Power
Section: Work, Energy and Power | Syllabus: Cambridge AS Level Physics 9702
Defining Power Power is the rate of transfer of energy or the rate at which work is done . P = fraction Units: Watts (W). 1W = 1 J s^-1. Worked Example: Race up Stairs Question: A 60 kg runner races up a tall building (vertical height 390 m) in 17 minutes 22 seconds.
(a) Calculate the work done. (b) Calculate the average power developed. Answer (a) Work Done: Lifting mass against gravity. W = mg Δ h = 60 × 9.81 × 390 = 230,000 J (230 kJ). (b) Power: Convert time to seconds.
t = (17 × 60) + 22 = 1042 s. P = fraction 220 W Power Needed to Maintain Critical Speed To keep a vehicle moving at constant speed against resistive forces, the engine must deliver power. P = Fv Where F is the driving force (equal to resistive forces at constant speed) and v is velocity.
Worked Example: Car on Highway Question: A car of mass 1400 kg travelling at a constant velocity of 27 m s^-1 has total resistive forces of 820 N. (a) Calculate the power developed. (b) If the car accelerates from 27 m s^-1 with a driving force of 1100 N, calculate the initial acceleration.
Answer (a) Power: P = Fv = 820 × 27 = 22,140 W = 22 kW (b) Acceleration: Resultant Force = Driving Force - Resistive Force = 1100 - 820 = 280 N. a = fraction = fraction = 0.20 m s^-2 Examiner Tips Constant Speed: When a question states "constant speed", it implies the driving force equals the resistive force (F_driving = F_resistive).
Use this F in P=Fv.
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