Question 182: Laws of Motion

Question

Two forces are such that the sum of their magnitudes is $18$ $N$ and their resultant is $12$ $N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

Accepted Answer

Let the two forces be ${F_1}$ and ${F_2}$ and let ${F_2}$ is smaller than $ {F_1} $ and assume $R$ is the resultant force.
Given ${F_1} + {F_2} = 18$ $\,\,\,\,\,\,$  ....$(i)$
From the right angle triangle, $F_2^2 + {R^2} = F_1^2$
or $F_1^2 - F_2^2 = {R^2}$
or $\left( {{F_1} + {F_2}} \right)$$\left( {{F_1} - {F_2}} \right)$ = ${R^2}$
or $\left( {18} \right)\left( {{F_1} - {F_2}} \right)$ = ${\left( {12} \right)^2}$ = 144
or $\left( {{F_1} - {F_2}} \right) = 8$ $\,\,\,\,\,\,$  ....$(ii)$
By solving equation $(i)$ and $(ii)$ we get,
${{F_1} = 13\,N}$ and ${{F_2} = 5\,N}$

Answer

$12N,$ $6N$

Answer

$13N,$ $5N$

Answer

$10N,$ $8N$

Answer

$16N$, $2N.$

Laws of Motion

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

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