A Level H2 Physics Mechanics Quiz

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A-Level Physics H2 Quiz - Mechanics

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 60 minutes
Total Marks: 40
Topic: Mechanics (Section II: Topics 5–9 of Syllabus 9478)

Instructions:

• Answer all 20 questions.
• Show your working clearly for calculation questions.
• Use the data booklet values where needed: $g = 9.81\ \text{m s}^{-2}$, $G = 6.67 \times 10^{-11}\ \text{N m}^2\ \text{kg}^{-2}$, $M_E = 5.97 \times 10^{24}\ \text{kg}$, $R_E = 6.37 \times 10^{6}\ \text{m}$.
• Marks are indicated at the end of each question.

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Section A: Short Structured Questions (1–10)

1. State the principle of conservation of linear momentum. [2]

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2. A ball of mass $0.20\ \text{kg}$ is thrown vertically upward with initial speed $12\ \text{m s}^{-1}$. Neglecting air resistance, calculate the maximum height reached. [3]

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3. A projectile is launched horizontally from a cliff of height $45\ \text{m}$ with speed $20\ \text{m s}^{-1}$. Calculate the time taken to reach the ground. [2]

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4. Define the term centripetal force. [1]

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5. A car of mass $1000\ \text{kg}$ moves around a circular track of radius $50\ \text{m}$ at constant speed $15\ \text{m s}^{-1}$. Calculate the centripetal force acting on it. [2]

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6. State Newton's law of gravitation in words. [2]

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7. A mass-spring system oscillates with simple harmonic motion of amplitude $0.05\ \text{m}$ and angular frequency $4.0\ \text{rad s}^{-1}$. Calculate the maximum acceleration. [2]

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8. For a body executing simple harmonic motion, state the relationship between displacement $x$ and acceleration $a$. [1]

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9. A satellite orbits Earth at a distance of $2R_E$ from Earth's centre. Given $g$ at surface is $9.81\ \text{m s}^{-2}$, calculate the gravitational field strength at that orbit. [2]

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10. Describe what is meant by resonance in the context of forced oscillations. [2]

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Section B: Calculation and Application (11–15)

11. A trolley of mass $2.0\ \text{kg}$ moving at $3.0\ \text{m s}^{-1}$ collides head-on with a stationary trolley of mass $1.0\ \text{kg}$. After the collision the $2.0\ \text{kg}$ trolley moves at $1.0\ \text{m s}^{-1}$ in the same direction. Calculate the velocity of the $1.0\ \text{kg}$ trolley after collision. [3]

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12. A ball is projected at $30^{\circ}$ above the horizontal with speed $25\ \text{m s}^{-1}$. (a) Calculate the horizontal component of the initial velocity. [1] (b) Calculate the time of flight assuming it lands at the same height. [2] (c) Calculate the range. [2]

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13. A pendulum of length $1.2\ \text{m}$ performs SHM with small amplitude. (a) Calculate its period. [2] (b) If the maximum angular displacement is $0.10\ \text{rad}$, find the maximum linear speed of the bob. [2]

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14. A $500\ \text{kg}$ satellite circles Earth at radius $7.0 \times 10^{6}\ \text{m}$. (a) Calculate the gravitational force on it. ($M_E = 5.97 \times 10^{24}\ \text{kg}$) [2] (b) Hence find the orbital speed. [2]

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15. A mass of $0.40\ \text{kg}$ on a spring ($k = 160\ \text{N m}^{-1}$) oscillates with amplitude $0.10\ \text{m}$. (a) Calculate the total energy of the oscillation. [2] (b) Calculate the speed when displacement is $0.06\ \text{m}$. [2]

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Section C: Data Interpretation and Extended Reasoning (16–20)

16. The velocity-time graph below shows the motion of a drone.

Image pending generation: graph for Q16.

(a) Calculate the acceleration during the first 4 s. [2] (b) Calculate the total distance travelled. [2]

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17. The diagram shows a mass $m$ attached to a string moving in a vertical circle of radius $r$.

Image pending generation: diagram for Q17.

(a) Calculate the tension at the bottom of the circle. [3] (b) State and explain whether the string is more likely to break at the top or bottom. [2]

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18. A student investigates damped oscillations of a spring-mass system. (a) Distinguish between light damping and critical damping. [2] (b) Suggest one practical application where heavy damping is desirable. [1]

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19. Two stars of masses $M$ and $2M$ are separated by distance $d$. (a) Show that the gravitational field strength at the midpoint between them is zero. [2] (b) A test mass placed at the midpoint is displaced slightly toward the smaller star. State the nature of the resultant force and explain. [2]

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20. A geostationary satellite orbits above the Equator. (a) State two conditions necessary for a satellite to be geostationary. [2] (b) Calculate the orbital radius of a geostationary satellite given Earth's rotation period is $24.0\ \text{h}$ and $GM_E = 3.99 \times 10^{14}\ \text{m}^3\ \text{s}^{-2}$. [3]

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A-Level Physics H2 Quiz - Mechanics: Answer Key

Topic: Mechanics (Syllabus 9478, Section II)
Total Marks: 40

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Section A: Short Structured Questions

1. [2 marks]
Principle: In a closed (isolated) system, the total linear momentum remains constant provided no external net force acts.
Teaching note: Must state "closed system" and "before = after" or "constant if net external force zero". Common mistake: omitting external-force condition.

