A railroad car with a mass of 12000 kg collides and couples with a second car of mass 18000 kg that is initially at rest. The first car is moving with a speed of 9 m/s before collision. If external forces can be ignored, what is the final speed of the two railroad cars after they couple?
I don't get why it says couples, what does that mean??? Thanks.
When it says the two cars "couple," it means that they combine or connect together after the collision. In this case, the first car, with a mass of 12000 kg, is moving at a speed of 9 m/s before the collision. When it collides with the second car, which is initially at rest and has a mass of 18000 kg, they will connect together and move as a single unit.
To find the final speed of the two cars after they couple, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). Mathematically, it can be represented as:
p = m * v
Before the collision, the momentum of the first car is given by:
p1 = m1 * v1
where:
m1 = mass of the first car = 12000 kg
v1 = velocity of the first car = 9 m/s
p1 = 12000 kg * 9 m/s
Before the collision, the second car is at rest, so its momentum is zero:
p2 = m2 * v2
where:
m2 = mass of the second car = 18000 kg
v2 = velocity of the second car = 0 m/s
p2 = 18000 kg * 0 m/s = 0
According to the law of conservation of momentum:
p1 + p2 = p_final
Since p2 is zero, the equation simplifies to:
p1 = p_final
Now, we can solve for the final velocity (v_final) of the combined cars by rearranging the equation:
v_final = p_final / (m1 + m2)
Substituting the known values:
v_final = (12000 kg * 9 m/s) / (12000 kg + 18000 kg)
Simplifying, we get:
v_final = (108000 kg * m/s) / 30000 kg
v_final ≈ 3.6 m/s
Therefore, the final speed of the two railroad cars after they couple will be approximately 3.6 m/s.
When the question mentions that the two railroad cars "couple," it means that they join together and move as a single unit after the collision. In other words, the two cars become connected, and their masses combine.
To find the final speed of the two coupled cars, 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, assuming there are no external forces acting.
First, let's calculate the initial momentum of the first car:
Initial momentum of first car = mass of first car * initial velocity of first car
= 12000 kg * 9 m/s
Since the second car is initially at rest, its initial momentum is zero.
Now, after the collision, the two cars couple and move together. Let's denote the final velocity of the coupled cars as V.
The final momentum of the two coupled cars is given by:
Final momentum of coupled cars = (mass of first car + mass of second car) * final velocity (V)
Since the final momentum is equal to the initial momentum (due to the conservation of momentum), we can set up the equation:
Initial momentum of first car = Final momentum of coupled cars
12000 kg * 9 m/s = (12000 kg + 18000 kg) * V
Now we can solve for V:
V = (12000 kg * 9 m/s) / (12000 kg + 18000 kg)
By simplifying the equation, we find that:
V ≈ 5.4 m/s
Therefore, the final speed of the two coupled railroad cars after the collision is approximately 5.4 m/s.