Cumulative summative evaluation across all 5 strands
⏱️ 3 hours · /100 marks · Worth up to 30% of final grade
Instructions. Show all work, including diagrams (FBDs, ray, vector, energy bars). Include units and significant figures. Calculators and a non-programmable scientific reference are permitted. Constants:
\(g=9.8\,\text{m/s}^2\), \(c=3.00\times10^8\,\text{m/s}\), \(h=6.63\times10^{-34}\,\text{J·s}\), \(k=8.99\times10^9\,\text{N·m}^2/\text{C}^2\), \(G=6.67\times10^{-11}\,\text{N·m}^2/\text{kg}^2\), \(e=1.60\times10^{-19}\,\text{C}\), \(m_e=9.11\times10^{-31}\,\text{kg}\), \(M_E=5.98\times10^{24}\,\text{kg}\), \(R_E=6.38\times10^6\,\text{m}\).
A \(2.0\,\text{kg}\) block on a horizontal surface (\(\mu_k=0.30\)) is pushed with \(F=15\,\text{N}\) horizontally. Find (a) friction force, (b) net force, (c) acceleration.
2. [3]
Strand C · Energy
A \(0.50\,\text{kg}\) ball is dropped from \(8.0\,\text{m}\) and hits the ground at \(11.0\,\text{m/s}\). (a) Find the KE at impact. (b) Find the energy dissipated by air resistance.
3. [3]
Strand C · Momentum
A \(60\,\text{kg}\) skater throws a \(2.0\,\text{kg}\) ball horizontally at \(15\,\text{m/s}\). Find the recoil speed of the skater (frictionless ice).
4. [3]
Strand D · Gravitation
Find the gravitational field strength on the surface of a planet with mass \(2.5\times10^{24}\,\text{kg}\) and radius \(4.0\times10^6\,\text{m}\).
5. [3]
Strand D · Coulomb
Two charges \(+8.0\,\mu\text{C}\) and \(-3.0\,\mu\text{C}\) are \(0.25\,\text{m}\) apart. Find the magnitude and direction of the electric force on the negative charge.
6. [3]
Strand E · Waves
Light of \(\lambda=600\,\text{nm}\) hits a double slit \(0.25\,\text{mm}\) apart. The screen is \(1.5\,\text{m}\) away. Find the spacing between adjacent bright fringes.
7. [2]
Strand E · Refraction
Find the critical angle for a glass-air interface (\(n_{glass}=1.50\)).
8. [2]
Strand F · Photon
Compute the energy of a photon with \(\lambda=400\,\text{nm}\), in eV.
9. [3]
Strand F · Half-life
A radioactive sample decays from \(8.0\,\text{g}\) to \(0.50\,\text{g}\) in \(20\,\text{years}\). Find the half-life.
Part B — Thinking & Investigation [25 marks]
10. [6]
Strand B · Inclined plane
A \(5.0\,\text{kg}\) block is released from rest on a \(30°\) ramp with \(\mu_k=0.20\). After sliding \(4.0\,\text{m}\) down the ramp it reaches a horizontal surface (same \(\mu_k\)). (a) Draw FBDs for both segments. (b) Find the speed at the bottom of the ramp using Newton's laws or energy. (c) Find how far the block travels on the horizontal surface before stopping.
[ FBDs: ramp (mg, N, friction) and horizontal segment ]
11. [6]
Strand C · 2-D collision
A \(1500\,\text{kg}\) car moving east at \(20\,\text{m/s}\) collides at an intersection with a \(2000\,\text{kg}\) truck moving north at \(12\,\text{m/s}\). They stick together. Find their velocity (magnitude and direction) after the collision and the kinetic energy lost.
12. [6]
Strand D · Charged particle in fields
An electron is accelerated from rest through a potential difference of \(1500\,\text{V}\) and then enters a magnetic field of \(0.020\,\text{T}\) perpendicular to its velocity. (a) Find the speed of the electron entering the field. (b) Find the radius of its circular path. (c) Sketch the motion (include direction of \(\vec B\) and circular path).
[ Electron path bending in B field ]
13. [7]
Strand E · Diffraction grating + Strand F · Photon
A diffraction grating with 5000 lines/cm is illuminated by light from a hydrogen lamp. The first-order maximum for the H-α line appears at \(\theta = 19.07°\). (a) Determine the wavelength. (b) From your answer to (a), determine the energy in eV of the photon. (c) Show that this matches the Bohr-model transition \(n=3 \to n=2\) within experimental tolerance.
