Question

chapter 8 key equations (page 272)
write the following equations according to the textbook.
write the equation for impulse-momentum theorem and define all the variables.
write the equation for linear momentum and define all the variables.
write the equation for law of conservation of momentum and define all the variables.

Explanation:

The Impulse - Momentum Theorem states that the change in momentum ($\Delta p$) of an object is equal to the impulse ($J$) applied to it. Impulse is calculated as the force ($F$) applied over a time interval ($\Delta t$), so $J = F\Delta t$. Thus, $\Delta p=F\Delta t$.

Linear momentum ($p$) of an object is the product of its mass ($m$) and velocity ($v$), so $p = mv$.

The Law of Conservation of Momentum states that for an isolated system (no external forces), the total initial momentum ($p_{i}$) is equal to the total final momentum ($p_{f}$). If we have two objects with initial momenta $p_{1i}$ and $p_{2i}$ and final momenta $p_{1f}$ and $p_{2f}$, then $p_{1i}+p_{2i}=p_{1f}+p_{2f}$. In general terms for a system of $n$ objects, $\sum_{i = 1}^{n}p_{i\text{(initial)}}=\sum_{i = 1}^{n}p_{i\text{(final)}}$.

Answer:

• Impulse - Momentum Theorem: $\Delta p=F\Delta t$, where $\Delta p$ is the change in momentum, $F$ is the force, and $\Delta t$ is the time interval.
• Linear Momentum: $p = mv$, where $p$ is the linear momentum, $m$ is the mass of the object, and $v$ is the velocity of the object.
• Law of Conservation of Momentum: $\sum_{i = 1}^{n}p_{i\text{(initial)}}=\sum_{i = 1}^{n}p_{i\text{(final)}}$ (for a system of $n$ objects). In the case of two - object system: $p_{1i}+p_{2i}=p_{1f}+p_{2f}$, where $p_{1i}$ and $p_{2i}$ are the initial momenta of the two objects and $p_{1f}$ and $p_{2f}$ are the final momenta of the two objects.