Question

How do you find impulse from a graph?

Answer 1

Impulse: impulse is the effect of force acting on an object with respect to time as the momentum of that object changes.

Impulse is the area under the curve of force vs. time graph.

Areas above the time axis of the graph are positive $\Delta p$and areas below the axis of the graph are negative $\Delta p$.

If the force is not be constant, we can divide the graph into two or more sections and add up the impulse in each section.

For Example, to find the total impulse on the object in the force vs. time graph in Figure over $t_1+t_2$, the areas of $A_1$ and $A_2$ can be added together.

$A_1$​ is a rectangle of height $F_0$ and width $t_1$. $A_2$ is a triangle of height $F_0$ and base $t_2$. The total impulse on the object over $t_1 + t_2$ is

$\begin{array}{rcl}\Delta p& =& A_1+A_2\\ & =& F_0{t}_1+\frac{1}{2}{F}_0{t}_2\end{array}$

Hence, we can find the impulse by force vs time graph.