| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2021 |
| Session | January |
| Marks | 8 |
| 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 two-part M2 power question requiring application of F=ma and P=Fv in two scenarios to form simultaneous equations. The method is routine (find R from first scenario, then P from second), though students must correctly handle the incline component. Slightly easier than average due to straightforward setup and clean numbers. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance Notes |
| Use of \(P=15F_1\) or \(P=10F_2\) | M1 | Seen or implied |
| \(F_1-R=600\times 0.2\) | M1 | Equation of motion. Needs all terms. Condone sign errors. Inclusion of \(g\) is an accuracy error |
| \(\dfrac{P}{15}-R=120\) | A1 | Correct equation in \(P\) and their \(R\) |
| Up the slope: \(F_2-R-600g\sin\theta=0\) | M1 | Equation of motion. Needs all terms and \(F_2\neq F_1\). Condone sign errors. Condone sin/cos confusion. Omission of \(g\) is an accuracy error |
| A1 | Unsimplified equation in \(P\) or \(F_2\) with at most 1 error | |
| \(\dfrac{P}{10}-R-30g=0\) | A1 | Correct equation in \(P\) and their same \(R\) |
| \(\dfrac{P}{15}-\dfrac{P}{10}+30g=120\) | DM1 | Solve for \(P\). Dependent on the 2 preceding M marks |
| \(P=5220\) (5200) | A1 | Correct, max 3 s.f. |
# Question 3:
| Working/Answer | Mark | Guidance Notes |
|---|---|---|
| Use of $P=15F_1$ or $P=10F_2$ | M1 | Seen or implied |
| $F_1-R=600\times 0.2$ | M1 | Equation of motion. Needs all terms. Condone sign errors. Inclusion of $g$ is an accuracy error |
| $\dfrac{P}{15}-R=120$ | A1 | Correct equation in $P$ and their $R$ |
| Up the slope: $F_2-R-600g\sin\theta=0$ | M1 | Equation of motion. Needs all terms and $F_2\neq F_1$. Condone sign errors. Condone sin/cos confusion. Omission of $g$ is an accuracy error |
| | A1 | Unsimplified equation in $P$ or $F_2$ with at most 1 error |
| $\dfrac{P}{10}-R-30g=0$ | A1 | Correct equation in $P$ and their same $R$ |
| $\dfrac{P}{15}-\dfrac{P}{10}+30g=120$ | DM1 | Solve for $P$. Dependent on the 2 preceding M marks |
| $P=5220$ (5200) | A1 | Correct, max 3 s.f. |3. A car of mass 600 kg travels along a straight horizontal road with the engine of the car working at a constant rate of $P$ watts. The resistance to the motion of the car is modelled as a constant force of magnitude $R$ newtons. At the instant when the speed of the car is $15 \mathrm {~ms} ^ { - 1 }$, the magnitude of the acceleration of the car is $0.2 \mathrm {~ms} ^ { - 2 }$.
Later the same car travels up a straight road inclined at angle $\theta$ to the horizontal, where $\sin \theta = \frac { 1 } { 20 }$. The resistance to the motion of the car from non-gravitational forces is modelled as a constant force of magnitude $R$ newtons. When the engine of the car is working at a constant rate of $P$ watts, the car has a constant speed of $10 \mathrm {~ms} ^ { - 1 }$.
Find the value of $P$.
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\hfill \mbox{\textit{Edexcel M2 2021 Q3 [8]}}