Lesson 2.13 • Competencies 2.1 – 2.8Interactive Simulation
Back to UnitUnit 2 Comprehensive Assessment
Summative 20-question randomized evaluation testing all 8 mechanics competencies (2.1 to 2.8) with instant grading, physical explanations, and targeted lesson recap links.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Synthesize concepts across all 8 mechanics competencies under exam-style conditions.
- Assess individual mastery across each competency to identify areas requiring targeted revision.
Syllabus Topic Outline
- 1Competency 2.1: Kinematics & Linear Graphs
- 2Competency 2.2: 2D Projectile Motion
- 3Competency 2.3: Dynamics & Momentum
- 4Competency 2.4: Equilibrium of Coplanar Forces (Force Board)
- 5Competency 2.5: Moments, Couples & Metre Rule
- 6Competency 2.6: Work, Energy & Power
- 7Competency 2.7: Circular Motion & Hydrostatics (U-Tube, Hare’s Apparatus)
- 8Competency 2.8: Rotational Dynamics & Flotation (Hydrometer)
Unit 2 Comprehensive Assessment: Mechanics
20-question summative evaluation covering all syllabus competencies (2.1 to 2.8) including all 5 laboratory investigations.
Answered: 0 / 20
Q1Competency 2.1: Kinematics
A car accelerates uniformly from rest to a velocity of 20 m s⁻¹ over a displacement of 50 m. What is its acceleration?
Hint: Use the third kinematic equation: v² = u² + 2as where u = 0.
Q2Competency 2.1: Kinematics
A ball is projected vertically upwards with a velocity of 30 m s⁻¹. Taking g = 9.8 m s⁻², calculate the maximum height reached (in metres, to 1 decimal place).
m
Hint: At the maximum height, v = 0. Use v² = u² - 2gh.
Q3Competency 2.1: Kinematics
A laboratory investigation determines the acceleration of free fall g using a 50 Hz ticker-timer attached to a falling weighted tape. The timer produces dots on paper tape at equal time intervals.
(a) Calculate the time interval T between two consecutive dots on the ticker tape.[1 marks]
(b) Explain why the distance between successive dot intervals increases down the tape, and state the relationship between the distance increment and acceleration g.[2 marks]
(c) The distance between the 1st dot and the 6th dot is 12.0 cm (5 intervals), and between the 6th dot and the 11th dot is 21.8 cm (5 intervals). Calculate the experimental value of the acceleration of free fall g.[4 marks]
(d) State two practical precautions taken during this experiment to minimize systematic and random errors.[2 marks]
Hint: Use the difference in mean velocities between two equal time intervals of 5 dots: Δv = g · Δt.
Q4Competency 2.2: Resultant Forces, Moments & Centres of Gravity
In the laboratory determination of the mass of a metre rule using the Principle of Moments, where does the weight of the uniform metre rule act?
Hint: For a uniform body of symmetrical geometry, the centre of gravity coincides with its geometric midpoint.
Q5Competency 2.2: Resultant Forces, Moments & Centres of Gravity
A uniform metre rule is balanced horizontally on a knife edge placed at the 40 cm mark when a mass of 60 g is suspended from the 10 cm mark. Calculate the mass of the metre rule in grams.
g
Hint: Take moments about the knife edge at 40 cm: Anti-clockwise moment = Clockwise moment. The rule weight acts at 50 cm.
Q6Competency 2.2: Resultant Forces, Moments & Centres of Gravity
A student uses the principle of moments to determine the mass M of an ordinary uniform metre rule. The rule is balanced horizontally on a knife edge placed at the 35.0 cm graduation mark by suspending a known mass m = 50.0 g at the 10.0 cm mark.
(a) State the principle of moments for a body in rotational equilibrium.[2 marks]
(b) Assuming the centre of gravity of the uniform metre rule lies at the 50.0 cm graduation mark, calculate the mass M of the metre rule.[3 marks]
(c) Explain why taking moments about the knife edge is the preferred choice of pivot.[2 marks]
(d) State two practical precautions to ensure high experimental accuracy in this balance experiment.[2 marks]
Hint: Clockwise moment about knife edge = Anticlockwise moment about knife edge: 50.0 × (35.0 - 10.0) = M × (50.0 - 35.0).
