A Level H2 Physics Practice Paper 2

TuitionGoWhere Practice Paper — Physics H2 A-Level

Answer Key — Mechanics (Version 2 of 5)

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Section A: Multiple Choice

1. (b) $20.4 \text{ m}$ [2 marks]

Working: At maximum height, final velocity $v = 0$. Using $v^2 = u^2 - 2gh$: $0 = (20)^2 - 2(9.81)h$ $h = \frac{400}{2 \times 9.81} = \frac{400}{19.62} = 20.4 \text{ m}$

Teaching note: This uses the kinematic equation for constant acceleration. The key insight is that at the highest point, the vertical velocity is zero. We use $v^2 = u^2 + 2as$ with $a = -g$ (deceleration due to gravity). Common mistake: forgetting that $v = 0$ at the top, or using $g = 10$ when the question specifies $9.81$.

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2. (a) $1.6 \text{ m s}^{-1}$ [2 marks]

Working: By conservation of linear momentum: $m_1 u_1 + m_2 u_2 = (m_1 + m_2)v$ $(2.0)(4.0) + (3.0)(0) = (2.0 + 3.0)v$ $8.0 = 5.0v$ $v = 1.6 \text{ m s}^{-1}$

Teaching note: Since the objects stick together, this is a perfectly inelastic collision. The total momentum before equals the total momentum after. The stationary object contributes zero initial momentum. Common mistake: dividing by only one of the masses instead of the total mass.

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3. (c) $8.0 \text{ m s}^{-2}$ [2 marks]

Working: Centripetal acceleration: $a_c = \frac{v^2}{r} = \frac{(20)^2}{50} = \frac{400}{50} = 8.0 \text{ m s}^{-2}$

Teaching note: Centripetal acceleration is always directed towards the centre of the circular path. The formula $a_c = v^2/r$ applies for uniform circular motion. Common mistake: confusing centripetal acceleration with angular velocity or using $a = v/r$ instead of $v^2/r$.

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4. (c) Both $Ft$ and $m(v - u)$ [2 marks]

Working: Impulse is defined as the product of force and time: $I = Ft$. By Newton's second law in momentum form, the impulse also equals the change in momentum: $I = \Delta p = m(v - u)$. Both expressions are equivalent and correct.

Teaching note: Impulse is a vector quantity. The impulse-momentum theorem states that the impulse delivered to an object equals the change in its momentum. Both $Ft$ and $m(v-u)$ represent the same physical quantity. Common mistake: choosing only one expression when both are valid definitions.

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5. (b) $10 \text{ N m}$ [2 marks]

Working: Torque = force × perpendicular distance from pivot: $\tau = F \times d = 10 \times \frac{2.0}{2} = 10 \times 1.0 = 10 \text{ N m}$

Teaching note: The pivot is at the centre of the rod, so the perpendicular distance from the pivot to the point of application of the force is half the length of the rod ($1.0 \text{ m}$). Torque (moment of a force) measures the turning effect. Common mistake: using the full length $2.0 \text{ m}$ instead of the distance from the pivot.

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Section B: Structured Questions

6. (a) [2 marks]

Answer: The principle of conservation of linear momentum states that the total momentum of a closed system remains constant (is conserved) provided that no net external force acts on the system. Equivalently: in an isolated system, the total momentum before a collision equals the total momentum after the collision.

Marking:

• [1] for stating that total momentum is conserved/remains constant
• [1] for specifying the condition (no external forces / closed/isolated system)

Common mistake: Simply saying "momentum is conserved" without mentioning the condition of no external forces. The condition is essential for full marks.

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6. (b)(i) [3 marks]

Working: Using conservation of linear momentum: $m_A u_A + m_B u_B = m_A v_A + m_B v_B$ $(0.50)(0.80) + (0.30)(0) = (0.50)(0.20) + (0.30)v_B$ $0.40 = 0.10 + 0.30v_B$ $0.30 = 0.30v_B$ $v_B = 1.0 \text{ m s}^{-1}$

Marking:

• [1] for correct substitution into conservation of momentum equation
• [1] for correct algebraic manipulation
• [1] for correct final answer with unit ($1.0 \text{ m s}^{-1}$)

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6. (b)(ii) [2 marks]

Working: Calculate total kinetic energy before and after.

