Why is steel used in bridges but not rubber? Materials science puts numbers on stiffness and strength.
Stress = force ÷ area (Pa) and strain = extension ÷ original length (no unit). The Young modulus = stress ÷ strain measures stiffness. Hooke’s law holds up to the limit of proportionality.
An elastic material returns to its shape; a plastic one is permanently deformed. Elastic energy = ½Fx = ½kx², which is the area under a force–extension graph.
The unit of the Young modulus is the:
Strain is:
Plastic deformation means the material:
A force of 200 N acts on an area of 2 × 10⁻⁶ m². Write stress in units of 10⁸ Pa.
What is the stress, in units of 10⁸ Pa?
Enter an exact answer, without rounding.A 2 m wire stretches by 1 mm.
What is the strain, in units of 10⁻⁴?
Enter an exact answer, without rounding.A spring with k = 400 N/m stretches 0.1 m.
What elastic energy does it store, in J?
Enter an exact answer, without rounding.A stiffer material has a:
The gradient of a stress–strain graph, in its linear part, gives the:
The area under a force–extension graph gives the:
To measure wire diameter you should use a:
The limit of proportionality is where:
Protons are not fundamental: they are made of quarks. The tiniest pieces of matter follow some of the simplest rules in physics.
Hadrons are made of quarks: baryons have three (qqq) and mesons have a quark and antiquark. Leptons, such as electrons and neutrinos, are fundamental. Antiparticles have the opposite charge.
In β⁻ decay, a down quark changes to an up quark, so a neutron becomes a proton and an electron and antineutrino are released. In β⁺ decay, an up quark becomes a down quark, releasing a positron and a neutrino. Charge and nucleon number are always conserved.
A baryon contains:
Which is a lepton?
The quark composition of a proton is:
In β⁻ decay, a quark changes from:
A neutron is udd, with u = +⅔ and d = −⅓.
What is the neutron’s total charge?
Enter an exact answer, without rounding.A baryon is uuu, with u = +⅔.
What is its total charge, in units of e?
Enter an exact answer, without rounding.A meson contains:
The antiparticle of the electron is the:
A β⁻ decay also releases an:
Which is conserved in every particle decay?
Which is a fundamental particle?
Pendulums, springs, bridges in the wind and molecules in a microwave all oscillate by the same mathematical rule.
In simple harmonic motion, acceleration is proportional to displacement and directed towards equilibrium: a = −ω²x, with ω = 2π/T. x = x₀ sin ωt and maximum speed is v₀ = ωx₀.
Damping removes energy, reducing amplitude. Damping can be light, critical or heavy. Resonance happens when the driving frequency equals the natural frequency, giving maximum amplitude. It is useful in MRI scanners and tuning, but a danger for bridges.
In SHM, acceleration is:
A simple pendulum is fastest at:
Resonance occurs when the driving frequency:
An oscillation has a period of 0.5 s.
What is its frequency, in Hz?
Enter an exact answer, without rounding.A mass oscillates with ω = 4 rad/s and amplitude 0.5 m.
What is its maximum speed, in m/s?
Enter an exact answer, without rounding.A mass oscillates with ω = 4 rad/s and amplitude 0.5 m.
What is its maximum acceleration, in m/s²?
Enter an exact answer, without rounding.Total energy in undamped SHM:
Light damping makes the amplitude:
Critical damping returns a system to equilibrium:
ω is measured in:
A sharper resonance peak results from:
The same physics that images the inside of your body also measures how far away the stars are.
Ultrasound uses piezoelectric crystals and reflections at boundaries, governed by acoustic impedance Z = ρc. X-rays are attenuated by I = I₀e^(−μx), so bone appears differently from tissue. CT builds 3D images from many X-ray slices. PET uses a positron-emitting tracer: annihilation gives two gamma photons.
Standard candles have known luminosity, so flux F = L ÷ 4πd² gives their distance. Wien’s law: λmax T = constant. Stefan–Boltzmann: L = 4πσr²T⁴. Hubble’s law: v = H₀d, and it supports the Big Bang. Redshift: Δλ/λ ≈ v/c.
Ultrasound is produced by a:
Gel is put on the skin in an ultrasound scan to:
In a PET scan, the detected gamma photons come from:
Hubble’s law says a galaxy’s recession speed is proportional to its:
A star’s temperature doubles and its radius stays the same.
By what factor does its luminosity increase?
Enter an exact answer, without rounding.A standard candle moves to 3 times the distance.
By what factor does its flux fall?
Enter an exact answer, without rounding.Acoustic impedance is:
A CT scan builds an image by:
Wien’s law links peak wavelength and:
Redshift shows that distant galaxies are:
Which is a standard candle?
Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.
Young modulus equals:
Doubling a wire’s cross-section area under the same force makes the stress:
The charge of a down quark is:
In β⁺ decay, a proton becomes a:
At maximum displacement in SHM, the speed is:
With T = 2 s, ω is:
X-ray intensity in tissue falls:
Hubble’s law supports: