Every question, cut by section

A string passes over a pulley described as "light and smooth." What does this actually allow you to assume about the tension in the string?

A particle slides down a rough plane inclined to the horizontal. In which direction does friction act on it, and why?

A light rod rests horizontally on two supports, with a single particle of weight 40 N attached to it somewhere between them. What is the total upward force supplied by the two reactions, and why?

A block Q rests on a rough table. Q is connected by one light string over a smooth pulley to a particle P hanging on its left, and by a SEPARATE light string over a second smooth pulley to a particle R hanging on its right. Both strings are taut and the system is moving. Which statement is correct?

A rod rests on supports at C and D. You are told the rod is on the point of tilting about C. Which single fact does that sentence give you?

Two particles are connected by a light inextensible string passing over a smooth fixed pulley. P (mass 3 kg) hangs freely on one side; Q (mass 5 kg) hangs freely on the other. Released from rest, Q (the heavier particle) descends and P rises. Using T for the tension and a for the common acceleration, which pair of equations correctly applies Newton's second law to each particle?

A non-uniform rod AB, length 6 m, weight 60 N, rests horizontally on supports at C (1 m from A) and D (5 m from A). The rod's centre of mass is 4 m from A (not the midpoint, since the rod is non-uniform). Find R_D by taking moments about C.

How many distinct WME01 series does WME01-verified-facts.md confirm contain a worked example of Newton's second law in vector form (spec 4.1), in the material reviewed for this lesson?

A rod rests on two supports, C and D, with an unknown reaction at each. You want an equation containing only R_D, with R_C absent entirely. About which point should you take moments?

A student's working reads: 'Resultant force = a = 5i + 2j (N), so...' — going on to use this directly as the resultant force for a particle of mass 3 kg. Based on the mark scheme's own general Mechanics-marking principles, what does this cost?

A uniform rod AB rests horizontally on two smooth supports at C and D. As a weight placed near B is increased, the rod is on the point of tilting about D. What must be true of the reaction at C at that moment?

Two forces, $F_1=(3\mathbf{i}-\mathbf{j})$ N and $F_2=(\mathbf{i}+4\mathbf{j})$ N, are the only forces acting on a particle of mass $2$ kg. A student writes $F_1 = m\mathbf{a}$ and solves for a from there. What's wrong?

Using Lami's theorem on the same three-force system as MCQ 1 (10 N horizontal; F N at 25°; T N at 55°): the angle opposite the 10 N force (between F's and T's own lines) is 80°; opposite F is 125°; opposite T is 155°. What is T, to 3 s.f.?

Why is it valid to separately equate the i-coefficients and the j-coefficients on the two sides of a vector equation such as $p\mathbf{i}+q\mathbf{j} = 8\mathbf{i}-6\mathbf{j}$, rather than needing some fresh justification each time it's used?

A light rigid rod connects a particle to a fixed point, and the rod is found to be under thrust rather than tension. What does this tell you about how the rod is acting on the particle?

Forces $F_1 = (5\mathbf{i}+2\mathbf{j})$ N and $F_2 = (p\mathbf{i}+q\mathbf{j})$ N act on a particle of mass $2$ kg, producing acceleration $\mathbf{a}=(4\mathbf{i}-3\mathbf{j})$ m s$^{-2}$. Find $p$ and $q$.

In this lesson's main worked example (5 N, F at 30°, T at 60°), resolving along F's own direction eliminates T completely, because F and T act at exactly 90° to each other. In the system from MCQ 1 (10 N, F at 25°, T at 55°), does resolving along F's own direction eliminate T in the same way?

Which of the following does the M1 section of the real exam formula booklet give you for Newton's second law, $\mathbf{F}=m\mathbf{a}$?

A particle is in equilibrium under three coplanar forces: a horizontal force of $10$ N, a force $F$ N at $25°$ above the horizontal, and a force $T$ N at $55°$ below the horizontal (structured exactly like this lesson's main example, different numbers). What is $F$, to 3 s.f.?

If $p\mathbf{i}+q\mathbf{j} = 6\mathbf{i} + 9\mathbf{j}$, what are $p$ and $q$?

A real WME01 examiner report on a three-force coplanar equilibrium question names three different methods candidates used successfully. Which of these is NOT one of the three?

A particle of mass $5$ kg experiences a single resultant force $\mathbf{F} = (10\mathbf{i} - 15\mathbf{j})$ N. What is its acceleration?

A particle is held in equilibrium by three coplanar forces: a known force of $5$ N, a force $F$ N acting at $30°$ to the direction of the $5$ N force, and a force $T$ N acting at $60°$ to that same direction (both $F$ and $T$ on the same side, opposing the $5$ N force). Resolving in the direction of the $5$ N force, which of these is the correct equation?