Before: $KE_{\text{before}} = \frac{1}{2}(0.50)(0.80)^2 + 0 = 0.16 \text{ J}$

After: $KE_{\text{after}} = \frac{1}{2}(0.50)(0.20)^2 + \frac{1}{2}(0.30)(1.0)^2 = 0.01 + 0.15 = 0.16 \text{ J}$

Since $KE_{\text{before}} = KE_{\text{after}}$, kinetic energy is conserved, so the collision is elastic.

Marking:

• [1] for calculating KE before and after (or showing the comparison)
• [1] for correct conclusion that the collision is elastic

Note: In this specific case, the KE values happen to be equal, making it elastic. In most "stick together" problems, the collision is inelastic, but here the objects separate after collision.

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7. (a) [2 marks]

Working: Vertical motion: $s = \frac{1}{2}gt^2$ (initial vertical velocity = 0) $45 = \frac{1}{2}(9.81)t^2$ $t^2 = \frac{90}{9.81} = 9.174$ $t = 3.03 \text{ s}$

Marking:

• [1] for correct substitution
• [1] for correct answer ($3.03 \text{ s}$ or $3.0 \text{ s}$ to 2 s.f.)

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7. (b) [2 marks]

Working: Horizontal distance: $x = v_x \times t = 15 \times 3.03 = 45.4 \text{ m}$

Marking:

• [1] for using horizontal velocity × time
• [1] for correct answer ($45.4 \text{ m}$ or $45 \text{ m}$ to 2 s.f.)

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7. (c) [3 marks]

Working: Vertical component of velocity just before impact: $v_y = gt = 9.81 \times 3.03 = 29.7 \text{ m s}^{-1}$

Resultant speed: $v = \sqrt{v_x^2 + v_y^2} = \sqrt{15^2 + 29.7^2} = \sqrt{225 + 882.1} = \sqrt{1107.1} = 33.3 \text{ m s}^{-1}$

Marking:

• [1] for calculating vertical component $v_y$
• [1] for using Pythagoras to find resultant
• [1] for correct final answer ($33.3 \text{ m s}^{-1}$)

Teaching note: In projectile motion, horizontal and vertical motions are independent. The horizontal velocity remains constant (no horizontal acceleration), while the vertical velocity increases due to gravity. The final speed is the vector sum of the two components.

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8. (a)(i) [1 mark]

Answer: The scale reads $687 \text{ N}$ (or $70g = 687 \text{ N}$). When the lift moves at constant velocity, acceleration is zero, so the net force is zero. The normal force (scale reading) equals the weight: $N = mg = 70 \times 9.81 = 687 \text{ N}$.

Marking:

• [1] for stating scale reads $mg$ (weight) with explanation that acceleration is zero

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8. (a)(ii) [1 mark]

Answer: The scale reads more than the student's weight. The scale reading is $N = m(g + a) = 70(9.81 + 2.0) = 70 \times 11.81 = 827 \text{ N}$. The student feels heavier because the normal force must exceed the weight to provide upward acceleration.

Marking:

• [1] for correct explanation and calculation showing increased reading

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8. (b) [2 marks]

Working: Taking downward as positive for the acceleration: $mg - N = ma$ $N = m(g - a) = 70(9.81 - 3.0) = 70 \times 6.81 = 477 \text{ N}$

Marking:

• [1] for correct equation setup
• [1] for correct answer ($477 \text{ N}$)

Teaching note: When the lift accelerates downward, the apparent weight decreases. If $a = g$ (free fall), the scale would read zero — this is the weightlessness condition. Common mistake: adding instead of subtracting when the acceleration is downward.

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9. (a) [2 marks]

Working: Net force: $F_{\text{net}} = 3600 - 1200 = 2400 \text{ N}$

Acceleration: $a = \frac{F_{\text{net}}}{m} = \frac{2400}{1200} = 2.0 \text{ m s}^{-2}$

Marking:

• [1] for calculating net force
• [1] for correct acceleration ($2.0 \text{ m s}^{-2}$)

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9. (b) [3 marks]

Working: Using the work-energy principle: Work done by net force = change in kinetic energy $F_{\text{net}} \times s = \frac{1}{2}mv^2 - 0$ $2400 \times 200 = \frac{1}{2}(1200)v^2$ $480\,000 = 600v^2$ $v^2 = 800$ $KE = \frac{1}{2}(1200)(800) = 480\,000 \text{ J} = 480 \text{ kJ}$

