Question

elastic collision problem 1 the red cart has a mass of 3.00 kg and an initial velocity of 4.00 m/s. the blue cart has a mass of 3.00 kg and is initially at rest. the carts collide in an elastic collision. after the collision the red cart is at rest. what is the total combined momentum of both the carts before the collision? what is the total combined momentum of both the carts after the collision? what is the velocity of the blue cart after the collision?
$m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}_1 + m_2\vec{v}_2$

Explanation:

Step1: List given values

$m_1=3.00\ \text{kg}, v_1=4.00\ \text{m/s}, m_2=3.00\ \text{kg}, v_2=0\ \text{m/s}, v_1'=0\ \text{m/s}$

Step2: Calculate total momentum before collision

Total momentum before: $p_{\text{total, initial}} = m_1v_1 + m_2v_2$
$p_{\text{total, initial}} = (3.00 \times 4.00) + (3.00 \times 0) = 12.0\ \text{kg·m/s}$

Step3: Apply conservation of momentum

For elastic collisions, total momentum is conserved, so $p_{\text{total, final}} = p_{\text{total, initial}}$
$p_{\text{total, final}} = 12.0\ \text{kg·m/s}$

Step4: Solve for blue cart's final velocity

Use $p_{\text{total, final}} = m_1v_1' + m_2v_2'$
$12.0 = (3.00 \times 0) + 3.00v_2'$
$v_2' = \frac{12.0}{3.00} = 4.00\ \text{m/s}$

Answer:

1. Total combined momentum before collision: $12.0\ \text{kg·m/s}$
2. Total combined momentum after collision: $12.0\ \text{kg·m/s}$
3. Velocity of the blue cart after collision: $4.00\ \text{m/s}$