Question

a 0.500-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 of the total momentum of the two-cart system after the collision?
a 0.22 kg·m/s
b 0.39 kg·m/s
c 1.98 kg·m/s
d 4.29 kg·m/s

Explanation:

Step1: Define sign convention

Let right be positive, left be negative.

Step2: Calculate initial momentum of cart 1

$p_1 = m_1v_1 = 0.500\ \text{kg} \times 2.20\ \text{m/s} = 1.10\ \text{kg·m/s}$

Step3: Calculate initial momentum of cart 2

$p_2 = m_2v_2 = 0.800\ \text{kg} \times (-1.10\ \text{m/s}) = -0.880\ \text{kg·m/s}$

Step4: Total momentum (conserved, no external force)

$p_{\text{total}} = p_1 + p_2 = 1.10 + (-0.880) = 0.22\ \text{kg·m/s}$
Take magnitude: $|p_{\text{total}}| = 0.22\ \text{kg·m/s}$

Answer:

A. 0.22 kg·m/s