OCR M2 2010 June — Question 3 9 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2010
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPower and driving force
TypeFind acceleration on incline given power
DifficultyStandard +0.8 This M2 question requires multiple connected steps: finding the resistance constant from maximum power conditions, applying P=Fv with v² resistance law, then resolving forces on an incline with acceleration. The climbing component adds geometric complexity beyond standard horizontal motion problems, and students must carefully manage the power equation with non-constant resistance across different speeds.
Spec3.03c Newton's second law: F=ma one dimension6.02k Power: rate of doing work6.02l Power and velocity: P = Fv

The maximum power produced by the engine of a small aeroplane of mass 2 tonnes is 128 kW. Air resistance opposes the motion directly and the lift force is perpendicular to the direction of motion. The magnitude of the air resistance is proportional to the square of the speed and the maximum steady speed in level flight is \(80 \text{ ms}^{-1}\).
  1. Calculate the magnitude of the air resistance when the speed is \(60 \text{ ms}^{-1}\). [5]
The aeroplane is climbing at a constant angle of \(2°\) to the horizontal.
  1. Find the maximum acceleration at an instant when the speed of the aeroplane is \(60 \text{ ms}^{-1}\). [4]

The maximum power produced by the engine of a small aeroplane of mass 2 tonnes is 128 kW. Air resistance opposes the motion directly and the lift force is perpendicular to the direction of motion. The magnitude of the air resistance is proportional to the square of the speed and the maximum steady speed in level flight is $80 \text{ ms}^{-1}$.

\begin{enumerate}[label=(\roman*)]
\item Calculate the magnitude of the air resistance when the speed is $60 \text{ ms}^{-1}$. [5]
\end{enumerate}

The aeroplane is climbing at a constant angle of $2°$ to the horizontal.

\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the maximum acceleration at an instant when the speed of the aeroplane is $60 \text{ ms}^{-1}$. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR M2 2010 Q3 [9]}}