Define each, with units: (a) work; (b) kinetic energy; (c) power. State the law of conservation of energy.
2. [3 marks]
A \(2.0\)-kg ball is thrown straight up at \(15\) m/s from ground level. Calculate (a) the kinetic energy at launch; (b) the maximum height (use conservation of energy); (c) speed at half the maximum height.
3. [3 marks]
A \(60\)-kg student climbs a flight of stairs (height \(3.0\) m) in \(5.0\) s. Calculate the work done against gravity and the student's average power output.
4. [3 marks]
A \(0.30\)-kg piece of aluminum at \(95Ā°\)C is dropped into \(0.40\) kg of water at \(15Ā°\)C. Final temperature is \(22Ā°\)C. Calculate the specific heat capacity of aluminum.
5. [3 marks]
MC: A 100-W incandescent light bulb produces 5 W of visible light and 95 W of heat. Its efficiency is:
Part B ā Thinking & Investigation [15 marks]
6. [5 marks]
A roller coaster car (mass \(800\) kg) starts at rest at a height of \(35\) m on a track. Friction does \(80\) kJ of work as the car descends to a low point at \(5.0\) m. (a) Use conservation of energy with non-conservative work to find the speed at the low point. (b) If the car climbs a second hill that is \(20\) m high, how fast is it moving at the top (assume negligible additional friction on this section)?
7. [5 marks]
A pump lifts \(120\) kg of water per minute through a vertical height of \(5.0\) m. (a) Calculate the rate of useful work (power). (b) If the pump's efficiency is \(72\%\), what electrical power input is required? (c) How much electrical energy (in J and in kWh) is used in 1 hour of continuous operation?
8. [5 marks]
Investigation design: Design an experiment to test whether mechanical energy is conserved when a marble rolls down a smooth, curved ramp. Identify variables, equipment, key measurements, calculation, and a major source of error. State an expected result and a plausible non-conservative loss.
Part C ā Communication [15 marks]
9. [5 marks]
Draw a Sankey-style energy flow diagram for a coal-fired power plant (input chemical energy ā electrical output) showing typical losses (waste heat, transmission). Label percentages adding to 100%.
[Sankey diagram space]
10. [5 marks]
Compare and contrast (table OR paragraph): (i) hydroelectric vs. wind, (ii) fossil-fuel thermal vs. solar PV. Use criteria: efficiency, intermittency, environmental impact, capacity factor.
11. [5 marks]
In one paragraph (4ā6 sentences), explain ā using correct physics vocabulary ā what "energy conservation" means in two different senses: (1) the physics law (conservation of energy in closed systems) and (2) the everyday meaning (energy efficiency / reduction). Why is the everyday meaning often called "negawatts"?
Part D ā Application [15 marks]
12. [5 marks]
STSE ā Home heating: A house in Ottawa has an electric baseboard heater rated at \(2000\) W operating for an average of 8 hours/day in January. (a) Calculate energy use per day (kWh). (b) At Ontario hydro rate of \(\$0.12\)/kWh, calculate the monthly cost (30 days). (c) A heat pump with COP = 3.0 produces 3 J of heat per 1 J of electricity input. Recalculate (a) and (b) if a heat pump replaces baseboards. (d) Comment on payback for a \(\$5000\) heat-pump installation.
13. [5 marks]
A \(1500\)-kg car accelerates from rest to \(20\) m/s in \(8.0\) s on a level road. (a) Calculate the kinetic energy at \(20\) m/s. (b) Calculate the average power required (ignoring friction and air resistance). (c) The car's engine actually delivers \(45\) kW; using the work-energy theorem and your answer to (b), what fraction of engine power went into kinetic energy? (Account for losses qualitatively.)
14. [5 marks]
A \(1.0\)-kg block slides from rest down a \(30Ā°\) incline of length \(5.0\) m, then onto a horizontal surface. Friction is present throughout (\( \mu_k = 0.20 \)). (a) Calculate the speed at the bottom of the incline (use energy conservation with friction work). (b) How far does the block slide on the horizontal surface before stopping?