Question

A blue lab cart is traveling west on a track
when it collides with and sticks to a red lab
cart traveling east. The magnitude of the
momentum of the blue cart before the collision
is 2.0 kilogram • meters per second, and the
magnitude of the momentum of the red cart before
the collision is 3.0 kilogram • meters per second.
The magnitude of the total momentum of the
two carts after the collision is

Answer 1

Answer on Question # 71590, Physics / Mechanics | Relativity

Question

A blue lab cart is traveling west on a track when it collides with and sticks to a red lab cart traveling east. The magnitude of the momentum of the blue cart before the collision is 2.0 kilogram • meters per second, and the magnitude of the momentum of the red cart before the collision is 3.0 kilogram • meters per second. The magnitude of the total momentum of the two carts after the collision is

Solution. Use the Conservation of Momentum Principle:

If the net external force acting on a system of objects is zero, the total momentum $p_{tot}$ of the system is conserved.

For this problem we have

$$p _ {t o t} = p _ {r e d} + p _ {b l u e} = \mathrm {c o n s t}$$

where $p_{red}$ is the magnitude of the momentum of the red cart before the collision

$$p _ {r e d} = 3. 0 \text { kilogram} \cdot \text { meters per second}$$

and $p_{blue}$ is the magnitude of the momentum of the blue cart before the collision

$$p _ {b l u e} = - 2. 0 \text { kilogram} \cdot \text { meters per second}$$

$p_{blue}$ has the minus sign since blue cart moves towards the opposite of the red cart

Find the total momentum $p_{tot}$ before the collision

$$p _ {t o t} = 3. 0 - 2. 0 = 1. 0 \text { kilogram} \cdot \text { meters per second}$$

Since the total momentum $p_{tot}$ of the system is conserved, then the total momentum of the two carts after the collision is the same as before the collision

$$p _ {t o t} = 1. 0 \text { kilogram} \cdot \text { meters per second}$$

Answer: The magnitude of the total momentum of the two carts after the collision is 1.0 kilogram • meters per second.

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