IB MYP 4-5 Physics- Power & Efficiency - Study Notes - New Syllabus
IB MYP 4-5 Physics-Power & Efficiency – Study Notes
Key Concepts
- Power & Efficiency
Power
Power
Power is the rate at which work is done or the rate at which energy is transferred or transformed.
The formula for power is:
P = \(\dfrac{W}{t}\) or \(P = \dfrac{E}{t}\)
Where:
- \(P\) = Power (watts, W)
- \(W\) = Work done (joules, J)
- \(E\) = Energy transferred (joules, J)
- \(t\) = Time taken (seconds, s)
In terms of force and velocity, power can also be expressed as:
\(P = F \cdot v\)
Where:
- \(F\) = Force applied (newtons, N)
- \(v\) = Velocity (m/s)
Key Notes
- Measured in watts (W), where 1 W = 1 J/s.
- Higher power means more work done in less time.
- Power is scalar; it does not have direction.
Example:
A crane lifts a 2000 N load to a height of 15 m in 30 seconds. Calculate the power output.
▶️ Answer/Explanation
Work done: \(W = F \cdot d = 2000 \times 15 = 30000 \ \text{J}\)
Power: \(P = \dfrac{30000}{30} = 1000 \ \text{W}\)
Final Answer: \(\boxed{1000 \ \text{W}}\)
Example:
A car engine exerts a constant force of 500 N while moving at 20 m/s. Find its power output.
▶️ Answer/Explanation
Power: \(P = F \cdot v = 500 \times 20 = 10000 \ \text{W}\)
Final Answer: \(\boxed{10.0 \ \text{kW}}\)
Efficiency
Efficiency
Efficiency is the measure of how effectively input energy is converted into useful output energy or work. It is expressed as a ratio or percentage.
\(\text{Efficiency} = \dfrac{\text{Useful Output Energy (or Power)}}{\text{Total Input Energy (or Power)}} \times 100\%\)
Where:
- Efficiency is always less than or equal to 100%.
- Friction, heat loss, and sound loss reduce efficiency.
Formula (Energy-based):
\(\eta = \dfrac{\text{Useful energy output}}{\text{Total energy input}} \times 100\%\)
Formula (Power-based):
\(\eta = \dfrac{\text{Useful power output}}{\text{Total power input}} \times 100\%\)
Formula (Work-based):
\(\eta = \dfrac{\text{Work output}}{\text{Work input}} \times 100\%\)
Formula (For mechanical advantage systems):
\(\eta = \dfrac{\text{Mechanical Advantage}}{\text{Velocity Ratio}} \times 100\%\)
Key Notes:
- 100% efficiency means no energy is wasted — practically impossible in real systems.
- Efficiency can be increased by reducing energy losses (e.g., using lubrication, better insulation).
- Often calculated for machines, engines, and power plants.
Example:
A motor consumes 2000 J of electrical energy and produces 1500 J of useful mechanical work. Calculate its efficiency.
▶️ Answer/Explanation
Efficiency = \(\dfrac{1500}{2000} \times 100\% = 75\%\)
Final Answer: \(\boxed{75\%}\)
Example:
An engine outputs 300 kW of power for a fuel input of 400 kW. Find the efficiency.
▶️ Answer/Explanation
Efficiency = \(\dfrac{300}{400} \times 100\% = 75\%\)
Final Answer: \(\boxed{75\%}\)