| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find acceleration given power |
| Difficulty | Moderate -0.3 This is a straightforward M2 power-force-velocity question requiring standard application of P=Fv and F=ma. Part (i) uses Newton's second law to find driving force, then P=Fv to find speed. Part (ii) applies P=Fv with forces in equilibrium on an incline. Both parts are routine textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Driving force = \(\frac{23000}{v}\) | B1 | |
| \(\frac{23000}{v} - 600 = 1400(0.3)\) | M1 | Attempt at N2L with 3 terms; allow \(D - 600 = 1400(0.3)\) |
| \(v = 22.5 \text{ m s}^{-1}\) | A1 [3] | \(v = 22.54901...\); allow \(^{1150}/_{51}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(D - 600 - mg \sin 10 = 0\) | M1 | Attempt at N2L with three terms (\(D = 2982.452998\)); \(g\) needed |
| \(P = (cv(D))(12)\) | M1 | Use of \(P = Dv\) |
| \(P = 35.8 \text{ kW or } 35800 \text{ W}\) | A1 [3] | \(P = 35789.43597\) |
## (i)
Driving force = $\frac{23000}{v}$ | B1 |
$\frac{23000}{v} - 600 = 1400(0.3)$ | M1 | Attempt at N2L with 3 terms; allow $D - 600 = 1400(0.3)$
$v = 22.5 \text{ m s}^{-1}$ | A1 [3] | $v = 22.54901...$; allow $^{1150}/_{51}$
## (ii)
$D - 600 - mg \sin 10 = 0$ | M1 | Attempt at N2L with three terms ($D = 2982.452998$); $g$ needed
$P = (cv(D))(12)$ | M1 | Use of $P = Dv$
$P = 35.8 \text{ kW or } 35800 \text{ W}$ | A1 [3] | $P = 35789.43597$
---A car of mass 1400 kg is travelling on a straight horizontal road against a constant resistance to motion of 600 N. At a certain instant the car is accelerating at $0.3 \text{ m s}^{-2}$ and the engine of the car is working at a rate of 23 kW.
\begin{enumerate}[label=(\roman*)]
\item Find the speed of the car at this instant. [3]
\end{enumerate}
Subsequently the car moves up a hill inclined at $10°$ to the horizontal at a steady speed of $12 \text{ m s}^{-1}$. The resistance to motion is still a constant 600 N.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Calculate the power of the car's engine as it moves up the hill. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 2016 Q1 [6]}}