A 12,000kg railroad car traveling at 12.0m/s couples with an identical car sitting on the tracks. What is the speed of the joined card?
To find the speed of the joined cars after coupling, we need to apply 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 of an object is calculated by multiplying its mass by its velocity. In this case, we have two identical railroad cars with a mass of 12,000 kg each. The velocity of the first car is 12.0 m/s, and the second car is initially stationary.
Let's calculate the total momentum before the collision:
Momentum of Car 1 = mass × velocity
Momentum of Car 1 = 12,000 kg × 12.0 m/s
Since the second car is stationary initially, its momentum is zero.
Total momentum before the collision = momentum of Car 1 + momentum of Car 2
Total momentum before the collision = (12,000 kg × 12.0 m/s) + 0
Now, suppose the velocity of the joined cars after coupling is V. The total momentum after the collision is equal to the sum of the momentum of the joined cars:
Total momentum after the collision = (mass of Car 1 + mass of Car 2) × V
Total momentum after the collision = (12,000 kg + 12,000 kg) × V
According to the principle of conservation of momentum, we can set the total momentum before the collision equal to the total momentum after the collision:
(12,000 kg × 12.0 m/s) + 0 = (12,000 kg + 12,000 kg) × V
Now, we can solve this equation to find the velocity of the joined cars:
(12,000 kg × 12.0 m/s) = (24,000 kg) × V
V = (12,000 kg × 12.0 m/s) / (24,000 kg)
By simplifying,
V = 6.0 m/s
Therefore, the final speed of the joined cars after coupling is 6.0 m/s.
To find the speed of the joined cars, we can use the principle of conservation of momentum. According to this principle, the total momentum before the coupling equals the total momentum after the coupling.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v).
Given:
Mass of each car (m) = 12,000 kg
Initial velocity of the first car (v1) = 12.0 m/s
Final velocity of the joined cars (v) = ?
Let's calculate the initial momentum (p1) of the first car:
p1 = m * v1
Now, since the second car is at rest initially, its momentum is zero:
p2 = 0
According to the conservation of momentum:
p1 + p2 = p
Since the two cars combine after coupling, the total mass of the system becomes twice the mass of a single car.
Total mass (M) = m1 + m2 = 12,000 kg + 12,000 kg = 24,000 kg
Let's substitute the values into the equation:
(m1 * v1) + (m2 * v2) = (M * v)
Now, let's solve for v:
(12,000 kg * 12.0 m/s) + (0 kg * v2) = (24,000 kg * v)
144,000 kg·m/s + 0 kg·m/s = 24,000 kg * v
144,000 kg·m/s = 24,000 kg * v
Divide both sides by 24,000 kg:
144,000 kg·m/s / 24,000 kg = v
v = 6.0 m/s
Therefore, the speed of the joined cars after coupling is 6.0 m/s.