| Exam Board | Edexcel |
|---|---|
| Module | FM1 AS (Further Mechanics 1 AS) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find acceleration on incline given power |
| Difficulty | Standard +0.3 This is a standard FM1 mechanics problem requiring application of P=Fv and Newton's second law on an incline. Students must resolve forces, use the power equation to find driving force, then apply F=ma. It's slightly above average difficulty due to being Further Maths and requiring careful bookkeeping of multiple forces, but follows a well-practiced method with no novel insight required. |
| Spec | 6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(F = \frac{32000}{20}\) | M1 | Use of \(P = Fv\). Allow \(\frac{32}{20}\). Allow \(32000 = 20F\) or \(32 = 20F\). M0 for \(32000 = 20(F-R)\) |
| Equation of motion | M1 | Correct no. of terms, condone sign errors and sin/cos confusion. M0 if they use power in equation of motion |
| \(F - 1200g\sin\alpha - R = 1200 \times 0.5\) | A1 | Correct equation |
| Substitute for \(g\), trig and \(F\) and solve for \(R\) | DM1 | Dependent on second M1 (allow if \(g\) missing) |
| \(R = 216\) or \(220\) (N) | A1 | cao (\(R = 215.2\) if they use \(g = 9.81\)) |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $F = \frac{32000}{20}$ | M1 | Use of $P = Fv$. Allow $\frac{32}{20}$. Allow $32000 = 20F$ or $32 = 20F$. M0 for $32000 = 20(F-R)$ |
| Equation of motion | M1 | Correct no. of terms, condone sign errors and sin/cos confusion. M0 if they use power in equation of motion |
| $F - 1200g\sin\alpha - R = 1200 \times 0.5$ | A1 | Correct equation |
| Substitute for $g$, trig and $F$ and solve for $R$ | DM1 | Dependent on second M1 (allow if $g$ missing) |
| $R = 216$ or $220$ (N) | A1 | cao ($R = 215.2$ if they use $g = 9.81$) |
---\begin{enumerate}
\item A car of mass 1200 kg moves up a straight road that is inclined to the horizontal at an angle $\alpha$, where $\sin \alpha = \frac { 1 } { 15 }$
\end{enumerate}
The total resistance to the motion of the car from non-gravitational forces is modelled as a constant force of magnitude $R$ newtons.
At the instant when the engine of the car is working at a rate of 32 kW and the speed of the car is $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the acceleration of the car is $0.5 \mathrm {~ms} ^ { - 2 }$
Find the value of $R$
\hfill \mbox{\textit{Edexcel FM1 AS 2022 Q1 [5]}}