Edexcel IAL Mathematics M1.5.2 particle equilibrium under coplanar forces

Practise equilibrium of particles under coplanar forces, resolving tensions, weights, reactions and friction to find unknown forces or masses.

[Maximum number: 12]

Figure 3

A washing line ABCD is fixed at the points A and D.
There are two heavy items of clothing hanging on the washing line, one fixed at B and the other fixed at C.

The washing line is modelled as a light inextensible string, the item at B is modelled as a particle of mass 3 kg and the item at C is modelled as a particle of mass $M \mathrm{~kg}$ .

The section AB makes an angle $\alpha$ with the horizontal, where $\tan \alpha=\frac{3}{4}$ , the section BC is horizontal and the section CD makes an angle $\beta$ with the horizontal, where $\tan \beta=\frac{12}{5}$ , as shown in Figure 3.

The system is in equilibrium.

(a)

Use of $\sin \alpha=\frac{3}{5}$ or $\cos \alpha=\frac{4}{5}$ or $\alpha=37$ or better

B1

Vert equilibrium at B

M1

$T_{A B} \sin \alpha=3 g$

A1

$T_{A B}=49(\mathrm{~N})$

A1

(4)

(a)

Find the tension in AB.

[ 4 ]

Use of $\sin \alpha=\frac{3}{5}$ or $\cos \alpha=\frac{4}{5}$ or $\alpha=37$ or better

B1

Vert equilibrium at B

M1

$T_{A B} \sin \alpha=3 g$

A1

$T_{A B}=49(\mathrm{~N})$

A1

(4)

(b)

Find the tension in BC.

[ 3 ]

Horiz equilibrium at B

M1

$T_{A B} \cos \alpha=T_{B C}$

A1

$T_{B C}=39$ or $39.2 \quad(\mathrm{~N})$

A1

(3)

(c)

Find the value of M.

[ 5 ]

Use equilibrium to form at least one equation in $T_{CD}$ .

Examples:
$T_{CD}\frac{5}{13}=T_{BC}$ $T_{CD}\frac{12}{13}=Mg$

Form an equation in M only, for example
$\frac{12}{5}T_{BC}=Mg$ M=9.6

M1 A1 A1 dM1 A1

Marking guidance for this part:
Only penalise use of 9.81 once per whole question, and only penalise over- or under-accuracy once per whole question.

All question bank results loaded

M1.5.2 - Equilibrium of a particle under question 1

Question (a)

Question (b)

Question (c)