by equating the initial momentum and the final momentum, we can solve for the final velocity of the joined cars.
Let's denote the final velocity of the joined cars as vf.
Initial momentum = Final momentum
(1.46 × 10^4 kg) * (7.05 m/s + 1.76 m/s) = (2 * 1.46 × 10^4 kg) * vf
Now, we can solve for vf:
vf = [(1.46 × 10^4 kg) * (7.05 m/s + 1.76 m/s)] / (2 * 1.46 × 10^4 kg)
Simplifying further:
vf = (1.46 × 10^4 kg * 8.81 m/s) / (2 * 1.46 × 10^4 kg)
The mass of both cars cancels out, and the final result is:
vf = 8.81 m/s
Therefore, the velocity of the joined cars after the collision is 8.81 m/s to the north.