Edexcel IAL M1 Statics of a Particle Questions
Resolving forces; equilibrium of a particle; friction and limiting equilibrium (F ≤ μR).
- M1 · Mechanics 1
- Calculator allowed
- 30 practice questions
What the questions test
The 30 M1 statics of a particle practice questions cover:
Worked example 1
A particle of mass $2 \text{ kg}$ is held in limiting equilibrium on a rough plane inclined at $40^{\circ}$ to the horizontal by a horizontal force $H$. The particle is on the point of sliding up the plane. The coefficient of friction is $0.3$. Find the value of $H$.
Mark scheme
- M1 for resolving perpendicular to the plane: $R = 2g \cos 40^{\circ} + H \sin 40^{\circ}$.
- M1 for resolving parallel to the plane (friction acts down): $H \cos 40^{\circ} = 2g \sin 40^{\circ} + F$.
- M1 for substituting $F = 0.3R$: $H \cos 40^{\circ} = 2g \sin 40^{\circ} + 0.3(2g \cos 40^{\circ} + H \sin 40^{\circ})$.
- M1 for rearranging to isolate $H$: $H(\cos 40^{\circ} - 0.3 \sin 40^{\circ}) = 2g \sin 40^{\circ} + 0.6g \cos 40^{\circ}$.
- A1 for calculating $H = \frac{12.60 + 4.50}{0.766 - 0.193} = \frac{17.10}{0.573} = 29.8 \text{ N}$ (to 3 s.f.).
Worked example 2
A particle of mass $2 \text{ kg}$ is pressed against a rough vertical wall by a force $P$ acting at an angle of $30^{\circ}$ to the upward vertical. The coefficient of friction is $0.4$. Find the minimum value of $P$ to prevent the particle sliding down the wall.
Mark scheme
- M1 for resolving horizontally to find $R$: $R = P \sin 30^{\circ}$.
- M1 for determining limiting friction: $F = 0.4(P \sin 30^{\circ}) = 0.2P$.
- M1 for resolving vertically: the upward components must balance the weight. $P \cos 30^{\circ} + F = 2g$.
- M1 for substituting $F$: $P \cos 30^{\circ} + 0.2P = 19.6$.
- A1 for calculating $P = \frac{19.6}{\cos 30^{\circ} + 0.2} = \frac{19.6}{0.866 + 0.2} = 18.4 \text{ N}$ (to 3 s.f.).
FAQ
What statics of a particle is in Edexcel IAL M1?
Resolving forces; equilibrium of a particle; friction and limiting equilibrium (F ≤ μR).
Is M1 a calculator paper?
Yes, a calculator is allowed in M1, but method marks are only given for working you write down.
How are M1 statics of a particle questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.