Statics: forces, equilibrium & moments

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1. 1Resultants of forcesThe resultant of two forces at an angle from the parallelogram of forces, and the resultant of several forces by resolving each into components.Done16 min
2. 2Equilibrium of a particleA particle is in equilibrium when the forces on it balance: resolve in two directions, use Lami's theorem or the triangle of forces, and handle friction on rough planes.Done20 min
3. 3Moments and beamsThe moment of a force, the principle of moments for a beam on a pivot or on two supports, and non-uniform beams.Done16 min

Past questions (48)

From 2008–2023: 44 WAEC, 4 NECO. Theory questions first, then objective, newest first.

Theory (41)

• NECO 2023 · Paper 2 · Q7Three men pushed a bus with forces of 204 N in the direction $030^\circ$, 300 N in the direction $090^\circ$ and 225 N in the direction $120^\circ$. …
• WAEC 2023 · Paper 2 · Q14A particle is projected at an angle of $42^\circ$ with a velocity of $68\text{ m s}^{-1}$. Calculate, correct to one decimal place, the: (i) …
• WAEC 2023 · Paper 2 · Q7Forces $(8\text{ N}, 080^\circ)$, $(18\text{ N}, 240^\circ)$ and $(6\text{ N}, 300^\circ)$ act on a particle. Find, correct to two decimal places, …
• WAEC 2022 · Paper 2 · Q7A body of mass $18\text{ kg}$ is suspended by an inextensible string from a rigid support and is pulled by a horizontal force $F$ until the angle …
• WAEC 2022 · Paper 2 · Q14An object of mass $40\text{ kg}$ sits at the end $T$ of a see-saw that consists of a uniform beam $ST$ of length $7\text{ m}$. Another object …
• WAEC 2022 · Paper 2 · Q7A body of mass $1.5\text{ kg}$ is suspended by two light inextensible ropes inclined at $30^\circ$ and $60^\circ$ to the horizontal. Calculate …
• WAEC 2020 · Paper 2 · Q14A body of mass $10\text{ kg}$ rests on a rough plane inclined at an angle of $\tan^{-1}\left(\frac{5}{12}\right)$ to the horizontal. The coefficient …
• WAEC 2019 · Paper 2 · Q5Three forces $10\text{ N}$, $14\text{ N}$ and $16\text{ N}$ acting on a particle keep it in equilibrium. Find the angle between the forces $10\text{ N}$ …
• WAEC 2019 · Paper 2 · Q6A uniform beam $WX$, of length $90\text{ cm}$ and weight $50\text{ N}$, is suspended on a pivot $35\text{ cm}$ from $W$. It is kept in equilibrium …
• WAEC 2019 · Paper 2 · Q15Forces $(5\text{ N}, 030^\circ)$, $(P\text{ N}, 060^\circ)$, $(Q\text{ N}, 150^\circ)$, $(3\text{ N}, 180^\circ)$ and $(5\text{ N}, 270^\circ)$ …
• WAEC 2019 · Paper 2 · Q8In the diagram, a mass of $12\text{ kg}$ hanging from a light inextensible string is pulled aside by a horizontal force $R$, such that the string …
• WAEC 2019 · Paper 2 · Q14Two forces $T(8\text{ N}, 030^\circ)$ and $Q(10\text{ N}, 150^\circ)$ act on a body. Find the: (i) component of the resultant force along the …
• WAEC 2019 · Paper 2 · Q15A body of mass $4\text{ kg}$ placed at the top of a smooth plane inclined at an angle of $35^\circ$ to the horizontal slides from rest down the …
• WAEC 2018 · Paper 2 · Q15A uniform beam $XY$, $4\text{ m}$ long and weighing $350\text{ N}$, rests on two pivots $P$ and $Q$. It is kept in equilibrium by weights of …
• WAEC 2018 · Paper 2 · Q14A body is under the action of forces $M = (4\text{ N}, 030^\circ)$, $N = (10\text{ N}, 300^\circ)$ and $P = (a\text{ N}, x^\circ)$ which keep …
• WAEC 2018 · Paper 2 · Q14Three forces $6\text{ N}$, $4.5\text{ N}$ and $8\text{ N}$ act on a body $A$ of mass $1.2\text{ kg}$ as shown in the diagram: the $6\text{ N}$ …
• WAEC 2017 · Paper 2 · Q14A body $P$ of mass $q\text{ kg}$ is suspended by two light inextensible strings $AB$ and $DB$ attached to a horizontal ceiling. The strings are …
• WAEC 2017 · Paper 2 · Q8Forces $F_1(18\text{ N}, 330^\circ)$, $F_2(10\text{ N}, 090^\circ)$ and $F_3(25\text{ N}, 180^\circ)$ act on a body at rest. Find, correct to …
• WAEC 2017 · Paper 2 · Q15The position vectors of the points $M$, $N$, $P$ relative to a fixed point $O$ are $\mathbf m = 2\mathbf i + 3\mathbf j$, $\mathbf n = 6\mathbf i + 23\mathbf j$, …
• WAEC 2016 · Paper 2 · Q14A block of mass $0.5\text{ kg}$ rests on the floor of a lift which is moving upwards with an acceleration of $2\text{ m s}^{-2}$. Calculate the …
• WAEC 2016 · Paper 2 · Q8Forces $(40\text{ N}, 045^\circ)$ and $(Q\text{ N}, 135^\circ)$ act on a body initially at rest. If the magnitude of their resultant is $50\text{ N}$, …
• WAEC 2014 · Paper 2 · Q15$A(-1, 2)$, $B(3, 5)$ and $C(4, 8)$ are the vertices of triangle $ABC$. Forces whose magnitudes are $5\text{ N}$ and $3\sqrt{10}\text{ N}$ act …
• WAEC 2014 · Paper 2 · Q8Find the direction of the resultant of the forces in the diagram. Give the direction as a bearing.
• WAEC 2014 · Paper 2 · Q15$PQRS$ is a square. Calculate the magnitude and direction of the resultant of the forces $5\text{ N}$ acting along $PQ$, $3\sqrt2\text{ N}$ acting …
• WAEC 2013 · Paper 2 · Q17A particle is under the action of forces $\mathbf P = (4\text{ N}, 030^\circ)$ and $\mathbf R = (10\text{ N}, 300^\circ)$. Find the force that …
• WAEC 2013 · Paper 2 · Q17A lorry of mass $1200\text{ kg}$ was kept in motion by a force of $120\text{ N}$. If the lorry was initially at rest, calculate the distance …
• WAEC 2012 · Paper 2 · Q17Forces $(30 \text{ N}, 030^\circ)$ and $(40 \text{ N}, 060^\circ)$ act on a body of mass 20 kg initially at rest on a smooth horizontal floor. …
• WAEC 2012 · Paper 2 · Q8The diagram shows a uniform rod of mass $2.4\text{ kg}$, held in equilibrium by means of two strings inclined at $25^\circ$ and $54^\circ$ to …
• WAEC 2011 · Paper 2 · Q16An object $P$ of mass $6.5\text{ kg}$ is suspended by two light inextensible strings $AP$ and $BP$. The strings make angles $50^\circ$ and $60^\circ$ …
• WAEC 2011 · Paper 2 · Q8A particle of mass $400\text{ g}$ is moving under the action of two forces $F_1 = (35\text{ N}, 210^\circ)$ and $F_2 = (35\sqrt3\text{ N}, 300^\circ)$ …
• WAEC 2011 · Paper 2 · Q18A uniform bar $PQ$ of length $60\text{ cm}$ and weight $20\text{ N}$ is supported at two points $C$ and $D$ such that $|PC| = 10\text{ cm}$ and …
• WAEC 2010 · Paper 2 · Q17A particle $Q$ is acted upon by three coplanar forces $40$ N, $15\sqrt3$ N and $20$ N, as shown in the diagram. Find the force required to prevent …
• WAEC 2010 · Paper 2 · Q18Two forces $(3\mathbf i + 5\mathbf j)$ N and $(-2\mathbf i + 3\mathbf j)$ N act on a body of mass 2 kg and cause it to move. Find, correct to …
• WAEC 2010 · Paper 2 · Q8A body of mass 6 kg is hung from a fixed point by a light inextensible string. A horizontal force is applied to the body such that the body is …
• WAEC 2009 · Paper 2 · Q17Coplanar forces of 4 N, 8 N, 6 N, 4 N and 5 N act at a point as shown in the diagram (not drawn to scale). If the 6 N force acts in the direction …
• WAEC 2009 · Paper 2 · Q18The position vectors of points $A$, $B$ and $C$ are $\mathbf i + 5\mathbf j$, $3\mathbf i + 9\mathbf j$ and $-\mathbf i + \mathbf j$ respectively. …
• WAEC 2009 · Paper 2 · Q17A body of mass 3 kg resting on a smooth surface is acted upon by forces $P(10\text{ N}, 045^\circ)$, $Q(12\text{ N}, 180^\circ)$, $R(15\text{ N}, 215^\circ)$ …
• WAEC 2009 · Paper 2 · Q18A body of mass 8 kg is placed on a smooth plane inclined at an angle of $40^\circ$ to the horizontal. Find the magnitude of the force: (i) acting …
• WAEC 2009 · Paper 2 · Q8A body of mass 4 kg hangs from a fixed point $O$ by a light inextensible string. It is pulled aside by a horizontal force $F$ N and rests in …
• WAEC 2008 · Paper 2 · Q18An object is thrown up a smooth plane inclined at an angle of $30^\circ$ to the horizontal. If the plane is $15\text{ m}$ long and the object …
• WAEC 2008 · Paper 2 · Q18The position vectors of the points $A$, $B$ and $C$ are $(4\mathbf i + 5\mathbf j)$, $(2\mathbf i + 2\mathbf j)$ and $(6\mathbf i + \mathbf j)$ …