Q7Competency 2.3: Newton’s Laws & Momentum
According to Newton’s Third Law, when a horse pulls a cart forward, what is the reaction force to the force exerted by the horse on the cart?
Hint: Action and reaction act on different bodies: if A exerts force on B, B exerts equal and opposite force on A.
Q8Competency 2.3: Newton’s Laws & Momentum
A 0.15 kg cricket ball moving at 30 m s⁻¹ is caught and brought to rest in 0.05 seconds by a fielder. What is the average braking force exerted on the ball (in Newtons)?
N
Hint: Impulse J = F · Δt = Δp = m(v - u).
Q9Competency 2.3: Newton’s Laws & Momentum
A student investigates the conservation of linear momentum using two dynamics trolleys A and B on a friction-compensated runway. Trolley A of mass mA = 0.500 kg moves at initial velocity uA = 1.20 m s⁻¹ towards stationary trolley B of mass mB = 0.300 kg. On impact, Velcro pads cause them to stick together.
(a) Explain how the runway is adjusted to achieve friction compensation.[2 marks]
(b) State the principle of conservation of linear momentum.[2 marks]
(c) Calculate the common velocity V of the coupled trolleys immediately after the collision.[3 marks]
(d) Calculate the kinetic energy lost during the collision and account for where this energy has gone.[3 marks]
Hint: Total momentum before collision equals total momentum after collision. Kinetic energy is not conserved in completely inelastic collisions.
Q10Competency 2.4: Equilibrium
In Gravesande’s force board experiment to verify the Parallelogram Law, why is a small plane mirror strip placed under the threads when marking their directions on drawing paper?
Hint: Parallax error occurs when viewing an object from an angle rather than perpendicularly.
Q11Competency 2.4: Equilibrium
Two forces of 30 N and 40 N act at right angles (90°) to each other on a particle. What is the magnitude of their resultant force?
Hint: Resultant R = √(P² + Q² + 2PQ cos 90°) = √(P² + Q²).
Q12Competency 2.4: Equilibrium
In an experiment to verify the triangle of forces using a vertical force board, three coplanar forces P, Q, and R act on a small junction ring O via light cords and friction-free pulleys, keeping it in static equilibrium.
(a) State the conditions necessary for three coplanar non-parallel forces to keep a body in equilibrium.[2 marks]
(b) Describe how the directions of the strings are transferred onto the paper behind the strings without parallax error.[2 marks]
(c) Explain how the drawn vector triangle confirms whether the experimental forces satisfy equilibrium.[2 marks]
(d) In an experiment, two cords make an angle of 90° with each other and support masses m1 = 0.300 kg and m2 = 0.400 kg. Calculate the mass m3 required on the third cord to maintain equilibrium, taking g = 9.80 m s⁻².[4 marks]
Hint: The resultant of the two perpendicular forces must be equal and opposite to the tension in the third string: m3 = √(m1² + m2²).
Q13Competency 2.5: Work, Energy & Power
How much work is done by a force of 50 N acting at an angle of 60° to the displacement when an object moves 8 metres along a flat surface?
Hint: Work W = F · s · cos θ.
Q14Competency 2.5: Work, Energy & Power
A small steel sphere of mass m = 0.050 kg is released from rest at height h above the lowest point on a smooth track that incorporates a vertical circular loop of radius r = 0.20 m. Neglect frictional dissipation and take g = 9.80 m s⁻².
(a) Derive an expression for the minimum speed v_top required at the highest point of the loop for the sphere to maintain contact with the track.[3 marks]
(b) Applying the principle of conservation of mechanical energy, determine the minimum release height h_min above the lowest point.[3 marks]
(c) Calculate the speed v_bot of the sphere at the bottom of the loop when released from height h_min = 0.50 m.[2 marks]
(d) Calculate the normal reaction force N_bot exerted by the track on the sphere at the bottom of the loop.[2 marks]
Hint: At the top N = 0 requires v_top = √(gr). Using energy conservation gives h_min = 2.5 r and normal force at bottom N_bot = 6 mg.