2. [3 marks]
Use $v^2 = u^2 + 2as$ with $v=0$, $u=12$, $a=-9.81$:
$0 = 12^2 + 2(-9.81)s$
$s = 144 / 19.62 = 7.34\ \text{m}$
Marks: 1 for correct eqn, 1 substitution, 1 answer with unit.

3. [2 marks]
Vertical motion: $s = \frac{1}{2}gt^2$ → $45 = 0.5 \times 9.81 \times t^2$
$t = \sqrt{90/9.81} = 3.03\ \text{s}$
Horizontal speed irrelevant to fall time.

4. [1 mark]
Centripetal force is the resultant force directed toward the centre of a circular path, causing centripetal acceleration.

5. [2 marks]
$F = mv^2/r = 1000 \times 15^2 / 50 = 4500\ \text{N}$

6. [2 marks]
Newton's law: Force between two point masses is directly proportional to product of masses and inversely proportional to square of distance between them, directed along line joining them.

7. [2 marks]
$a_{max} = \omega^2 x_0 = 4.0^2 \times 0.05 = 0.80\ \text{m s}^{-2}$

8. [1 mark]
$a = -\omega^2 x$ (acceleration proportional to displacement, opposite direction).

9. [2 marks]
$g \propto 1/r^2$; at $2R_E$: $g = 9.81 / 4 = 2.45\ \text{m s}^{-2}$

10. [2 marks]
Resonance occurs when driving frequency equals natural frequency, causing large amplitude buildup. Need mention frequency match and amplitude growth.

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Section B: Calculation and Application

11. [3 marks]
Conservation of momentum: $2.0\times3.0 + 0 = 2.0\times1.0 + 1.0\times v$
$6 = 2 + v$ → $v = 4.0\ \text{m s}^{-1}$
Marks: eqn (1), sub (1), ans (1).

12. [5 marks total]
(a) [1] $u_x = 25\cos30^{\circ} = 21.7\ \text{m s}^{-1}$
(b) [2] $t_{flight} = 2u_y/g = 2(25\sin30^{\circ})/9.81 = 2.55\ \text{s}$
(c) [2] Range $= u_x \times t = 21.7 \times 2.55 = 55.3\ \text{m}$

13. [4 marks]
(a) [2] $T = 2\pi\sqrt{l/g} = 2\pi\sqrt{1.2/9.81} = 2.20\ \text{s}$
(b) [2] $v_{max} = \omega L\theta_{max} = (2\pi/T)\times1.2\times0.10 = 0.343\ \text{m s}^{-1}$

14. [4 marks]
(a) [2] $F = GMm/r^2 = (6.67\times10^{-11}\times5.97\times10^{24}\times500)/(7.0\times10^6)^2 = 4.06\times10^{3}\ \text{N}$
(b) [2] $F = mv^2/r$ → $v = \sqrt{Fr/m} = \sqrt{4060\times7.0\times10^6/500} = 7.53\times10^{3}\ \text{m s}^{-1}$

15. [4 marks]
(a) [2] $E = \frac{1}{2}kA^2 = 0.5\times160\times0.10^2 = 0.80\ \text{J}$
(b) [2] $v = \omega\sqrt{A^2-x^2}$, $\omega=\sqrt{k/m}=20$; $v = 20\sqrt{0.10^2-0.06^2} = 1.60\ \text{m s}^{-1}$

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Section C: Data Interpretation and Extended Reasoning

16. [4 marks]
(a) [2] $a = \Delta v/\Delta t = 16/4 = 4.0\ \text{m s}^{-2}$
(b) [2] Area: triangle $0.5\times4\times16=32$; rect $4\times16=64$; triangle $0.5\times2\times16=16$; total $=112\ \text{m}$

17. [5 marks]
(a) [3] At bottom: $T_B - mg = mv^2/r$ → $T_B = 0.50\times9.81 + 0.50\times6.0^2/0.80 = 4.91 + 22.5 = 27.4\ \text{N}$
(b) [2] Bottom: tension larger due to adding weight; more likely break at bottom.

18. [3 marks]
(a) [2] Light: amplitude decays gradually, oscillates many cycles; critical: returns to equilibrium in shortest time without oscillating.
(b) [1] e.g. car shock absorber.

19. [4 marks]
(a) [2] Field from M: $GM/(d/2)^2$ left; from 2M: $2GM/(d/2)^2$ right; equal magnitude opposite → net zero.
(b) [2] Toward smaller star (M): nearer M so its attraction stronger; net force toward M.

20. [5 marks]
(a) [2] (i) period = 24 h, (ii) above Equator, (iii) same direction as Earth rotation. (any two)
(b) [3] $r^3 = GM_E T^2 / 4\pi^2$; $T=86400\ \text{s}$; $r = (3.99\times10^{14}\times86400^2/4\pi^2)^{1/3} = 4.23\times10^{7}\ \text{m}$