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AP Physics 1: Work, Power & Mechanical Energy

Welcome to Unit 4, where we abandon force vectors and start using the universal currency of physics: Energy (Joules). This approach often makes difficult mechanics problems much easier to solve.

This guide covers the foundations: how energy is transferred (Work), the different types of mechanical energy, and the rate at which transfer happens (Power).

AP Physics 1 Unit 4 (Topics 4.1-4.3): Work as energy transfer, kinetic energy, mechanical energy forms, power as rate of work. (18-23% exam weight)

1. What is Work? ( $W$ )

In physics, “Work” has a very specific definition. You aren’t doing work just by getting tired. Work is only done when a force causes a displacement.

If you push against a solid wall for an hour, you get exhausted, but you have done zero work on the wall because it didn’t move ( $d=0$ ).

$W = Fd \cos\theta$

Where F is force, d is displacement, and θ is the angle between them.

The “Angle Trap” (Crucial)

The most common mistake students make is forgetting the angle $\theta$ . Work is a scalar product (dot product). This means only the part of the force that is parallel to the direction of motion counts.

Physics free body diagram showing a force applied at an angle theta. The horizontal component (F cos theta) does work, while the vertical component (F sin theta) does zero work.

The “Angle Trap”: Only the force component parallel to the displacement ( $F_{\parallel} = F \cos \theta$ ) does Work. The vertical component does zero work.

⚠️ Exam Tip: If a force is perpendicular to motion (like Normal Force on a flat surface, or Centripetal Force in a circle), the angle is 90°. Since $\cos(90°) = 0$ , perpendicular forces do ZERO WORK.

2. Types of Mechanical Energy

Mechanical energy is the energy possessed by an object due to its motion or position. In AP Physics 1, we focus on three main types.

1. Kinetic Energy ( $K$ )

The energy of motion. If it’s moving, it has $K$ .

$K = \frac{1}{2}mv^2$

Note: Since $v$ is squared, doubling your speed quadruples your kinetic energy.

2. Gravitational Potential Energy ( $U_g$ )

Energy stored due to height. You must define a “zero height” ( $h=0$ ) line, usually the lowest point in the problem.

$U_g = mgh$

3. Elastic Potential Energy ( $U_s$ )

Energy stored in a compressed or stretched spring.

$U_s = \frac{1}{2}kx^2$

Where $k$ is the spring constant (stiffness) and $x$ is the displacement from equilibrium.

Work-Energy Theorem (AP Favorite)

The work-energy theorem connects work directly to kinetic energy change:

$W_{net} = \Delta K = K_f - K_i$

Net work equals change in kinetic energy. Friction does negative work.

⚠️ Key Insight: Work changes kinetic energy. Potential energy changes come from conservative forces (gravity, springs).

3. Power ( $P$ )

Power tells you how fast energy is transferred.

Illustration comparing Low Power vs High Power. Lifting a weight slowly takes 10 seconds (Low Watts), while lifting quickly takes 1 second (High Watts).

Power = Rate of Work: Both lifters do the exact same amount of Work (lifting the same mass), but the one who does it faster has higher Power.

Power is measured in Watts (W), where $1 \text{ Watt} = 1 \text{ Joule/second}$ . Two ways to calculate:

$P = \frac{W}{\Delta t}$

Total work ÷ total time

$P = Fv \cos\theta$

Constant velocity + force

📚 AP Practice Problems

1. 50N at 30° pushes box 10m. Work?

Answer

$W = 50 \times 10 \times \cos30° = 433J$

2. 2kg drops 20m. Bottom speed?

Answer

$v = \sqrt{2gh} = 19.8 \, \text{m/s}$

3. Spring $k=200N/m$ , 0.1m compression. PE?

Answer

$U_s = \frac{1}{2}kx^2 = 1J$

AP Physics 1: Work, Power & Mechanical Energy

1. What is Work? ()

The “Angle Trap” (Crucial)

2. Types of Mechanical Energy

1. Kinetic Energy ()

2. Gravitational Potential Energy ()

3. Elastic Potential Energy ()

Work-Energy Theorem (AP Favorite)

3. Power ()

📚 AP Practice Problems

🔗 Related AP Physics Resources

1. What is Work? ( $W$ )

1. Kinetic Energy ( $K$ )

2. Gravitational Potential Energy ( $U_g$ )

3. Elastic Potential Energy ( $U_s$ )

3. Power ( $P$ )