| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2020 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Engine power on road constant/variable speed |
| Difficulty | Standard +0.3 This is a standard M2 power-resistance problem requiring application of P=Fv, Newton's second law, and resolving forces on an incline. It involves multiple steps (resolving parallel to slope, using F=ma, substituting into power equation) but follows a well-practiced procedure with no novel insight required. Slightly easier than average due to straightforward setup and given numerical values. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| Use of \(56 = FV\) | B1 | |
| Equation of motion | M1 | Require all terms. Dimensionally correct. Omission of \(g\) is an accuracy error. Condone sine/cosine confusion and sign errors |
| \(F + 75g\sin\alpha - 40 = 75 \times \frac{1}{3}\) | A1 | Unsimplified equation with at most one error. In \(F\) or in \(V\). Two signs inconsistent is 2 errors. |
| \(\left(\frac{56}{V} = 65 - 49 = 16\right)\) | A1 | Correct unsimplified equation. In \(F\) or in \(V\) |
| \(V = \frac{56}{16} = 3.5\) | A1 | Max 3 s.f. Not \(\frac{7}{2}\). Not \(3\frac{1}{2}\) |
## Question 1:
| Working/Answer | Mark | Guidance |
|---|---|---|
| Use of $56 = FV$ | B1 | |
| Equation of motion | M1 | Require all terms. Dimensionally correct. Omission of $g$ is an accuracy error. Condone sine/cosine confusion and sign errors |
| $F + 75g\sin\alpha - 40 = 75 \times \frac{1}{3}$ | A1 | Unsimplified equation with at most one error. In $F$ or in $V$. Two signs inconsistent is 2 errors. |
| $\left(\frac{56}{V} = 65 - 49 = 16\right)$ | A1 | Correct unsimplified equation. In $F$ or in $V$ |
| $V = \frac{56}{16} = 3.5$ | A1 | Max 3 s.f. Not $\frac{7}{2}$. Not $3\frac{1}{2}$ |
**Total: [5]**
---\begin{enumerate}
\item A cyclist and his bicycle have a total mass of 75 kg . The cyclist is moving down a straight road that is inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 15 }$
\end{enumerate}
The cyclist is working at a constant rate of 56 W . The magnitude of the resistance to motion is modelled as a constant force of magnitude 40 N . At the instant when the speed of the cyclist is $\mathrm { Vm } \mathrm { s } ^ { - 1 }$, his acceleration is $\frac { 1 } { 3 } \mathrm {~ms} ^ { - 2 }$
Find the value of $V$.\\
(5)\\
\hfill \mbox{\textit{Edexcel M2 2020 Q1 [5]}}