SPS SPS FM Mechanics 2022 January — Question 3 9 marks

Exam BoardSPS
ModuleSPS FM Mechanics (SPS FM Mechanics)
Year2022
SessionJanuary
Marks9
TopicPower and driving force
TypeTowing system: horizontal road
DifficultyStandard +0.3 This is a standard multi-part mechanics question testing power-force-velocity relationships and equilibrium on inclines. Part (a) requires integration of P=Fv with F=ma, part (b) is straightforward equilibrium with P=Fv, and part (c) involves setting up two-body resistance equations. All techniques are routine for FM mechanics students with no novel problem-solving required, making it slightly easier than average.
Spec6.02k Power: rate of doing work6.02l Power and velocity: P = Fv
A car of mass 800 kg is driven with its engine generating a power of 15 kW.
  1. The car is first driven along a straight horizontal road and accelerates from rest. Assuming that there is no resistance to motion, find the speed of the car after 6 seconds. [2]
  2. The car is next driven at constant speed up a straight road inclined at an angle \(\theta\) to the horizontal. The resistance to motion is now modelled as being constant with magnitude of 150 N. Given that \(\sin \theta = \frac{1}{20}\), find the speed of the car. [3]
  3. The car is now driven at a constant speed of 30 ms\(^{-1}\) along the horizontal road pulling a trailer of mass 150 kg which is attached by means of a light rigid horizontal towbar. Assuming the resistance to motion of the car is three times the resistance to motion of the trailer. Find:
    1. the resistance to motion of the car,
    2. the magnitude of the tension in the towbar
    [4]
A car of mass 800 kg is driven with its engine generating a power of 15 kW.

\begin{enumerate}[label=(\alph*)]
\item The car is first driven along a straight horizontal road and accelerates from rest. Assuming that there is no resistance to motion, find the speed of the car after 6 seconds.
[2]

\item The car is next driven at constant speed up a straight road inclined at an angle $\theta$ to the horizontal. The resistance to motion is now modelled as being constant with magnitude of 150 N.

Given that $\sin \theta = \frac{1}{20}$, find the speed of the car.
[3]

\item The car is now driven at a constant speed of 30 ms$^{-1}$ along the horizontal road pulling a trailer of mass 150 kg which is attached by means of a light rigid horizontal towbar.

Assuming the resistance to motion of the car is three times the resistance to motion of the trailer. Find:
\begin{enumerate}[label=(\roman*)]
\item the resistance to motion of the car,
\item the magnitude of the tension in the towbar
\end{enumerate}
[4]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM Mechanics 2022 Q3 [9]}}
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