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In the figure, what value of F_{max} gives an impulse of 6.0 N.s?

♦ Relevant knowledge

It is necessary to apply the idea along with the formula of impulse in order to discover the solution to this problem. We are aware that the impulse is the change in momentum, or it can be defined as the combination of force and time. So by calculating the area of the time and force diagram, we can calculate the required values.

Concepts and ReasonThis problem can be solved using the concepts of the impulse concept, area under the curve and the concept of the impulse concept.

First, calculate the area under curve at the moment when the impulse is given in a problem to find the maximum force.

FundamentalsYou can express your impulses as:

[katex]{\rm{impulse}} = Ft[/katex]

Here,[katex]F[/katex]

You can calculate the area under the curve by following these steps:

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

Substitute [katex]8{\rm{ ms}}[/katex]

[katex]\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}[/katex]

The impulse is equal to [katex]0.004\left( {{F_{\max }}} \right){\rm{s}}[/katex]

This is how you can calculate the maximum force.

[katex]{\rm{impulse}} = {F_{\max }}t[/katex]

Substitute 6.0 N.s

[katex]\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}[/katex]

Ans: The maximum force equals 1500 N