Questions Further AS Paper 2 Mechanics (61 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
AQA Further AS Paper 2 Mechanics 2023 June Q8
8 In this question use \(g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) Omar, a bungee jumper of mass 70 kg , has his ankles attached to one end of an elastic cord. The other end of the cord is attached to a bridge which is 80 metres above the surface of a river. Omar steps off the bridge at the point where the cord is attached and falls vertically downwards. The cord can be modelled as a light elastic string of natural length \(L\) metres and modulus of elasticity 2800 N Model Omar as a particle. 8
  1. Given that Omar just reaches the surface of the river before being pulled back up, find the value of \(L\) Fully justify your answer.
    8
  2. If Omar is not modelled as a particle, explain the effect of revising this assumption on your answer to part (a).
AQA Further AS Paper 2 Mechanics 2023 June Q18
1 marks
18 J
34 J 2 Two particles are moving directly towards each other when they collide.
Given that the collision is perfectly elastic, state the value of the coefficient of restitution. Circle your answer.
\(e = - 1\)
\(e = 0\)
\(e = \frac { 1 } { 2 }\)
\(e = 1\) 3 A stone of mass 0.2 kg is thrown vertically upwards with a speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Find the initial kinetic energy of the stone.
Circle your answer.
[0pt] [1 mark]
1 J
5 J
10 J
AQA Further AS Paper 2 Mechanics 2023 June Q20
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
    1. Find the magnitude of the horizontal resultant force acting on Reena.
      4
  3. (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
  4. Calculate the magnitude of the impulse. 5
  5. 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
  6. Use dimensional analysis to find the dimensions of \(k\)
    6
  7. 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
    1. Show that \(A\) does not change its direction of motion as a result of the collision.
      7
  9. (ii) Find the value of \(e\)
    7
  10. Given that the mass of \(B\) is 0.6 kg , find the mass of \(A\)
AQA Further AS Paper 2 Mechanics 2024 June Q1
1 marks
1 An elastic string has modulus of elasticity 20 newtons and natural length 2 metres.
The string is stretched so that its extension is 0.5 metres.
Find the elastic potential energy stored in the string.
Circle your answer.
[0pt] [1 mark]
1.25 J
5.5 J
5 J
10 J
AQA Further AS Paper 2 Mechanics 2024 June Q2
1 marks
2 State the dimensions of impulse.
Circle your answer.
[0pt] [1 mark]
\(M L T ^ { - 2 }\)
\(M L T ^ { - 1 }\)
MLT
\(M L T { } ^ { 2 }\)
AQA Further AS Paper 2 Mechanics 2024 June Q3
1 marks
3 A cyclist travels around a circular track of radius 20 m at a constant speed of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the angular speed of the cyclist in radians per second. Circle your answer.
[0pt] [1 mark]
\(0.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(0.4 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(2.5 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(3.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
AQA Further AS Paper 2 Mechanics 2024 June Q5
2 marks
5 J
10 J 2 State the dimensions of impulse.
Circle your answer.
[0pt] [1 mark]
\(M L T ^ { - 2 }\)
\(M L T ^ { - 1 }\)
MLT
\(M L T { } ^ { 2 }\) 3 A cyclist travels around a circular track of radius 20 m at a constant speed of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the angular speed of the cyclist in radians per second. Circle your answer.
[0pt] [1 mark]
\(0.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(0.4 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(2.5 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(3.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
AQA Further AS Paper 2 Mechanics 2024 June Q6
6 Kepler's Third Law of planetary motion for the period of a circular orbit around the Earth is given by the formula, $$t = 2 \pi \sqrt { \frac { r ^ { 3 } } { G m } }$$ where,
\(t\) is the time taken for one orbit
\(r\) is the radius of the circular orbit
\(m\) is the mass of the Earth
\(G\) is a gravitational constant. Use dimensional analysis to determine the dimensions of \(G\)
\includegraphics[max width=\textwidth, alt={}, center]{ce05dedd-515b-49e2-92f3-f5ec22bab4be-08_2491_1755_173_123}
AQA Further AS Paper 2 Mechanics 2024 June Q7
7 A single force, \(F\) newtons, acts on a particle moving on a straight, smooth, horizontal line. The force \(F\) acts in the direction of motion of the particle.
At time \(t\) seconds, \(F = 6 \mathrm { e } ^ { t } + 2 \mathrm { e } ^ { 2 t }\) where \(0 \leq t \leq \ln 8\) 7
  1. Find the impulse of \(F\) over the interval \(0 \leq t \leq \ln 8\)
    7
  2. The particle has a mass of 2 kg and at time \(t = 0\) has velocity \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the velocity of the particle when \(t = \ln 8\)
AQA Further AS Paper 2 Mechanics 2024 June Q8
5 marks
8 Two spheres, \(A\) and \(B\), of equal size are moving in the same direction along a straight line on a smooth horizontal surface. Sphere \(A\) has mass \(m\) and is moving with speed \(4 u\) Sphere \(B\) has mass \(6 m\) and is moving with speed \(u\)
The diagram shows the spheres and their velocities. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ce05dedd-515b-49e2-92f3-f5ec22bab4be-10_227_446_648_781} \captionsetup{labelformat=empty} \caption{A}
\end{figure} B Subsequently \(A\) collides directly with \(B\) The coefficient of restitution between \(A\) and \(B\) is \(e\) 8
  1. Find, in terms of \(m\) and \(u\), the total momentum of the spheres before the collision.
    8
  2. Show that the speed of \(B\) immediately after the collision is \(\frac { u ( 3 e + 10 ) } { 7 }\)
    8
  3. After the collision sphere \(A\) moves in the opposite direction.
    Find the range of possible values for \(e\)
    [0pt] [5 marks]
AQA Further AS Paper 2 Mechanics 2024 June Q10
2 marks
10 J 2 State the dimensions of impulse.
Circle your answer.
[0pt] [1 mark]
\(M L T ^ { - 2 }\)
\(M L T ^ { - 1 }\)
MLT
\(M L T { } ^ { 2 }\) 3 A cyclist travels around a circular track of radius 20 m at a constant speed of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the angular speed of the cyclist in radians per second. Circle your answer.
[0pt] [1 mark]
\(0.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(0.4 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(2.5 \mathrm { rad } \mathrm { s } ^ { - 1 }\)
\(3.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\)