AQA Further AS Paper 2 Mechanics 2023 June — Question 20

Exam BoardAQA
ModuleFurther AS Paper 2 Mechanics (Further AS Paper 2 Mechanics)
Year2023
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeAngular speed conversion and basic circular motion quantities
DifficultyEasy -1.2 This is a straightforward circular motion question requiring only basic recall and application of standard formulas. Part (a) involves simple conversion (10 revolutions in 60 seconds → ω = 2π×10/60), and part (b)(i) is direct substitution into F = mω²r. The diagram task in (b)(ii) is trivial (force points toward center). No problem-solving insight or multi-step reasoning required—purely routine mechanics calculations well below average A-level difficulty.
Spec1.10c Magnitude and direction: of vectors6.01c Dimensional analysis: error checking6.03g Impulse in 2D: vector form6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r
20 J 4 Reena is skating on an ice rink, which has a horizontal surface. She follows a circular path of radius 5 metres and centre \(O\) She completes 10 full revolutions in 1 minute, moving with a constant angular speed of \(\omega\) radians per second. The mass of Reena is 40 kg
4
  1. Find the value of \(\omega\) 4
  2. (i) Find the magnitude of the horizontal resultant force acting on Reena.
    4 (b) (ii) Show the direction of this horizontal resultant force on the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-03_380_442_2017_861} 5 An impulse of \(\left[ \begin{array} { r } - 5 \\ 12 \end{array} \right] \mathrm { N } \mathrm { s }\) is applied to a particle of mass 5 kg which is moving with velocity \(\left[ \begin{array} { l } 6 \\ 2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }\) 5 (a) Calculate the magnitude of the impulse. 5 (b) Find the speed of the particle immediately after the impulse is applied.
    6 A ball is thrown with speed \(u\) at an angle of \(45 ^ { \circ }\) to the horizontal from a point \(O\) When the horizontal displacement of the ball is \(x\), the vertical displacement of the ball above \(O\) is \(y\) where $$y = x - \frac { k x ^ { 2 } } { u ^ { 2 } }$$ 6 (a) Use dimensional analysis to find the dimensions of \(k\) 6 (b) State what can be deduced about \(k\) from the dimensions that you found in part (a).
    7 Two smooth, equally sized spheres, \(A\) and \(B\), are moving in the same direction along a straight line on a smooth horizontal surface, as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-06_314_465_420_849} The spheres subsequently collide.
    Immediately after the collision, \(A\) has speed \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) has speed \(3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) The coefficient of restitution between the spheres is \(e\) 7 (a) (i) Show that \(A\) does not change its direction of motion as a result of the collision.
    7 (a) (ii) Find the value of \(e\) 7 (b) Given that the mass of \(B\) is 0.6 kg , find the mass of \(A\)
20 J

4 Reena is skating on an ice rink, which has a horizontal surface.

She follows a circular path of radius 5 metres and centre $O$\\
She completes 10 full revolutions in 1 minute, moving with a constant angular speed of $\omega$ radians per second.

The mass of Reena is 40 kg\\
4
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\omega$\\

4
\item (i) Find the magnitude of the horizontal resultant force acting on Reena.\\

4 (b) (ii) Show the direction of this horizontal resultant force on the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-03_380_442_2017_861}

5 An impulse of $\left[ \begin{array} { r } - 5 \\ 12 \end{array} \right] \mathrm { N } \mathrm { s }$ is applied to a particle of mass 5 kg which is moving with velocity $\left[ \begin{array} { l } 6 \\ 2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$

5 (a) Calculate the magnitude of the impulse.

5 (b) Find the speed of the particle immediately after the impulse is applied.\\

6 A ball is thrown with speed $u$ at an angle of $45 ^ { \circ }$ to the horizontal from a point $O$

When the horizontal displacement of the ball is $x$, the vertical displacement of the ball above $O$ is $y$ where

$$y = x - \frac { k x ^ { 2 } } { u ^ { 2 } }$$

6 (a) Use dimensional analysis to find the dimensions of $k$\\

6 (b) State what can be deduced about $k$ from the dimensions that you found in part (a).\\

7 Two smooth, equally sized spheres, $A$ and $B$, are moving in the same direction along a straight line on a smooth horizontal surface, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-06_314_465_420_849}

The spheres subsequently collide.\\
Immediately after the collision, $A$ has speed $2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $B$ has speed $3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

The coefficient of restitution between the spheres is $e$

7 (a) (i) Show that $A$ does not change its direction of motion as a result of the collision.\\

7 (a) (ii) Find the value of $e$\\

7 (b) Given that the mass of $B$ is 0.6 kg , find the mass of $A$
\end{enumerate}

\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2023 Q20}}
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