Objective (7)

• NECO 2023 · Paper 1 · Q36Two forces $X$ and $Y$ have magnitudes 15 N and 20 N respectively, and their resultant is $R$. If the angle between $X$ and $R$ is $30^\circ$, …
• NECO 2023 · Paper 1 · Q38Find the magnitude of the resultant of two forces of 5 N and 4 N acting at a point if the angle between them is $60^\circ$.
• NECO 2023 · Paper 1 · Q39A horizontal force of 3500 N is capable of moving an abandoned vehicle of mass 750 kg on a rough horizontal road. Find the coefficient of friction …
• WAEC 2023 · Paper 1 · Q35A uniform beam $PQ$ of length 80 cm and weight 60 N rests on a support at $X$ where $|PX| = 30$ cm. If the body is kept in equilibrium by a mass …
• WAEC 2022 · Paper 1 · Q37A particle is acted upon by forces $F = (10\text{ N}, 060^\circ)$, $P = (15\text{ N}, 120^\circ)$ and $Q = (12\text{ N}, 200^\circ)$. Express …
• WAEC 2020 · Paper 1 · Q19Given that $\mathbf{F} = 3\mathbf{i} - 12\mathbf{j}$, $\mathbf{R} = 7\mathbf{i} + 5\mathbf{j}$ and $\mathbf{N} = p\mathbf{i} + q\mathbf{j}$ are …
• WAEC 2020 · Paper 1 · Q30A force of 230 N acts in the direction $065^\circ$. Find its horizontal component.