A candidate substitutes correctly into $v = u + at$, but then makes an arithmetic slip and arrives at the wrong final velocity. Based on how M1 mark schemes define M and A marks, what is most likely to happen to their marks for this line?

A particle is acted on by several coplanar forces and remains stationary indefinitely. Which condition must these forces satisfy?

A block decelerates uniformly from $10$ m s$^{-1}$ at $2$ m s$^{-2}$ until it comes to rest. While it is moving, its displacement is modelled by $s = 10t - t^2$. Solving $10t - t^2 = 16$ for the time at which the block has travelled $16$ m gives $t = 2$ or $t = 8$. Which is the correct final answer, and why?

A crate is on the point of sliding down a rough plane inclined at $35°$ to the horizontal, held in equilibrium only by friction (no other applied forces). What is the coefficient of friction $\mu$, and which method finds it fastest?

Particle $P$ is thrown vertically upward, its height modelled by $s_P = 20t - 5t^2$, where $t$ is the time in seconds since $P$ was thrown. Particle $Q$ is thrown from the same point $2$ s after $P$, and its height (using its OWN clock, $\tau$ = time since $Q$ was thrown) is modelled by $s_Q = 15\tau - 5\tau^2$. A student wants the value of $t$ (measured on P's clock) at which the two particles are at the same height, and writes $20t - 5t^2 = 15t - 5t^2$, using $t$ in both expressions. What has gone wrong?

A sled slides down a rough plane, and its acceleration is calculated in part (a) of a question. In part (b), a rope now pulls the sled up the plane with an additional force while it continues to slide down, and a student reuses part (a)'s acceleration value as the answer to part (b) without further working. What has actually gone wrong?

A real examiner report on this exact graph shape — acceleration phase, then deceleration phase, over an unknown total time — records: "a common error was to halve the time taken to decelerate rather than double it" (Jan 2023, Q1). Suppose a journey's acceleration phase takes $5$ s, and the deceleration phase is stated to take twice as long as the acceleration phase. What time would a candidate who made exactly this documented error write down for the deceleration phase?

A box rests on a rough plane inclined at $25°$ to the horizontal, with no other applied forces, and is stated to be on the point of sliding (limiting equilibrium). In which direction does the friction force act, and why?

A parcel slides down a smooth ramp, accelerating uniformly at $2.5$ m s$^{-2}$ from rest for $6$ s, then slides onto a horizontal floor, where friction decelerates it uniformly at $1$ m s$^{-2}$ until it stops. What is the total distance travelled by the parcel?

A parcel rests on a rough plane inclined at $15°$ to the horizontal, held in place by nothing but gravity, the normal reaction, and friction — no other applied force. Which of these correctly describes the friction force $F$ acting on it?

Which of the five constant-acceleration (suvat) formulae — $v=u+at$, $s=ut+\frac{1}{2}at^2$, $s=vt-\frac{1}{2}at^2$, $v^2=u^2+2as$, $s=\frac{1}{2}(u+v)t$ — appear in the M1 section of the exam formula booklet?

A crate is sliding down a rough plane, speeding up. As its speed increases, does the kinetic friction force $F = \mu R$ acting on it also increase?

A cyclist travels from $P$ to $Q$ with constant acceleration $2$ m s$^{-2}$, then immediately from $Q$ to $R$ with constant acceleration $-0.5$ m s$^{-2}$. To find the total time from $P$ to $R$ using suvat equations, what is the minimum number of separate suvat equations needed, and why?

A block is pushed up a rough plane by an applied force and is actually sliding up the slope at the moment in question. In which direction does the kinetic friction force act on it?

A velocity-time graph is a straight line from $(0, 2)$ to $(5, 12)$, then a second straight line from $(5, 12)$ to $(9, 0)$. What is the acceleration during the second stage, from $t = 5$ to $t = 9$?

A particle rests on a rough plane, in equilibrium, and the question does not state that it is on the point of sliding. Which of these must be true of the friction force $F$ acting on it?

Which of these is a legitimate reason to reach for Lami's theorem instead of resolving into components, based on how real WME01 examiner reports describe it?

Particles J (mass 5 kg) and K (mass 3 kg) collide directly. After the collision, J's velocity is $-1$ m/s (taking J's original direction of motion as positive). A question part asks: "Find the speed of J after the collision." What is the correct final answer?

A real WME01 examiner report directly compared two methods on the same resultant-of-two-forces question and found one had "more success" than the other. Which method, and why is that consistent with the mechanics of the two approaches rather than just a coincidence of that one series?

