Slide 1

• Topic: Problem Solving in Modern Physics
• Objective: To solve example problems related to modern physics

Slide 2

• The concept of energy
  • Kinetic energy
  • Potential energy
  • Conservation of energy

Slide 3

• Example problem 1:
  • A car of mass 1000 kg is moving with a velocity of 20 m/s. Calculate its kinetic energy.
• Solution:
  • Given: mass (m) = 1000 kg, velocity (v) = 20 m/s
  • Formula: Kinetic energy (KE) = 1/2 * m * v^2
  • Calculation: KE = 1/2 * 1000 kg * (20 m/s)^2
  • KE = 200,000 J

Slide 4

• Example problem 2:
  • A bookshelf of height 2 m is raised to a height of 4 m. If the mass of the bookshelf is 50 kg, calculate the potential energy.
• Solution:
  • Given: height difference (h) = 2 m, mass (m) = 50 kg, acceleration due to gravity (g) = 9.8 m/s^2
  • Formula: Potential energy (PE) = m * g * h
  • Calculation: PE = 50 kg * 9.8 m/s^2 * 2 m
  • PE = 980 J

Slide 5

• The concept of power
  • Definition of power
  • Unit of power
  • Calculation of power

Slide 6

• Example problem 3:
  • A motor lifts a load of 200 N to a height of 4 m in 10 seconds. Calculate the power.
• Solution:
  • Given: force (F) = 200 N, height (h) = 4 m, time (t) = 10 s
  • Formula: Power (P) = Work (W) / time (t)
  • Calculation: Work (W) = force (F) * distance (d) = 200 N * 4 m = 800 J
  • Power (P) = 800 J / 10 s
  • P = 80 W

Slide 7

• The concept of work
  • Definition of work
  • Calculating work done by a force
  • Positive and negative work

Slide 8

• Example problem 4:
  • A person pushes a cart with a force of 50 N. The cart moves a distance of 10 m in the direction of the force. Calculate the work done.
• Solution:
  • Given: force (F) = 50 N, distance (d) = 10 m
  • Formula: Work (W) = force (F) * distance (d)
  • Calculation: W = 50 N * 10 m
  • W = 500 J

Slide 9

• The concept of impulse
  • Definition of impulse
  • Impulse-momentum theorem
  • Relationship between force, time, and change in momentum

Slide 10

• Example problem 5:
  • A ball of mass 0.5 kg collides with a wall and bounces back with a velocity of -5 m/s. If the time of collision is 0.1 s, calculate the impulse experienced by the ball.
• Solution:
  • Given: mass (m) = 0.5 kg, initial velocity (u) = 0 m/s, final velocity (v) = -5 m/s, time (t) = 0.1 s
  • Formula: Impulse (I) = change in momentum (Δp) = m * (v - u)
  • Calculation: Δp = 0.5 kg * (-5 m/s - 0 m/s) = -2.5 kg m/s
  • Impulse (I) = -2.5 kg m/s

Slide 11

• Problem Solving Modern Physics - Example Problems
• Objective: To solve example problems related to modern physics

Slide 12

• Example problem 6:
  • A block of mass 2 kg is pushed with a force of 10 N for a distance of 5 m. Calculate the work done on the block.
• Solution:
  • Given: force (F) = 10 N, distance (d) = 5 m
  • Formula: Work (W) = force (F) * distance (d)
  • Calculation: W = 10 N * 5 m
  • W = 50 J

Slide 13

• Example problem 7:
  • A rocket of mass 1000 kg is launched upwards with an initial velocity of 50 m/s. If the rocket experiences an acceleration of -10 m/s^2 due to gravity, calculate its maximum height.
• Solution:
  • Given: mass (m) = 1000 kg, initial velocity (u) = 50 m/s, acceleration (a) = -10 m/s^2
  • Formula: Final velocity (v)^2 = initial velocity (u)^2 + 2 * acceleration (a) * distance (d)
  • Calculation: 0 = (50 m/s)^2 + 2 * (-10 m/s^2) * d
  • d = (50 m/s)^2 / (2 * 10 m/s^2) = 125 m

Slide 14

• Example problem 8:
  • A pendulum of length 2 m is displaced to one side and released. If the maximum displacement angle is 30 degrees, calculate its maximum potential energy.
• Solution:
  • Given: length (l) = 2 m, maximum displacement angle (θ) = 30 degrees, acceleration due to gravity (g) = 9.8 m/s^2
  • Formula: Potential energy (PE) = m * g * h
  • Calculation: PE = m * g * l * (1 - cosθ)
  • PE = m * g * l * (1 - cos(30 degrees))
  • PE = m * g * l * (1 - √3/2)

