Question

2b. calculate cart 1s change in momentum.
known\tcart 1
\t\tm₁ =
\t\tvᵢ =
\t\tvբ =
unknown\t
tool box\tmomentum
\t\tp = (m)(v)
\t\tinelastic collision
\t\tm₁vᵢ + m₂vᵢ = vբ(m₁ + m₂)
\t\telastic collision
\t\tm₁vᵢ + m₂vᵢ = m₁vբ + m₂vբ
\t\tchange in momentum
\t\tδp = (mv)բ - (mv)ᵢ
\t\tδp = m(vբ - vᵢ)
substitute and solve\t
2c. calculate cart 2s change in momentum.
known\tcart 2
\t\tm₂ =
\t\tvᵢ =
\t\tvբ =
unknown\t

Explanation:

To solve for the change in momentum of Cart 1 (and similarly for Cart 2), we use the formula for change in momentum:

For Cart 1:

Step 1: Recall the formula for change in momentum

The formula for change in momentum ($\Delta p$) is $\Delta p = m(v_f - v_i)$, where $m$ is the mass of the cart, $v_f$ is the final velocity, and $v_i$ is the initial velocity.

Step 2: Substitute known values

Let the known values for Cart 1 be $m_1$ (mass), $v_{i1}$ (initial velocity), and $v_{f1}$ (final velocity). Substitute these into the formula:
$\Delta p_1 = m_1(v_{f1} - v_{i1})$

For Cart 2:

Step 1: Recall the formula for change in momentum

The formula for change in momentum ($\Delta p$) is $\Delta p = m(v_f - v_i)$, where $m$ is the mass of the cart, $v_f$ is the final velocity, and $v_i$ is the initial velocity.

Step 2: Substitute known values

Let the known values for Cart 2 be $m_2$ (mass), $v_{i2}$ (initial velocity), and $v_{f2}$ (final velocity). Substitute these into the formula:
$\Delta p_2 = m_2(v_{f2} - v_{i2})$

Example (if values were provided):

Suppose for Cart 1: $m_1 = 2\ \text{kg}$, $v_{i1} = 3\ \text{m/s}$, $v_{f1} = 5\ \text{m/s}$.
Then:
$\Delta p_1 = 2(5 - 3) = 2(2) = 4\ \text{kg·m/s}$

If specific values for mass and velocities are provided, substitute them into the formula $\boldsymbol{\Delta p = m(v_f - v_i)}$ to find the change in momentum.

Answer:

Step 1: Recall the formula for change in momentum

The formula for change in momentum ($\Delta p$) is $\Delta p = m(v_f - v_i)$, where $m$ is the mass of the cart, $v_f$ is the final velocity, and $v_i$ is the initial velocity.

Step 2: Substitute known values

Let the known values for Cart 2 be $m_2$ (mass), $v_{i2}$ (initial velocity), and $v_{f2}$ (final velocity). Substitute these into the formula:
$\Delta p_2 = m_2(v_{f2} - v_{i2})$

Example (if values were provided):

Suppose for Cart 1: $m_1 = 2\ \text{kg}$, $v_{i1} = 3\ \text{m/s}$, $v_{f1} = 5\ \text{m/s}$.
Then:
$\Delta p_1 = 2(5 - 3) = 2(2) = 4\ \text{kg·m/s}$

If specific values for mass and velocities are provided, substitute them into the formula $\boldsymbol{\Delta p = m(v_f - v_i)}$ to find the change in momentum.