A particle P 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 12 N is applied to P. The particle P is in equilibrium with the string taut and OP making an angle of 20° with the downward vertical, as shown in Figure 1. Find a) the tension in the string. b) the weight of P.

A-Level Edexcel Maths Mechanics Moments: A particle P is attached to one

A particle P is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2007 - Paper 1

Question 1

A particle P 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 12 N ... show full transcript

Worked Solution & Example Answer:A particle P is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2007 - Paper 1

Step 1

Find (a) the tension in the string.

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Answer

To find the tension in the string, we can use the equilibrium condition in the vertical direction. The vertical component of the tension must balance the horizontal force:

We know that: $T ext{ sin } 20° = 12$

Solving for T: $T = rac{12}{ ext{sin } 20°}$

Calculating:

First, find ext{sin } 20°: $ext{sin } 20° ext{ is approximately } 0.342.$

Then: $T ext{ is approximately } rac{12}{0.342} ext{ N} ext{ or } 35.1 ext{ N} ext{ (to one decimal place).}$

Step 2

Find (b) the weight of P.

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Answer

To find the weight of P, we'll use the equilibrium conditions in the vertical direction again, where the weight is balanced by the vertical component of tension:

From the earlier tension calculation, we have:

Weight (W) is given by: $W = T ext{ cos } 20°$

Substituting in the tension value: $W = 35.1 ext{ N} imes ext{cos } 20°$

Calculating:

First, find ext{cos } 20°: $ext{cos } 20° ext{ is approximately } 0.940.$

Then: $W ext{ is approximately } 35.1 imes 0.940 ext{ N} ext{ or } 33.0 ext{ N} ext{ (to one decimal place).}$

A particle P is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2007 - Paper 1

Worked Solution & Example Answer:A particle P is attached to one end of a light inextensible string - Edexcel - A-Level Maths Mechanics - Question 1 - 2007 - Paper 1

Find (a) the tension in the string.

Find (b) the weight of P.

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