Slide 15

• Example problem 9:
  • A car starts from rest and accelerates uniformly at 2 m/s^2 for a distance of 100 m. Calculate the final velocity of the car.
• Solution:
  • Given: initial velocity (u) = 0 m/s, acceleration (a) = 2 m/s^2, distance (d) = 100 m
  • Formula: Final velocity (v)^2 = initial velocity (u)^2 + 2 * acceleration (a) * distance (d)
  • Calculation: v^2 = 0 + 2 m/s^2 * 100 m
  • v^2 = 200 m^2/s^2
  • v = √200 m/s

Slide 16

• The concept of capacitance
  • Definition of capacitance
  • Factors affecting capacitance
  • Calculation of capacitance

Slide 17

• Example problem 10:
  • A parallel plate capacitor has an area of 0.5 m^2 and a separation distance of 0.1 m. If the dielectric constant is 5, calculate the capacitance.
• Solution:
  • Given: area (A) = 0.5 m^2, separation distance (d) = 0.1 m, dielectric constant (κ) = 5
  • Formula: Capacitance (C) = (κ * ε₀ * A) / d
  • Calculation: C = (5 * 8.85 x 10^-12 F/m * 0.5 m^2) / 0.1 m
  • C = 2.925 x 10^-11 F

Slide 18

• The concept of resistors
  • Definition of resistance
  • Factors affecting resistance
  • Calculation of resistance

Slide 19

• Example problem 11:
  • A wire has a resistance of 10 Ω. If the potential difference across the wire is 50 V, calculate the current passing through the wire.
• Solution:
  • Given: resistance (R) = 10 Ω, potential difference (V) = 50 V
  • Formula: Current (I) = V / R
  • Calculation: I = 50 V / 10 Ω
  • I = 5 A

Slide 20

• Example problem 12:
  • Three resistors of 2 Ω, 3 Ω, and 4 Ω are connected in series. If a potential difference of 12 V is applied across the circuit, calculate the current passing through the resistors.
• Solution:
  • Given: resistors (R₁, R₂, R₃) = (2 Ω, 3 Ω, 4 Ω), potential difference (V) = 12 V
  • Formula: Total resistance (R_total) = R₁ + R₂ + R₃
  • Total current (I_total) = V / R_total
  • Calculation: R_total = 2 Ω + 3 Ω + 4 Ω = 9 Ω
  • I_total = 12 V / 9 Ω
  • I_total = 4/3 A

Slide 21

• The concept of electric circuits
  • Definition of an electric circuit
  • Symbols used in circuit diagrams
  • Series and parallel circuits
• Example problem 13:
  • Three resistors of 5 Ω, 10 Ω, and 15 Ω are connected in parallel. If a voltage of 12 V is applied across the circuit, calculate the total resistance.

Slide 22

• Example problem 14:
  • A circuit contains a battery with an emf of 10 V and an internal resistance of 2 Ω. If a resistor of 4 Ω is connected to the circuit, calculate the current passing through the circuit.

Slide 23

• The concept of electromagnetic induction
  • Definition of electromagnetic induction
  • Faraday’s law and Lenz’s law
  • Calculation of induced emf and magnetic flux
• Example problem 15:
  • A coil with 100 turns and an area of 0.1 m^2 is placed in a magnetic field with a flux density of 0.5 T. If the coil rotates at a frequency of 50 Hz, calculate the induced emf.

Slide 24

• Example problem 16:
  • A coil with an initial magnetic flux of 5 T·m^2 experiences a change in flux of -2 T·m^2. If the time taken for the change is 0.1 s, calculate the induced emf.

Slide 25

• The concept of nuclear physics
  • Definition of nuclear physics
  • Alpha, beta, and gamma radiation
  • Radioactive decay and half-life
• Example problem 17:
  • A radioactive substance has a half-life of 20 minutes. If the initial amount of the substance is 100 g, calculate the amount remaining after 1 hour.

Slide 26

• Example problem 18:
  • A sample of radioactive material has a decay rate of 5000 disintegrations per minute. If the half-life of the material is 10 minutes, calculate the initial activity of the sample.

Slide 27

• The concept of particles and waves
  • Definition of particles and waves
  • Particle-wave duality
  • The wave-particle nature of light
• Example problem 19:
  • Calculate the de Broglie wavelength of an electron with a mass of 9.11 x 10^-31 kg and a velocity of 5 x 10^6 m/s.

Slide 28

• Example problem 20:
  • Calculate the energy of a photon with a frequency of 2 x 10^15 Hz.

Slide 29

• The concept of special relativity
  • Definition of special relativity
  • Time dilation and length contraction
  • Einstein’s mass-energy equivalence
• Example problem 21:
  • Calculate the time dilation factor for an object moving at a velocity of 0.8c relative to an observer.

Slide 30

• Example problem 22:
  • Calculate the increase in mass of an object with an energy of 1 x 10^6 J.