Q15Competency 2.6: Rotational & Circular Motion
A particle moves in a horizontal circle of radius r with constant speed v. What is the direction of its acceleration?
Hint: Centripetal acceleration arises because the velocity vector direction continuously changes toward the centre.
Q16Competency 2.6: Rotational & Circular Motion
A conical pendulum consists of a small bob of mass m = 0.150 kg suspended from a fixed ceiling hook by a light inextensible string of length L = 0.800 m. The bob describes a horizontal circle at steady speed, with the string maintaining a constant angle θ = 30.0° to the vertical. Take g = 9.80 m s⁻².
(a) Identify the forces acting on the pendulum bob and state which force component provides the centripetal acceleration.[2 marks]
(b) Show that the tension in the string is T = mg / cosθ, and calculate its numerical value in newtons.[3 marks]
(c) Derive the formula for the period of revolution T_rev in terms of L, θ, and g, and calculate its value.[4 marks]
(d) State how the period of revolution changes if the bob is replaced with one of mass 2m while maintaining the same string length L and angle θ.[1 marks]
Hint: Resolve tension into vertical component T cosθ = mg and horizontal centripetal component T sinθ = m ω² L sinθ.
Q17Competency 2.7: Hydrostatics
In determining the relative density of an oil immiscible with water using a U-tube, how is the reference datum level established?
Hint: Hydrostatic pressure is equal across any continuous connected horizontal layer of the same liquid.
Q18Competency 2.7: Hydrostatics
A student uses Hare’s apparatus to determine the density ρ_L of an unknown liquid by comparing its column height with that of distilled water (ρ_w = 1000 kg m⁻³). The apparatus consists of an inverted U-tube connected to an air pump via a pinch clip.
(a) Explain the working principle of Hare’s apparatus and derive the relationship between the column heights (h_w, h_L) and densities (ρ_w, ρ_L).[3 marks]
(b) State why knowledge of atmospheric pressure H is not required when calculating the density of the liquid using this method.[1 marks]
(c) In an experiment, the height of the water column is h_w = 24.5 cm while the height of the unknown liquid column is h_L = 30.6 cm. Calculate the density of the unknown liquid ρ_L in kg m⁻³.[3 marks]
(d) State two practical precautions taken to minimize experimental error when taking height measurements in Hare’s apparatus.[3 marks]
Hint: The pressure difference (H - P) is identical for both limbs: h_w ρ_w g = h_L ρ_L g.
Q19Competency 2.8: Fluid Dynamics
In an incompressible, steady streamline fluid flow through a horizontal pipe, water flows from a cross-section of area 4.0 cm² at 2.0 m s⁻¹ into a narrow constriction of area 1.0 cm². What is the flow speed in the constriction?
Hint: Use the equation of continuity: A₁ · v₁ = A₂ · v₂.
Q20Competency 2.8: Fluid Dynamics
A horizontal Venturi meter is used to measure the flow rate of water (density ρ = 1000 kg m⁻³) flowing through a horizontal pipeline. The cross-sectional area of the wide main pipe is A₁ = 20.0 cm² and the area of the constricted throat is A₂ = 5.00 cm². Two vertical manometer tubes are tapped into the wide section and throat respectively. Take g = 9.80 m s⁻².
(a) State Bernoulli’s principle for steady streamline flow of an ideal incompressible fluid, and state two assumptions required for the principle to hold.[2 marks]
(b) Using the continuity equation A₁ v₁ = A₂ v₂ and Bernoulli’s equation for a horizontal pipe, derive the expression for flow speed v₁ in the wide section in terms of A₁, A₂, ρ, and the pressure difference ΔP = P₁ - P₂.[3 marks]
(c) The height difference between the water columns in the two vertical manometer tubes is measured as h = 15.0 cm. Calculate the pressure difference ΔP in Pa and the flow velocity v₁ in the main pipe in m s⁻¹.[3 marks]
(d) Explain why the cross-sectional area of the Venturi tube expands gradually rather than abruptly after the throat.[2 marks]
Hint: Apply continuity v₂ = (A₁/A₂) v₁ and horizontal Bernoulli equation: ΔP = ½ ρ (v₂² - v₁²). For the manometer: ΔP = h ρ g.