Part C — Communication [25 marks]
14. [6]
Strands B/C/D — synthesis
Compare the three conservation laws used in Grade 12 physics: conservation of energy, conservation of linear momentum, and conservation of charge. For each: state the law precisely, give one situation where it applies, and identify a physical quantity it does not equate to.
15. [6]
Strand E · Misconception
A student claims: "Light slows down when it enters glass because the photons are heavier in glass." Write a corrective explanation, using the wave model and including refractive index, to teach a peer.
16. [7]
Strand F · STSE essay
Write a 200–300 word response: "How have advances in modern physics changed everyday life?" Address at least three specific technologies (e.g., GPS, lasers, transistors, MRI, nuclear power). Include both benefits and concerns.
17. [6]
Strand A · Lab communication
A student claims to have measured \(g\) by timing a falling object as \(g=10.4\,\text{m/s}^2 \pm 0.6\,\text{m/s}^2\). Critique: (a) Is the accepted value \(9.81\,\text{m/s}^2\) within the reported uncertainty? (b) Identify two likely sources of systematic error in a free-fall timing experiment. (c) Suggest one method to reduce each error.
Part D — Application [25 marks]
18. [6]
Strands B/C · Roller coaster
A roller-coaster car (\(800\,\text{kg}\)) starts from rest at the top of a \(40\,\text{m}\) hill. It enters a circular vertical loop of radius \(15\,\text{m}\). Friction loses 20% of the initial PE. (a) Speed at the bottom of the loop. (b) Speed at the top of the loop. (c) Normal force on a \(70\,\text{kg}\) rider at the top of the loop.
19. [6]
Strand D · Satellites
A communications satellite is to be placed in geostationary orbit (\(T = 24\,\text{h}\)). (a) Calculate the orbital radius. (b) Calculate the orbital speed. (c) Discuss one social benefit and one environmental concern for geostationary technology.
20. [6]
Strand E · Optical tech
An optical fibre has core \(n=1.50\) and cladding \(n=1.46\). (a) Calculate the critical angle at the core-cladding interface. (b) Compute the maximum acceptance angle in air. (c) Explain how fibre-optic technology has impacted communication globally.
21. [7]
Strand F · Medical & nuclear
A medical isotope, technetium-99m, has \(T_{1/2}=6.0\,\text{h}\). A patient is injected with \(0.040\,\text{g}\) of the isotope. (a) Find the mass remaining after \(18\,\text{h}\). (b) Discuss why short half-life is desirable in diagnostic imaging. (c) Identify one social-equity concern with medical isotope production worldwide.
📖 Complete Answer Key (click to reveal)
Part A — K/U
Q1. N = mg = 19.6 N. f = μN = 5.88 N. Net = 15 − 5.88 = 9.12 N. a = 4.56 m/s².
Q2. KE = ½(0.5)(11)² = 30.25 J. PE lost = mgh = 0.5·9.8·8 = 39.2 J. Air resistance dissipated 39.2 − 30.25 = 8.95 J.
Q3. 0 = 60v + 2(15) ⇒ v = −0.50 m/s (skater moves opposite at 0.50 m/s).
Q4. g = GM/r² = (6.67e-11)(2.5e24)/(4e6)² = 10.4 m/s².
Q5. F = k|q₁q₂|/r² = (8.99e9)(8e-6)(3e-6)/(0.25)² = 3.45 N, directed toward the +q (attractive).
Q6. Δy = λL/d = (6e-7)(1.5)/(2.5e-4) = 3.6 mm.
Q7. sin θ_c = 1/1.50 ⇒ θ_c = 41.8°.
Q8. E = hc/λ = 1240 eV·nm / 400 nm = 3.10 eV.
Q9. 8.0 → 0.5 = factor of 16 = (1/2)⁴, so 4 half-lives = 20 yr ⇒ T_½ = 5.0 yr.
Part B — Thinking
Q10. On ramp: a = g(sin30 − μcos30) = 9.8(0.5 − 0.2·0.866)=3.20 m/s². v² = 2·3.20·4.0 ⇒ v = 5.06 m/s. On flat: a = −μg = −1.96 m/s². d = v²/(2|a|) = 25.6/3.92 = 6.53 m.
