Section 1

Mechanics: Worked Examples for IGCSE Physics

EXAMPLE PROBLEMS

🧩 Physics Exam - Example Problems

📚 Example Problems - Chapter 1: Mechanics

🔢 Problem 1:

A car accelerates from rest to $25 m/s$ in $8$ seconds. Calculate the average acceleration.

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Mathematical work: $v_i = 0 m/s$ , $v_f = 25 m/s$ , $t = 8 s$

Step 2: Apply the formula for average acceleration.

Mathematical work: $a = \frac{v_f - v_i}{t}$

Step 3: Substitute the values and calculate.

Mathematical work: $a = \frac{25 m/s - 0 m/s}{8 s} = 3.125 m/s^2$

Key Insight: Average acceleration is the change in velocity over the change in time.

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Final Answer:

a = 3.125 \, m/s^2

🔢 Problem 2:

A ball is thrown vertically upwards with an initial velocity of $15 m/s$ . Neglecting air resistance, calculate the maximum height reached by the ball. (Assume $g = 9.8 m/s^2$ ).

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Mathematical work: $v_i = 15 m/s$ , $v_f = 0 m/s$ (at maximum height), $a = -9.8 m/s^2$

Step 2: Apply the appropriate equation of motion.

Mathematical work: $v_f^2 = v_i^2 + 2as$

Step 3: Rearrange to solve for

s

(displacement or height).

Mathematical work: $s = \frac{v_f^2 - v_i^2}{2a}$

Step 4: Substitute the values and calculate.

Mathematical work: $s = \frac{0^2 - (15 m/s)^2}{2(-9.8 m/s^2)} = \frac{-225}{-19.6} m = 11.48 m$

Key Insight: At maximum height, the final velocity of the ball is zero.

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Final Answer:

s = 11.48 \, m

🔢 Problem 3:

A force of $50 N$ is applied to a $10 kg$ block. Calculate the acceleration of the block.

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Mathematical work: $F = 50 N$ , $m = 10 kg$

Step 2: Apply Newton's second law of motion.

Mathematical work: $F = ma$

Step 3: Rearrange to solve for

a

(acceleration).

Mathematical work: $a = \frac{F}{m}$

Step 4: Substitute the values and calculate.

Mathematical work: $a = \frac{50 N}{10 kg} = 5 m/s^2$

Key Insight: Newton's second law relates force, mass, and acceleration.

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Final Answer:

a = 5 \, m/s^2

Section 2

📚 Example Problems - Chapter 2: Thermal Physics

🔢 Problem 1:

Explain Brownian motion and its significance in the kinetic theory of matter.

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Explanation: Brownian motion is the random movement of particles suspended in a fluid (a liquid or a gas).

Step 2: Relate Brownian motion to kinetic theory.

Explanation: It provides direct evidence for the kinetic theory of matter, which states that matter is made up of constantly moving particles. The random motion of the visible particles is caused by collisions with the smaller, invisible molecules of the fluid.

Step 3: Explain the significance.

Explanation: Brownian motion supports the idea that molecules are in constant, random motion and that temperature is a measure of the average kinetic energy of these molecules.

Key Insight: Brownian motion is observable evidence of the kinetic theory.

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Final Answer: Brownian motion is the random movement of particles caused by collisions with fluid molecules, supporting the kinetic theory.

🔢 Problem 2:

A $2 kg$ block of aluminum absorbs $18,000 J$ of heat. If the initial temperature of the aluminum is $20^\circ C$ , what is its final temperature? (Specific heat capacity of aluminum is $900 J/kg^\circ C$ ).

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Mathematical work: $m = 2 kg$ , $Q = 18000 J$ , $c = 900 J/kg^\circ C$ , $T_i = 20^\circ C$

Step 2: Apply the formula for heat transfer.

Mathematical work: $Q = mc\Delta T$

Step 3: Rearrange to solve for

\Delta T

(change in temperature).

Mathematical work: $\Delta T = \frac{Q}{mc}$

Step 4: Substitute the values and calculate.

Mathematical work: $\Delta T = \frac{18000 J}{(2 kg)(900 J/kg^\circ C)} = 10^\circ C$

Step 5: Calculate the final temperature.

Mathematical work: $T_f = T_i + \Delta T = 20^\circ C + 10^\circ C = 30^\circ C$

Key Insight: Specific heat capacity relates heat transfer to temperature change.

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Final Answer:

T_f = 30 \, ^\circ C

🔢 Problem 3:

Describe the three modes of heat transfer and give an example of each.

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Explanation: Conduction is the transfer of heat through a material without any movement of the material itself. Example: Heating a metal rod at one end.

Step 2: Define convection.

Explanation: Convection is the transfer of heat through a fluid (liquid or gas) by the movement of the fluid itself. Example: Boiling water in a pot.

Step 3: Define radiation.

Explanation: Radiation is the transfer of heat through electromagnetic waves. Example: Heat from the sun reaching the Earth.

Key Insight: Each mode of heat transfer involves different mechanisms.

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Final Answer: Conduction (metal rod), Convection (boiling water), Radiation (sun's heat).

