A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?
A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?
To determine the common speed of the railroad cars after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity.
Before the collision, we have:
Mass of first car (m1) = 10,000 kg
Velocity of first car (v1) = 24.0 m/s
Momentum of first car (p1) = m1 * v1
Since the second car is at rest before the collision, its momentum (p2) is zero.
The total momentum before the collision (p_tot_before) is the sum of the initial momentum of both cars:
p_tot_before = p1 + p2 = m1 * v1 + 0 = m1 * v1
After the collision, the two cars lock together, meaning they move with a common velocity (v_common).
The total momentum after the collision (p_tot_after) is the product of the combined mass and the common velocity:
p_tot_after = (m1 + m2) * v_common
According to the conservation of momentum principle, p_tot_before = p_tot_after:
m1 * v1 = (m1 + m2) * v_common
Now we can solve for the common velocity (v_common). In this case, both cars have the same mass, so we can substitute m1 = m2:
m1 * v1 = 2 * m1 * v_common
Simplifying the equation:
v_common = (m1 * v1) / (2 * m1) = v1 / 2
Now let's substitute the values to calculate the common velocity:
v_common = 24.0 m/s / 2 = 12.0 m/s
Therefore, the common speed of the railroad cars after the collision is 12.0 m/s.
A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?
Apply the law of conservation of momentum to this problem
10,000 * 24.0 = V' * 20,000
V' is the final velocity after collision. Solve for it.