Standard +0.3 This is a straightforward M2 work-energy-power question requiring standard application of P=Fv and F=ma. Part (a) uses equilibrium at constant speed (forces balance), part (b) applies Newton's second law with power. Both parts follow textbook methods with no novel problem-solving required, making it slightly easier than average.
A cyclist and his bicycle have a total mass of 75 kg . The cyclist is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 21 }\). The non-gravitational resistance to motion is modelled as a constant force of magnitude \(R\) newtons. The cyclist is working at a constant rate of 280 W and moving at a constant speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the value of \(R\).
Later the cyclist cycles down the same road on the same bicycle. He is again working at a constant rate of 280 W and the resistance to motion is now modelled as a constant force of magnitude 60 N .
Find the acceleration of the cyclist at the instant when his speed is \(3.5 \mathrm {~ms} ^ { - 1 }\).
\begin{enumerate}
\item A cyclist and his bicycle have a total mass of 75 kg . The cyclist is moving up a straight road inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac { 1 } { 21 }$. The non-gravitational resistance to motion is modelled as a constant force of magnitude $R$ newtons. The cyclist is working at a constant rate of 280 W and moving at a constant speed of $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(a) Find the value of $R$.
\end{enumerate}
Later the cyclist cycles down the same road on the same bicycle. He is again working at a constant rate of 280 W and the resistance to motion is now modelled as a constant force of magnitude 60 N .\\
(b) Find the acceleration of the cyclist at the instant when his speed is $3.5 \mathrm {~ms} ^ { - 1 }$.
\hfill \mbox{\textit{Edexcel M2 2017 Q2 [8]}}