A0.500-kilogram cart traveling to the right on a horizontal, frictionless surface at 2.20 meters per second collides head on with a 0.800-kilogram cart moving to the left at 1.10 meters per second. what is the magnitude ofthe total momentum of the two-cart system after the collision?

Consider the motion towards right as positive and motion towards left as negative.

m₁ = mass of the cart moving to right = 0.500 kg

v₁ = initial velocity before collision of the cart moving towards right = 2.2 m/s

m₂ = mass of cart moving to left = 0.800 kg

v₂ = initial velocity before collision of the cart moving towards left = - 1.1 m/s

initial momentum of the system of carts before the collision is given as

P₁ = m₁ v₁ + m₂ v₂

P₁ = (0.500) (2.2) + (0.800) (- 1.1)

P₁ = 0.22 kg m/s

P₂ = momentum of system of carts after collision

As per conservation of momentum,

Momentum of system of carts after collision = Momentum of system of carts before collision

P₂ = P₁

P₂ = 0.22 kg m/s

The final momentum of the system before the collision is 1.02 kg-m/s.

Given data:

The mass of first cart is, m = 0.500 kg.

The initial velocity of first cart before collision is, u = 2.20 m/s.

The mass of another cart is, m' =0.800 kg.

The initial velocity of second cart before collision is, u' = -1.10 m/s. (Negative sign shows the opposite direction)

Use the conservation of linear momentum, which says that momentum of a system before collision is equal to the momentum of the system after the collision.

Total momentum before collision = Total momentum after collision

Thus, we can conclude that the final momentum of the system before the collision is 1.02 kg-m/s.

Learn more about the conservation of linear momentum here:

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