Question

The greater and least resultant of two forces are 9N and 5N respectively. If they are applied at 60 degrees. The magnitude of the resultant is

Answer 1

Greater resultant = a + b = 14
Least resultant = a_ b = 4

At 60° ... use law of cosine
Ans is 12.28


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Answer 2

Answer:

The resultant force's magnitude measured is $8.18N$.

Explanation:

The greater of two forces, i.e., $F_{1} + F_{2}$ = $9N$

The least of two forces, i.e., $F_{1} - F_{2}$ = $5N$

The angle between them, θ = $60\textdegree$

The resultant force's magnitude =?

Now, as given,

• $F_{1} + F_{2}$ = $9N$     -------equation (1)
• $F_{1} - F_{2}$ = $5N$     -------equation (2)

After adding the two equations, we get:

• $2F_{1}$ = $14N$
• $F_{1}$ = $7N$

Now, after putting the value of $F_{1}$ in equation 1, we get:

• $7 + F_{2}$ = $9N$  
• $F_{2}$ = $2N$

Now, as we know,

• Resultant force, R = $\sqrt{F_{1}^{2} + F_{2}^{2} +2F_{1} F_{2} cos\theta }$
• R = $\sqrt{(7)^{2} + (2)^{2} +2(7)(2)cos60\textdegree }$
• R = $\sqrt{(7)^{2} + (2)^{2} +2(7)(2)cos60\textdegree }$                 ( $cos60\textdegree = \frac{1}{2}$ )
• R = $\sqrt{49 + 4 +28\times\frac{1}{2} }$
• R = $\sqrt{53 + 14 }$
• R = $\sqrt{67 }$
• R = $8.18N$

Hence, the magnitude of the resultant force calculated is $8.18N$.