Q11. p_x = (1500)(20) = 30000 kg·m/s; p_y = (2000)(12) = 24000 kg·m/s. Total mass 3500 kg. v_x = 8.57 m/s, v_y = 6.86 m/s. |v| = 10.98 m/s, θ = arctan(6.86/8.57) = 38.7° N of E. KE_i = ½(1500)(20)² + ½(2000)(12)² = 300000 + 144000 = 444000 J. KE_f = ½(3500)(10.98)² = 211000 J. ΔKE = −233 kJ lost.
Q12. (a) eV = ½m_e v² ⇒ v = √(2·1.6e-19·1500/9.11e-31) = 2.30×10⁷ m/s. (b) r = m_e v/(eB) = (9.11e-31)(2.30e7)/((1.6e-19)(0.020)) = 6.55×10⁻³ m = 6.55 mm. (c) Circle in plane perpendicular to B.
Q13. (a) d = 1/5000 cm = 2.0×10⁻⁶ m. λ = d sinθ = 2e-6 · sin(19.07°) = 6.534×10⁻⁷ m = 653 nm. (b) E = hc/λ = 1240/653 = 1.90 eV. (c) Bohr: ΔE = −13.6(1/9 − 1/4) = 1.89 eV. Matches within 0.01 eV.
Part C — Communication
Q14. Energy: total mechanical energy is conserved when only conservative forces do work; e.g., free-fall in vacuum; not equal to momentum. Momentum: in absence of external net force, total p is conserved (vector); e.g., collisions; not equal to KE. Charge: total electric charge in an isolated system is constant; e.g., chemical reactions and beta decay; not equal to current.
Q15. Photons are massless. In glass, the wave model says light interacts with bound electrons that re-emit slightly delayed waves; the resulting wave packet has a phase velocity \(v=c/n\). Photon energy is unchanged (frequency stays the same); only wavelength and speed change.
Q16. Free-response — assess use of three named technologies, mention of underlying physics, and balanced benefits/concerns.
Q17. (a) 9.81 is within 10.4 ± 0.6 (range 9.8–11.0) — barely. (b) Reaction-time error in start/stop, air resistance. (c) Use a photogate or motion sensor; use a denser/smaller object.
Part D — Application
Q18. E_initial = mgh = 800·9.8·40 = 313600 J. After 20% loss: 250880 J → all KE at the bottom of the loop (taking loop bottom as reference). v_bottom = √(2·250880/800) = 25.0 m/s. At top: extra height 2r = 30 m. KE_top = 250880 − 800·9.8·30 = 15800 J → v_top = √(2·15800/800) = 6.29 m/s. (c) For a 70 kg rider at top: N + mg = mv²/r ⇒ N = m(v²/r − g) = 70(6.29²/15 − 9.8) = 70(2.64 − 9.8) = −501 N. Negative ⇒ the loop is too slow at the top: the rider would lose contact (would need to be strapped in, or initial energy must be greater).
Q19. (a) T² = 4π² r³/(GM_E) ⇒ r = ∛(GM_E T²/(4π²)) = ∛((6.67e-11)(5.98e24)(86400)²/(4π²)) = 4.22×10⁷ m. (b) v = 2π r/T = 3.07×10³ m/s. (c) Benefit: continuous TV/internet over fixed footprint. Concern: orbital debris and end-of-life satellite disposal.
Q20. (a) sin θ_c = 1.46/1.50 ⇒ θ_c = 76.7°. (b) sin θ_a = √(n₁² − n₂²) = √(2.25 − 2.13) = 0.343 ⇒ θ_a = 20.1°. (c) High-bandwidth, low-loss data — global internet, healthcare telemedicine, finance.
Q21. (a) 18/6 = 3 half-lives ⇒ remaining = 0.040·(1/2)³ = 5.0×10⁻³ g = 5 mg. (b) Short half-life reduces patient radiation dose after imaging. (c) Production relies on a few aging research reactors (Canada/Netherlands); shortages can disrupt cancer/cardiac diagnostics globally.
Final Exam Rubric (per category)
Level
Description
%
4
Thorough, insightful, demonstrates a high degree of effectiveness
80–100%
3
Considerable effectiveness — provincial standard
70–79%
2
Some effectiveness
60–69%
1
Limited effectiveness
50–59%
R
Insufficient — has not demonstrated the required knowledge or skills