| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle on inclined plane |
| Difficulty | Moderate -0.3 This is a standard M1 mechanics question requiring Newton's second law (F=ma) and resolving forces on an incline. Part (a) is straightforward kinematics and force calculation with given values. Part (b) uses equilibrium on a slope (standard technique). Part (c) tests understanding of modeling assumptions. All techniques are routine for M1 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03f Weight: W=mg3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\text{acc}^n = \frac{10-0}{13} = \frac{2}{3} \text{ ms}^{-2}\) eqn. of motion is \(D - 60 = 78 \times \frac{2}{3}\) \(D = 112 \text{ N}\) | M1 A1 M1 A1 | |
| (b) eqn. of motion is \(112 - 60 - 78g\sin\alpha = 0\) (since no acc\(^n\)) \(\sin\alpha = \frac{52}{78g} = \frac{2}{3g}\) \(\alpha = 3.901 \therefore \alpha = 4°\) (to nearest degree) | M1 A1 M1 A1 | |
| (c) in (a) unlikely as increase in speed will cause increase in air resistance in (b) more reasonable as speed is constant | B1 B1 | (10) |
**(a)** $\text{acc}^n = \frac{10-0}{13} = \frac{2}{3} \text{ ms}^{-2}$ eqn. of motion is $D - 60 = 78 \times \frac{2}{3}$ $D = 112 \text{ N}$ | M1 A1 M1 A1 |
**(b)** eqn. of motion is $112 - 60 - 78g\sin\alpha = 0$ (since no acc$^n$) $\sin\alpha = \frac{52}{78g} = \frac{2}{3g}$ $\alpha = 3.901 \therefore \alpha = 4°$ (to nearest degree) | M1 A1 M1 A1 |
**(c)** in (a) unlikely as increase in speed will cause increase in air resistance in (b) more reasonable as speed is constant | B1 B1 | (10)
---A cyclist and her bicycle have a combined mass of 78 kg. While riding on level ground and using her greatest driving force, she is able to accelerate uniformly from rest to 10 ms$^{-1}$ in 15 seconds against constant resistive forces that total 60 N.
\begin{enumerate}[label=(\alph*)]
\item Show that her maximum driving force is 112 N. [4 marks]
\end{enumerate}
The cyclist begins to ascend a hill, inclined at an angle $\alpha$ to the horizontal, riding with her maximum driving force and against the same resistive forces. In this case, she is able to maintain a steady speed.
\begin{enumerate}[label=(\alph*)]\setcounter{enumi}{1}
\item Find the angle $\alpha$, giving your answer to the nearest degree. [4 marks]
\item Comment on the assumption that the resistive force remains constant
\begin{enumerate}[label=(\roman*)]
\item in the case when the cyclist is accelerating,
\item in the case when she is maintaining a steady speed. [2 marks]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [10]}}