2. Boxcar A, with mass of 1500 kg, is travelling at 25 m/s to the east. Boxcar B has a mass of 2000 kg, and is initially at rest. The box cars collide inelastically and move together after they get stuck. What is their combined velocity?
east is +
1500 * 25 - 2000 * 0 = 3500 v
To find the combined velocity of the two boxcars after the collision, we need to apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces are acting on it.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v). Mathematically, it can be expressed as:
p = m * v
Before the collision, the initial momentum of Boxcar A is given by:
p₁ = m₁ * v₁
where:
m₁ = mass of Boxcar A = 1500 kg
v₁ = velocity of Boxcar A = 25 m/s to the east
The initial momentum of Boxcar B is zero since it is initially at rest.
After the collision, the combined mass of the two boxcars is:
m₂ = m₁ + m₂
= 1500 kg + 2000 kg
= 3500 kg
The combined velocity of the two boxcars after the collision is represented by the variable v₂. To find v₂, we can equate the initial momentum to the final momentum and solve for v₂.
p₁ + p₂ = p₃
Here, p₂ is the initial momentum of Boxcar B, which is zero.
m₁ * v₁ + m₂ * 0 = m₃ * v₂
m₁ * v₁ = m₃ * v₂
Substituting the known values:
1500 kg * 25 m/s = 3500 kg * v₂
37500 kg·m/s = 3500 kg * v₂
Dividing both sides of the equation by 3500 kg:
37500 kg·m/s ÷ 3500 kg = v₂
10.71 m/s ≈ v₂
Therefore, the combined velocity of the two boxcars after the collision is approximately 10.71 m/s.