A particle P of weight W newtons is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point O. A horizontal force of magnitude 5 N is applied to P. The particle P is in equilibrium with the string taut and OP making an angle of 25° to the downward vertical, as shown in Figure 1. Find (a) the tension in the string. (b) the value of W.

A-Level Edexcel Maths Mechanics Moments: A particle P of weight W newtons

A particle P of weight W newtons is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2014 - Paper 1

Question 1

A particle P of weight W newtons is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point O. A horizontal forc... show full transcript

Worked Solution & Example Answer:A particle P of weight W newtons is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2014 - Paper 1

Step 1

Find (a) the tension in the string.

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Answer

To find the tension $T$ in the string, we resolve the horizontal forces acting on the particle P.

Given that the horizontal force is 5 N, we have:

$5 = T \cos(25^\circ)$

From this equation, we can solve for $T$ :

$T = \frac{5}{\cos(25^\circ)}$

Now, calculating this value:

$T \approx 5 / 0.9063 \approx 5.51 \text{ N}$

Thus, the tension in the string is approximately 5.51 N.

Step 2

Find (b) the value of W.

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Answer

Next, we resolve the vertical forces acting on particle P. The weight $W$ acts downwards while the vertical component of the tension acts upwards. We can set the equilibrium condition:

$W = T \sin(25^\circ)$

Replacing $T$ from the previous step, we have:

$W = \left(\frac{5}{\cos(25^\circ)}\right) \sin(25^\circ)$

Evaluating:

$W = 5 \cdot \frac{\sin(25^\circ)}{\cos(25^\circ)} \approx 5 \cdot 0.4663 \cdot 1.188 \approx 5 \cdot 0.5547 \approx 2.77 \text{ N}$

Finally, the value of $W$ is approximately 2.77 N.

A particle P of weight W newtons is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2014 - Paper 1

Worked Solution & Example Answer:A particle P of weight W newtons is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2014 - Paper 1

Find (a) the tension in the string.

Find (b) the value of W.

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