Two freight cars, each with a mass of 2.5 multiplied by 10^5 kg, collide and stick together. One was initially moving at 3.4 m/s and the other was at rest. What is their final speed?
Assume conservation of linear momentum. Let us know if you have difficulty and show your work
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To find the final velocity of the two freight cars after collision, 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.
The formula for momentum is given by:
Momentum = mass × velocity
Let's denote the initial velocity of the first freight car as v1, the initial velocity of the second freight car as v2, and the final velocity of the combined freight cars as vf.
Before the collision:
- The mass of the first freight car (m1) = 2.5 × 10^5 kg
- The mass of the second freight car (m2) = 2.5 × 10^5 kg
- The initial velocity of the first freight car (v1) = 3.4 m/s
- The initial velocity of the second freight car (v2) = 0 m/s
The total momentum before the collision (P_initial) is equal to the sum of the momenta of the two freight cars:
P_initial = (m1 × v1) + (m2 × v2)
After the collision, the two freight cars stick together and move with a final velocity (vf) as a combined mass.
The total momentum after the collision (P_final) is equal to the momentum of the combined freight cars:
P_final = (m1 + m2) × vf
Since momentum is conserved, P_initial = P_final.
Therefore,
(m1 × v1) + (m2 × v2) = (m1 + m2) × vf
Substituting the known values:
(2.5 × 10^5 kg × 3.4 m/s) + (2.5 × 10^5 kg × 0 m/s) = (2.5 × 10^5 kg + 2.5 × 10^5 kg) × vf
(8.5 × 10^5 kg·m/s) = (5 × 10^5 kg) × vf
Now, let's solve for vf:
vf = (8.5 × 10^5 kg·m/s) / (5 × 10^5 kg)
vf = 1.7 m/s
Therefore, the final velocity of the combined freight cars after collision is 1.7 m/s.