Which of the following, unlike on some other exam boards' Mechanics syllabuses, is explicitly NOT required knowledge for a WME01 momentum/impulse question (spec 4.3)?

Two forces of magnitude 9 N and 4 N act at a point, with an angle of 100° between them as drawn from their common point. Using the cosine rule on the triangle of forces, what is the magnitude of the resultant?

A question asks for the magnitude of the impulse exerted on particle H, which was at rest before colliding directly with G (already moving). Which single method reaches that answer in one substitution into I = mv − mu, with no further reasoning step needed?

A force of magnitude 12 N acts on a bearing of 200°. Which pair of components, to 3 s.f., correctly expresses it as $p\mathbf{i} + q\mathbf{j}$ (N)?

Particles E (mass 4 kg, speed 3 m/s) and F (mass 6 kg, speed 4 m/s) move towards each other along the same straight line on a smooth horizontal surface and collide directly, coalescing into a single particle. Taking the direction E was moving as positive, what is the velocity of the combined particle after the collision?

Two forces P and Q act at a point O, with an angle of 40° between them as drawn from O. To find the resultant by drawing P and Q head-to-tail as a triangle and applying the cosine rule to the third side, what angle belongs INSIDE that triangle, at the vertex where P and Q meet?

Working through a collision question, you correctly solve a conservation-of-momentum equation and find that particle P's velocity after the collision is $-2.5$ m/s. The next part asks: "Find the speed of P after the collision." What should you write as your final answer?

Two forces of magnitude 6 N and 8 N act at a point, at right angles to each other. Which single technique finds the magnitude of their resultant fastest?

Particles P (mass 3 kg, speed 4 m/s) and Q (mass 2 kg, speed 5 m/s) move towards each other along the same straight line. Taking the direction P is moving as positive, what is the total momentum of the system before they collide, in kg m/s?

A force of magnitude 10 N acts on a bearing of 030°. Taking i as a unit vector due east and j as a unit vector due north, which is the correct component form?

A particle of mass $0.8$ kg is moving with velocity $5$ m/s. What is its momentum?

A question states: "A car decelerates uniformly from 24 m s⁻¹ to rest, modelled as a particle moving in a straight line." A later part asks for one way to make the model more realistic and its effect on the calculated stopping distance. Which answer best satisfies the marking discipline named in this lesson?

A car and trailer, connected by a rigid tow-bar, are decelerating because the driving force has been removed. Solving the trailer's equation of motion gives a NEGATIVE value for the tow-bar force, where positive was defined as tension (pulling the trailer forward). What does this negative value mean?

A bead, threaded on a fixed circular wire, is held in equilibrium at a point on the wire by its own weight and the wire's reaction alone (no friction). Why does the object need to be threaded on a WIRE rather than a STRING for this equilibrium to be possible in general?

A lift of mass 500 kg carries one passenger of mass 80 kg and accelerates upward at 0.4 m/s². Which is a correctly-formed equation for finding the cable tension T?

A "show that" part asks candidates to show that a tension is 31.4 N (3 s.f.). A candidate correctly applies Newton's second law throughout and arrives at the unrounded value T = 31.36 N, which they then round and state as T = 31.4 N. Have they satisfied what the marking discipline for this kind of part actually requires?

A particle is held at rest on a rough plane inclined at 30° by a string running up the line of greatest slope to a fixed point at the top. The string is cut, and the particle immediately begins to slide down. At the instant just after the string is cut, in which direction does friction act, and does its value change from the instant just before?

A question's stem reads: "A skydiver's fall is modelled in two phases. During free fall, air resistance is ignored, so her acceleration is g throughout." A later part asks: "State one way this model could be refined to be more realistic for the free-fall phase, and describe the effect on the calculated duration of that phase." Which answer best satisfies what real examiner reports document for this question type?

A parcel Q of mass 6 kg rests on a smooth horizontal table. Q is attached by a string over a pulley at one edge to a hanging particle P, and by a SEPARATE string over a pulley at the opposite edge to a hanging particle R. The tension in the P–Q string is found to be 20 N. Can you conclude anything about the tension in the Q–R string without further working?

A block on a rough horizontal table is connected by a light inextensible string, passing over a smooth pulley at the table's edge, to a second block hanging freely. While the string stays taut, what can be said about the two blocks' accelerations?

A car (mass 800 kg) tows a trailer (mass 200 kg) along a horizontal road with driving force D. Resistances totalling 150 N act on the whole system. The system accelerates at 0.5 m/s². Which route gives D fastest, using the fewest unknowns?