In Fig. 1, $ angle AOC = 90^ ext{°}$ and $ angle BOC = heta^ ext{°}$. A particle at O is in equilibrium under the action of three coplanar forces. The three forces have magnitude 8 N, 12 N and X N and act along OA, OB and OC respectively. Calculate (a) the value, to one decimal place, of $ heta$, (b) the value, to 2 decimal places, of $X$.

A-Level Edexcel Maths Mechanics Moments: In Fig. 1, $ angle AOC = 90^ ext

In Fig. 1, $ angle AOC = 90^ ext{°}$ and $ angle BOC = heta^ ext{°}$ - Edexcel - A-Level Maths Mechanics - Question 2 - 2003 - Paper 1

Question 2

$In-Fig.-1,-$-angle-AOC-=-90^-ext{°}$-and-$-angle-BOC-=--heta^-ext{°}$-Edexcel-A-Level Maths Mechanics-Question 2-2003-Paper 1.png$

In Fig. 1, $ angle AOC = 90^ ext{°}$ and $ angle BOC = heta^ ext{°}$. A particle at O is in equilibrium under the action of three coplanar forces. The three forces ... show full transcript

Worked Solution & Example Answer:In Fig. 1, $ angle AOC = 90^ ext{°}$ and $ angle BOC = heta^ ext{°}$ - Edexcel - A-Level Maths Mechanics - Question 2 - 2003 - Paper 1

Step 1

(a) the value, to one decimal place, of θ

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Answer

To find the angle $heta$ , we can utilize the equilibrium condition for the forces acting on point O. The force acting along OA is 8 N, and along OB is 12 N.

Using the cosine law for the triangle formed by the forces:

egin{align*} R(&) = 8N ext{ (force along OA)}
&= 12 ext{ (force along OB)}
\angle AOB = 90^ ext{°} \end{align*}

We find that: $R = 12 \cos(\beta) + 12 \sin(\alpha)$ where $eta = 41.8^ ext{°}$ or $heta = 138.2^ ext{°}$ .

Thus, the calculated value for $heta$ to one decimal place is $138.2^ ext{°}$ .

Step 2

(b) the value, to 2 decimal places, of X

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Answer

To calculate the value of $X$ , we can apply the sine or cosine rules based on the previously determined angle.

Using: $X = 12 \cos(41.8^ ext{°}) \text{ or } 12 \sin(48.2^ ext{°})$

By calculating this we find: $X \approx 8.94$ Hence, the value of $X$ to two decimal places is $8.94$ .

In Fig. 1, $ angle AOC = 90^ ext{°}$ and $ angle BOC = heta^ ext{°}$ - Edexcel - A-Level Maths Mechanics - Question 2 - 2003 - Paper 1

Worked Solution & Example Answer:In Fig. 1, $ angle AOC = 90^ ext{°}$ and $ angle BOC = heta^ ext{°}$ - Edexcel - A-Level Maths Mechanics - Question 2 - 2003 - Paper 1

(a) the value, to one decimal place, of θ

(b) the value, to 2 decimal places, of X

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