Question

In the figure, what value of F_max gives an impulse of 6.0 N*s?

Answer 1

Concepts and reason

The given problem can be solved by using the concept of the impulse concept and area under the curve.

To find the maximum force, first calculate the area under the curve when the impulse is given in the problem.

Fundamentals

The expression of impulse can be expressed as,

${\rm{impulse}} = Ft$

Here,$F$ is the force and $t$ is the time.

The area under the curve of the curve can be calculated as follows,

$\begin{array}{c}\\{\rm{impulse}} = {\rm{Area}}\\\\ = \frac{1}{2}\left( {{\rm{base}}} \right)\left( {{\rm{height}}} \right)\\\end{array}$

Substitute $8{\rm{ ms}}$ for ${\rm{base}}$ and ${F_{\max }}$ for ${\rm{height}}$ in the area under the curve expression.

$\begin{array}{c}\\{\rm{impulse}} = \frac{1}{2}\left( {8{\rm{ ms}}} \right)\left( {{F_{\max }}} \right)\\\\ = \left( {4{\rm{ms}}} \right)\left( {\frac{{{{10}^{ - 3}}{\rm{ s}}}}{{1{\rm{ ms}}}}} \right){\rm{ }}{F_{\max }}\\\\ = 0.004\left( {{F_{\max }}} \right){\rm{s}}\\\end{array}$

The impulse equals to $0.004\left( {{F_{\max }}} \right){\rm{s}}$.

The maximum force can be calculated as follows,

${\rm{impulse}} = {F_{\max }}t$

Substitute $6.0{\rm{ N}} \cdot {\rm{s}}$ for ${\rm{impulse}}$and $0.004\left( {{F_{\max }}} \right){\rm{ N}} \cdot {\rm{s}}$ in the impulse expression.

$\begin{array}{c}\\6.0{\rm{ N}} \cdot {\rm{s}} = 0.004\left( {{F_{\max }}} \right){\rm{s}}\\\\{F_{\max }}{\rm{ = 1500 N}}\\\end{array}$

Ans:

The maximum force is equal to ${\rm{1500 N}}$.