| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Single angled force - find limiting friction or coefficient |
| Difficulty | Standard +0.3 This is a standard M1 friction problem requiring resolution of forces and application of F=μR. Part (a) is routine 'show that' with given answer; part (b) applies F=ma after finding resultant force. Both parts follow textbook methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03e Resolve forces: two dimensions3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) resolve \(\uparrow\): \(R + 200\sin40° - 50g = 0 \therefore R = 50g - 200\sin40°\) resolve \(\rightarrow\): \(200\cos40° - F = 0 \therefore F = 200\cos40°\) \(F = \mu R\), so \(\mu = \frac{200\cos40°}{50g - 200\sin40°} = 0.424\) (3sf) | M1 A1 M1 A1 M1 A1 | |
| (b) resolve \(\uparrow\): \(R + 200\sin30° - 50g = 0 \therefore R = 50g - 200\sin30° = 390\) resolve \(\rightarrow\): \(200\cos30° - \mu R = 50a\) \(50a = 100\sqrt{3} - 0.424(390)\) \(a = 0.16 \text{ ms}^{-2}\) | M1 A1 M1 A1 M1 A1 | (12) |
**(a)** resolve $\uparrow$: $R + 200\sin40° - 50g = 0 \therefore R = 50g - 200\sin40°$ resolve $\rightarrow$: $200\cos40° - F = 0 \therefore F = 200\cos40°$ $F = \mu R$, so $\mu = \frac{200\cos40°}{50g - 200\sin40°} = 0.424$ (3sf) | M1 A1 M1 A1 M1 A1 |
**(b)** resolve $\uparrow$: $R + 200\sin30° - 50g = 0 \therefore R = 50g - 200\sin30° = 390$ resolve $\rightarrow$: $200\cos30° - \mu R = 50a$ $50a = 100\sqrt{3} - 0.424(390)$ $a = 0.16 \text{ ms}^{-2}$ | M1 A1 M1 A1 M1 A1 | (12)
---\includegraphics{figure_2}
Figure 2 shows a large block of mass 50 kg being pulled on rough horizontal ground by means of a rope attached to the block. The tension in the rope is 200 N and it makes an angle of 40° with the horizontal. Under these conditions, the block is on the point of moving.
Modelling the block as a particle,
\begin{enumerate}[label=(\alph*)]
\item show that the coefficient of friction between the block and the ground is 0.424 correct to 3 significant figures. [6 marks]
\end{enumerate}
The angle with the horizontal at which the rope is being pulled is reduced to 30°. Ignoring air resistance and assuming that the tension in the rope and the coefficient of friction remain unchanged,
\begin{enumerate}[label=(\alph*)]\setcounter{enumi}{1}
\item find the acceleration of the block. [6 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [12]}}