Alternatively, directly: $KE = F_{\text{net}} \times s = 2400 \times 200 = 480\,000 \text{ J}$

Marking:

• [1] for using work-energy principle or kinematic approach
• [1] for correct substitution
• [1] for correct answer ($480 \text{ kJ}$ or $4.80 \times 10^5 \text{ J}$)

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9. (c) [2 marks]

Working: Power = driving force × velocity: $P = F \times v = 3600 \times 30 = 108\,000 \text{ W} = 108 \text{ kW}$

Marking:

• [1] for using $P = Fv$
• [1] for correct answer ($108 \text{ kW}$)

Teaching note: The power is calculated using the driving force, not the net force. $P = Fv$ gives the instantaneous power when $F$ is the force in the direction of velocity. Common mistake: using net force instead of driving force.

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10. (a) [3 marks]

Working: At the lowest point, the tension and weight both act along the radial direction. The net force towards the centre (upward) provides the centripetal force: $T - mg = \frac{mv^2}{r}$ $T = mg + \frac{mv^2}{r} = 0.20 \times 9.81 + \frac{0.20 \times (6.0)^2}{0.80}$ $T = 1.962 + \frac{0.20 \times 36}{0.80} = 1.962 + 9.0 = 10.96 \text{ N} \approx 11.0 \text{ N}$

Marking:

• [1] for correct equation $T - mg = mv^2/r$
• [1] for correct substitution
• [1] for correct answer ($11.0 \text{ N}$ to 3 s.f.)

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10. (b) [3 marks]

Working: To just complete the vertical circle, the minimum speed at the top of the circle is when tension is zero at the top: $\frac{mv_{\text{top}}^2}{r} = mg \implies v_{\text{top}}^2 = gr$

Using conservation of energy from bottom to top (height difference = $2r$): $\frac{1}{2}mv_{\text{bottom}}^2 = \frac{1}{2}mv_{\text{top}}^2 + mg(2r)$ $\frac{1}{2}v_{\text{bottom}}^2 = \frac{1}{2}(gr) + 2gr = \frac{5}{2}gr$ $v_{\text{bottom}}^2 = 5gr = 5 \times 9.81 \times 0.80 = 39.24$ $v_{\text{bottom}} = \sqrt{39.24} = 6.26 \text{ m s}^{-1}$

Marking:

• [1] for minimum speed at top: $v_{\text{top}}^2 = gr$
• [1] for applying energy conservation between bottom and top
• [1] for correct answer ($6.26 \text{ m s}^{-1}$ to 3 s.f.)

Teaching note: The critical condition for completing a vertical circle is that the speed at the top must be at least $\sqrt{gr}$ (when tension/ normal force just reaches zero). The minimum speed at the bottom is then $\sqrt{5gr}$ by energy conservation. This is a standard result worth remembering.

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Section C: Longer Structured Questions

11. (a) [2 marks]

Answer: The free-body diagram should show:

• Weight ($mg$) acting vertically downward from the centre of the block
• Normal reaction ($R$) acting perpendicular to the slope, away from the surface
• Frictional force ($f$) acting up the slope (opposing the motion down the slope)

Marking:

• [1] for all three forces present and correctly directed
• [1] for clear labels on all forces

Common mistake: Drawing friction in the wrong direction (down the slope instead of up), or drawing the normal force vertically instead of perpendicular to the surface.

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11. (b) [1 mark]

Working: $W_{\parallel} = mg\sin\theta = 4.0 \times 9.81 \times \sin 30° = 4.0 \times 9.81 \times 0.5 = 19.6 \text{ N}$

Marking:

• [1] for correct answer ($19.6 \text{ N}$)

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11. (c) [1 mark]

Working: $R = mg\cos\theta = 4.0 \times 9.81 \times \cos 30° = 4.0 \times 9.81 \times 0.866 = 34.0 \text{ N}$

Marking:

• [1] for correct answer ($34.0 \text{ N}$ to 3 s.f.)

