#AP Physics 1: Power - Your Ultimate Guide 🚀

Hey there, future AP Physics master! Let's break down power, a key concept for your exam. Think of power as the speed at which energy is transferred or transformed. Ready to make it click? Let's dive in!

#Energy Transfer and Power

# Power as Energy Rate 🕰️

Power is all about how quickly energy changes. It's the rate of energy transfer or conversion.
Think of it as energy moving from one place to another or changing forms within a system. 💡
Examples:
- A lightbulb: Electrical energy ➡️ light + heat energy.
- A car engine: Chemical energy ➡️ kinetic energy.

# Average Power Calculation

Average power tells us the average rate at which energy is transferred or converted over a time interval.
Formula: $P_{avg} = \frac{\Delta E}{\Delta t}$
- $P_{avg}$ : Average power (watts)
- $\Delta E$ : Change in energy (joules)
- $\Delta t$ : Change in time (seconds)

Quick Fact

1 Watt = 1 Joule per second (1 W = 1 J/s)

- **Examples:** - A 60-watt bulb uses 60 joules of energy every second. - A battery delivering 1000 J in 10 s has an average power of 100 W.

# Power as Work Rate

Power can also be seen as the rate at which work is done.
Work is the energy transferred by a force acting over a distance.
Formula: $P_{avg} = \frac{W}{\Delta t}$
- $P_{avg}$ : Average power (watts)
- $W$ : Work done (joules)
- $\Delta t$ : Change in time (seconds)

Memory Aid

Remember: Work (W) is the change in energy, so both formulas for P_avg are really saying the same thing!

- **Examples:** - Lifting a 10 N weight 2 m in 4 s (20 J of work) requires 5 W of power. - A machine doing 1000 J of work in 5 s has a power of 200 W.

# Instantaneous Power from Force 🏃‍♂️💨

Instantaneous power is the power at a specific moment in time.

Key Concept

It's calculated using the force and velocity at that instant.

- **Formula:**

P\_{inst} = F\_{||} v = Fv \cos \theta

-

P\_{inst}

: Instantaneous power (watts) -

F\_{||}

: Force component parallel to velocity (newtons) -

v

: Velocity (m/s) -

F

: Total force (newtons) -

\theta

: Angle between force and velocity (degrees) - **Examples:** - A car with 500 N force parallel to its motion at 20 m/s has an instantaneous power of 10,000 W. - Pushing a cart with 100 N at 30° to its motion at 1 m/s gives an instantaneous power of 86.6 W.

Practice Question

Multiple Choice Questions

A 70 kg student runs up a flight of stairs 4.5 m high in 5 s. The average power output of the student is most nearly: (A) 63 W (B) 310 W (C) 620 W (D) 1400 W
A crane lifts a 200 kg object vertically upward at a constant speed of 3 m/s. The power output of the crane is most nearly: (A) 600 W (B) 2000 W (C) 6000 W (D) 12000 W

Free Response Question

A 1000 kg car accelerates from rest to 20 m/s in 10 s on a horizontal road. Assume the acceleration is uniform and the force is applied parallel to the direction of motion.

(a) Calculate the work done by the car's engine during this acceleration. (b) Calculate the average power output of the car's engine during this acceleration. (c) Calculate the instantaneous power output of the car's engine at t = 5s. (d) If the car then travels at a constant speed of 20 m/s, what is the instantaneous power output of the car's engine at t = 15s?

Answer Key and Scoring Rubric

Multiple Choice Answers:

(C) 620 W
(C) 6000 W

Free Response Answers:

(a) Work Done (3 points)

Use the work-energy theorem: $W = \Delta KE$
$KE_i = 0$ (starts from rest)
$KE_f = (1/2)mv^2 = (1/2)(1000 kg)(20 m/s)^2 = 200,000 J$
$W = 200,000 J$ (1 point each for formula, substitution, and answer)

(b) Average Power (2 points)

$P_{avg} = W / \Delta t$
$P_{avg} = 200,000 J / 10 s = 20,000 W$ (1 point each for formula and answer)

(c) Instantaneous Power at t=5s (3 points)

First, find the velocity at t=5s: $v = at$ , $a = \Delta v/\Delta t = 20 m/s / 10 s = 2 m/s^2$ , so $v = (2 m/s^2)(5 s) = 10 m/s$
Find the force: $F = ma = (1000 kg)(2 m/s^2) = 2000 N$
$P_{inst} = Fv = (2000 N)(10 m/s) = 20,000 W$ (1 point each for velocity, force, and power)

(d) Instantaneous Power at Constant Speed (2 points)

At constant speed, the net force is zero, so the force from the engine is equal to the resistive forces.
However, the power is still $P = Fv$ , where F is the force required to maintain the constant speed
$P_{inst} = Fv = (2000 N)(20 m/s) = 40,000 W$ (1 point for concept, 1 point for correct answer)

#Final Exam Focus

Okay, you've made it this far! Here's what to focus on for the final push:

High-Priority Topics:
- Understanding the relationship between work, energy, and power.
- Applying the power equations ( $P = \frac{\Delta E}{\Delta t}$ , $P = \frac{W}{\Delta t}$ , and $P = Fv \cos \theta$ ) in various scenarios.
- Distinguishing between average and instantaneous power.
Common Question Types:
- Calculating power given work and time.
- Determining instantaneous power using force and velocity.
- Analyzing energy transfer and conversion in systems.

Exam Tip

Time Management: Don't spend too long on a single question. If you're stuck, move on and come back later.

-

Common Mistake

#Common Pitfalls: - Forgetting to use the component of force parallel to the velocity for instantaneous power. - Mixing up average and instantaneous power. - Incorrect units: Make sure you are using Joules for energy/work and seconds for time.

Exam Tip

Last-Minute Tips: - Review key formulas and definitions. - Go through a few practice problems to refresh your memory. - Stay calm and confident—you've got this! 💪

Remember, physics is about understanding the world around you. You've got the tools and the knowledge. Now go ace that exam!