📚 Example Problems - Chapter 3: Electricity

🔢 Problem 1:

Calculate the total resistance of three resistors connected in series: $R_1 = 10 \Omega$ , $R_2 = 20 \Omega$ , and $R_3 = 30 \Omega$ .

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Mathematical work: $R_1 = 10 \Omega$ , $R_2 = 20 \Omega$ , $R_3 = 30 \Omega$

Step 2: Apply the formula for total resistance in series.

Mathematical work: $R_{total} = R_1 + R_2 + R_3$

Step 3: Substitute the values and calculate.

Mathematical work: $R_{total} = 10 \Omega + 20 \Omega + 30 \Omega = 60 \Omega$

Key Insight: Resistors in series add up to the total resistance.

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Final Answer:

R_{total} = 60 \, \Omega

🔢 Problem 2:

Calculate the total resistance of two resistors connected in parallel: $R_1 = 4 \Omega$ and $R_2 = 6 \Omega$ .

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Mathematical work: $R_1 = 4 \Omega$ , $R_2 = 6 \Omega$

Step 2: Apply the formula for total resistance in parallel.

Mathematical work: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}$

Step 3: Substitute the values and calculate.

Mathematical work: $\frac{1}{R_{total}} = \frac{1}{4 \Omega} + \frac{1}{6 \Omega} = \frac{3 + 2}{12 \Omega} = \frac{5}{12 \Omega}$

Step 4: Invert to find

R_{total}

Mathematical work: $R_{total} = \frac{12 \Omega}{5} = 2.4 \Omega$

Key Insight: The reciprocal of the total resistance in parallel is the sum of the reciprocals of individual resistances.

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Final Answer:

R_{total} = 2.4 \, \Omega

🔢 Problem 3:

A circuit has a voltage of $12 V$ and a resistance of $3 \Omega$ . Calculate the current flowing through the circuit.

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Mathematical work: $V = 12 V$ , $R = 3 \Omega$

Step 2: Apply Ohm's Law.

Mathematical work: $V = IR$

Step 3: Rearrange to solve for

I

(current).

Mathematical work: $I = \frac{V}{R}$

Step 4: Substitute the values and calculate.

Mathematical work: $I = \frac{12 V}{3 \Omega} = 4 A$

Key Insight: Ohm's law relates voltage, current, and resistance.

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Final Answer:

I = 4 \, A

📚 Example Problems - Chapter 4: Electromagnetism

🔢 Problem 1:

Explain Fleming's left-hand rule and its application.

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Explanation: If you point your first finger in the direction of the magnetic field, your second finger in the direction of the current, then your thumb will point in the direction of the force on the conductor.

Step 2: Describe its application.

Explanation: It is used to determine the direction of the force on a current-carrying conductor in a magnetic field, such as in an electric motor.

Key Insight: Fleming's left-hand rule relates magnetic field, current, and force direction.

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Final Answer: Fleming's left-hand rule helps determine the force direction on a current-carrying conductor in a magnetic field.

🔢 Problem 2:

Describe the construction and operation of a simple A.C. generator.

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Explanation: An A.C. generator consists of a coil of wire rotating in a magnetic field. Slip rings and brushes are used to connect the coil to an external circuit.

Step 2: Explain the operation.

Explanation: As the coil rotates, it cuts through the magnetic field lines, inducing an electromotive force (EMF) according to Faraday's law of electromagnetic induction. The slip rings allow the current to flow in alternating directions, producing an alternating current (A.C.).

Key Insight: Faraday's law is the basis for A.C. generator operation.

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Final Answer: A coil rotating in a magnetic field induces an alternating current.

🔢 Problem 3:

A transformer has 500 turns in the primary coil and 100 turns in the secondary coil. If the input voltage is 240 V, what is the output voltage?

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Mathematical work: $N_p = 500$ , $N_s = 100$ , $V_p = 240 V$

Step 2: Apply the transformer equation.

Mathematical work: $\frac{V_p}{V_s} = \frac{N_p}{N_s}$

Step 3: Rearrange to solve for

V_s

(secondary voltage).

Mathematical work: $V_s = V_p \frac{N_s}{N_p}$

Step 4: Substitute the values and calculate.

Mathematical work: $V_s = 240 V \cdot \frac{100}{500} = 48 V$

Key Insight: The transformer equation relates voltage and number of turns.

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Final Answer:

V_s = 48 \, V

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Mechanics: Worked Examples for IGCSE Physics

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Mechanics: Worked Examples for IGCSE Physics

🧩 Physics Exam - Example Problems

📚 Example Problems - Chapter 1: Mechanics

🔢 Problem 1:

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🔢 Problem 2:

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🔢 Problem 3:

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📚 Example Problems - Chapter 2: Thermal Physics

🔢 Problem 1:

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🔢 Problem 2:

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🔢 Problem 3:

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📚 Example Problems - Chapter 3: Electricity

🔢 Problem 1:

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🔢 Problem 2:

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🔢 Problem 3:

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📚 Example Problems - Chapter 4: Electromagnetism

🔢 Problem 1:

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🔢 Problem 2:

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🔢 Problem 3:

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5 more sections