Chapter 5, Problem 4RAT

If the mass of a cart full of groceries decreases to half and its speed doubles, the momentum of the cart

$\left(\text{a}\right)$ remains unchanged.

$\left(\text{b}\right)$ is doubled.

$\left(\text{c}\right)$ is quadrupled.

$\left(\text{a}\right)$ decreases.

To determine

The correct option for the statement “If the mass of a cart full of groceries decreases to half and its speed doubles, the momentum of the cart”.

Answer to Problem 4RAT

The correct option for the statement “If the mass of a cart full of groceries decreases to half and its speed doubles, the momentum of the cart” is option (a).

Explanation of Solution

Given info: The initial mass of the grocery cart is $m$, initial speed of the cart is $v$, final mass of the grocery cart is $\frac{m}{2}$ and final speed of the cart is $2v$.

Write the expression to calculate the initial momentum of the cart.

$P_1=m_1\cdot v_1$

Here,

$P_1$ is the initial momentum of the grocery cart

$m_1$ is the initial mass of the grocery cart

$v_1$ is the initial speed of the car

Substitute $m$for $m_1$ and $v$ for $v_1$ in the above expression to find $P_1$.

$P_1=mv$

Write the expression to calculate the final momentum of the cart.

$P_2=m_2\cdot v_2$

Here,

$P_2$ is the final momentum of the grocery cart

$m_2$ is the final mass of the grocery cart

$v_2$ is the final speed of the car

Substitute $\frac{m}{2}$ for $m_2$ and $2v$ for $v_2$ in the above expression to find $P_2$.

$\begin{array}{c}{P}_2=\left(\frac{m}{2}\right)\left(2v\right)\\ =mv\end{array}$

The initial and final momentum of the grocery car is same, so the momentum of the grocery cart remain unchanged if mass decreases to half and speed doubles.

Conclusion:

Therefore, the correct option for the statement “If the mass of a cart full of groceries decreases to half and its speed doubles, the momentum of the cart” is option (a).