If a 9800kg train car traveling at 15m/s impacts another train car at rest and after the impact the 2 are going 6m/s. What is the mass of the second train car?
To find the mass of the second train car, we can 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.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, it can be expressed as:
p = mv
Let's denote the mass of the first train car as m1 and the mass of the second train car as m2. Given that the first car has a mass of 9800 kg and is traveling at 15 m/s, its initial momentum (p1i) can be calculated as:
p1i = m1 * v1i = 9800 kg * 15 m/s
Since the second car is at rest, its initial momentum (p2i) is zero:
p2i = m2 * v2i = 0
After the collision, the two cars will move together at a velocity of 6 m/s. Therefore, their combined momentum (pf = p1f + p2f) can be expressed as:
pf = (m2 + m2) * v3f
Using the principle of conservation of momentum, we can equate the initial momentum to the final momentum:
p1i + p2i = p1f + p2f
Substituting the known values, we have:
9800 kg * 15 m/s + 0 = (m1 + m2) * 6 m/s
Now, let's solve for m2:
144,000 kg·m/s = 6 m/s * (m1 + m2)
Dividing both sides of the equation by 6 m/s:
24,000 kg = m1 + m2
Since we know that m1 is 9800 kg, we can substitute it in the equation and solve for m2:
24,000 kg = 9800 kg + m2
m2 = 24,000 kg - 9800 kg
m2 = 14,200 kg
Therefore, the mass of the second train car is 14,200 kg.