diff --git a/docs/sph3u7.md b/docs/sph3u7.md index a8cb8a8..a5bc4e9 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -404,27 +404,27 @@ Newton's second law of motion states that the **net** force on an object is equa ### Momentum -The momentum of an object describes the difficulty of changing its motion. It is expressed mathematically as $\vec{P}$, and is equal to mass times initial velocity, or: +The momentum of an object describes the difficulty of changing its motion. Its unit is **Newton seconds** ($\text{Ns}$) and it is expressed mathematically as $\vec{P}$ such that $\vec{P}$ is equal to mass times velocity, or: $$\vec{P} = m\vec{v}$$ +Newton's second law can be manipulated so that momentum of an object — if its mass is constant — is equal to the net average force on that object multiplied by time. +$$ +\Sigma \vec{F}_\text{avg} = m\vec{a} \\ + = m(\frac{\vec{v_2}-\vec{v_1}}{\Delta t}) \\ + = \frac{m \vec{v_2} - m \vec{v_1}}{\Delta t}) \\ + = \frac{\vec{P_2} - \vec{P_1}}{\Delta t} \\ +\Sigma \vec{F}_\text{avg} = \frac{\Delta \vec{P}}{\Delta t} \\ +\Delta \vec{P} = \Sigma \vec{F}_\text{avg} · \Delta t +$$ + +This means that to achieve the *same momentum*, a smaller force can be applied for a longer period of time or a larger force can be applied in a smaller period of time. + ### Impulse -Impulse is the average net force $\Sigma F_{\text{avg}}$ applied over a time interval $\Delta t$. It is expressed mathematically as $\vec{J}$, and is represented in **Newton seconds** ($\text{Ns}$). It is equal to: +Impulse is the change in momentum of an object because of a force. It is expressed mathematically as $\vec{J}$, and is also represented in Newton seconds. $$\vec{J} = \Sigma \vec{F}_\text{avg} · \Delta t$$ -This can be rearranged and combined with other formulas, if the mass of the object is **constant**, so that impulse is equal to the difference in linear momentum. -$$ -\vec{J} = m\vec{a_\text{avg}} · \Delta t \\ -\vec{J} = mt (\frac{\vec{v_2} - \vec{v_1}}{\Delta t}) \\ -\vec{J} = m\vec{v_2} - m\vec{v_1} \\ -\vec{J} = \vec{P}_2 - \vec{P}_1 \\ -\vec{J} = \Delta \vec{P} -$$ - -Using the above, the net average force on an object can also be written as the rate of change of its momentum with respect to time. -$$ -\Sigma \vec{F}_\text{avg} = \frac{\Delta \vec{P}}{\Delta t} -$$ +Note that that is also equal to $\Delta \vec{P}$ above. ## 3.1 - Thermal concepts