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11. (d) [2 marks]

Working: $f = \mu_k \times R = 0.25 \times 34.0 = 8.50 \text{ N}$

Marking:

• [1] for using $f = \mu_k R$
• [1] for correct answer ($8.50 \text{ N}$)

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11. (e) [4 marks]

Working: Using the work-energy principle: $\text{Net work done} = \Delta KE$

Work done by the parallel component of gravity (positive, down the slope): $W_g = mg\sin\theta \times d = 19.6 \times 3.0 = 58.8 \text{ J}$

Work done by friction (negative, opposing motion): $W_f = -f \times d = -8.50 \times 3.0 = -25.5 \text{ J}$

Net work: $W_{\text{net}} = 58.8 - 25.5 = 33.3 \text{ J}$

This equals the change in kinetic energy (starting from rest): $33.3 = \frac{1}{2}mv^2 - 0 = \frac{1}{2}(4.0)v^2$ $v^2 = \frac{33.3 \times 2}{4.0} = 16.65$ $v = 4.08 \text{ m s}^{-1}$

Marking:

• [1] for calculating work done by the component of weight along the slope
• [1] for calculating work done by friction (with correct sign)
• [1] for applying work-energy principle correctly
• [1] for correct final answer ($4.08 \text{ m s}^{-1}$ to 3 s.f.)

Teaching note: The work-energy principle states that the net work done on an object equals its change in kinetic energy. Friction does negative work because it opposes motion. An alternative approach using Newton's second law and kinematics ($v^2 = u^2 + 2as$) would also be valid and yield the same result.

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12. (a) [2 marks]

Answer: A geostationary orbit is one in which the satellite:

• Orbits above the Earth's equator in the same direction as the Earth's rotation
• Has an orbital period equal to the Earth's rotational period (24 hours)
• Therefore remains stationary relative to a fixed point on the Earth's surface

Marking:

• [1] for stating the period is 24 hours (same as Earth's rotation)
• [1] for stating the satellite remains above the same point on Earth's surface (or orbits above the equator)

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12. (b) [1 mark]

Working: $r = R_E + h = 6.37 \times 10^6 + 35\,800 \times 10^3 = 6.37 \times 10^6 + 3.58 \times 10^7$ $r = 4.217 \times 10^7 \text{ m} \approx 4.22 \times 10^7 \text{ m} \quad \checkmark$

Marking:

• [1] for correct addition and answer

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12. (c) [3 marks]

Working: For a satellite in circular orbit, gravitational force provides centripetal force: $\frac{GMm}{r^2} = \frac{mv^2}{r}$ $v = \sqrt{\frac{GM}{r}} = \sqrt{\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{4.22 \times 10^7}}$ $v = \sqrt{\frac{3.983 \times 10^{14}}{4.22 \times 10^7}} = \sqrt{9.438 \times 10^6} = 3072 \text{ m s}^{-1} \approx 3.07 \times 10^3 \text{ m s}^{-1}$

Marking:

• [1] for equating gravitational force to centripetal force
• [1] for correct substitution
• [1] for correct answer ($3.07 \times 10^3 \text{ m s}^{-1}$ to 3 s.f.)

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12. (d) [2 marks]

Answer: The student's claim is incorrect. The satellite is not in equilibrium.

• For an object to be in equilibrium, the net force acting on it must be zero.
• The satellite is in circular motion, so it has a centripetal acceleration directed towards the centre of the Earth.
• The gravitational force provides the centripetal force, so there is a non-zero net force acting on the satellite.
• The satellite remains above the same point on Earth not because forces are balanced, but because its orbital period matches the Earth's rotational period.

Marking:

• [1] for stating the claim is incorrect with a valid reason (non-zero net force / centripetal acceleration exists)
• [1] for explaining that gravitational force provides the centripetal force (not balanced by another force)

Common mistake: Confusing "appears stationary" with "in equilibrium." An object can appear stationary relative to a rotating reference frame while still experiencing a net force. Equilibrium requires zero net force, which is not the case for circular motion.

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Mark Summary

Question	Marks
1	2
2	2
3	2
4	2
5	2
6(a)	2
6(b)(i)	3
6(b)(ii)	2
7(a)	2
7(b)	2
7(c)	3
8(a)(i)	1
8(a)(ii)	1
8(b)	2
9(a)	2
9(b)	3
9(c)	2
10(a)	3
10(b)	3
11(a)	2
11(b)	1
11(c)	1
11(d)	2
11(e)	4
12(a)	2
12(b)	1
12(c)	3
12(d)	2
Total	60