2024-10-0211:12
Status:PHYS106
Tags: Kinematics
Because of the conservation of momentum,
If there is some change in time is taken, , then,
\frac {\Delta \vec p_A}{\Delta t }=\frac {\Delta \vec p_B}{\Delta t } \\ \vec F_A=-\vec F_B \end {gather} $$ This relates to the normal force as a consequence of the acceleration due to the applied force. The opposite reaction in the electrostatic repulsion of the atoms forced infinitely close: i.e. if a ball is on a table, the $\vec F_A$ is the gravitational force on the ball, and $-\vec F_B$ is the electrostatic repulsion. (The applied force can be weight, pressing a hand against a wall etc.) --- Suppose $\frac F m = t^2$ What is $\Delta v$ from $t_0$ to $t_1$. $$\begin{gather} \frac {dv}{dt}=\frac F m \\ \frac {dv} {dt}=t^2 \\ v = \frac {t^3} 3+C \\ v(t_1)= \frac {t^3} 3+C \\ v(t_0)= \frac {t^3} 3+C \\ \Delta v = v(t_1)-v(t_0)= \frac {t^3_1} 3- \frac {t^3_0} 3 \end{gather}$$ So generally, if $\frac F m$ is a known function $a (t)$ then, $w$ is a function whose derivative is $a$. However, there is another method to solving the same problem in [[Area method for predicting velocities]]. The equivalence between these two methods relates to the fundamental theorem of [[Calculus]]: integration: ![[Pasted image 20241002113419.png]] *INTEGRAL IS CHANGE IN ...*