a 20,000kg railroad car is traveling at 3m/s when it collides and couples with a second, identical car at reat. What is the resulting speed of the combined cars?
To find the resulting speed of the combined railroad cars after they collide and couple, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v), using the formula: p = m * v.
Let's break down the problem and calculate the momentum before and after the collision:
Given:
Mass of each railroad car (m) = 20,000 kg
Initial velocity of the first car (v1) = 3 m/s
Initial velocity of the second car (v2) = 0 m/s (as it is at rest)
1. Calculate the momentum of the first car before the collision:
Momentum of first car (p1) = mass of first car (m1) * velocity of first car (v1)
= 20,000 kg * 3 m/s
= 60,000 kg·m/s
2. Calculate the momentum of the second car before the collision:
Momentum of second car (p2) = mass of second car (m2) * velocity of second car (v2)
= 20,000 kg * 0 m/s
= 0 kg·m/s
Since the second car is at rest, its momentum is zero.
3. Find the total momentum before the collision:
Total momentum before collision (p_before) = p1 + p2
= 60,000 kg·m/s + 0 kg·m/s
= 60,000 kg·m/s
Next, we need to calculate the total momentum after the collision, assuming the cars couple together.
4. After the collision, the two cars will move as a single unit with a common velocity (v_after).
To find v_after, we'll again use the conservation of momentum principle:
Total momentum after collision (p_after) = (m1 + m2) * v_after
Since the two cars have the same mass (20,000 kg), the total mass is 2 * 20,000 kg = 40,000 kg.
Therefore, we can write the equation for the total momentum after the collision as:
p_after = 40,000 kg * v_after
The total momentum before the collision is equal to the total momentum after the collision, hence:
p_before = p_after
5. Solve for v_after:
60,000 kg·m/s = 40,000 kg * v_after
Dividing both sides of the equation by 40,000 kg gives:
v_after = 60,000 kg·m/s / 40,000 kg
= 1.5 m/s
Hence, the resulting speed of the combined railroad cars after colliding and coupling is 1.5 m/s.