1. What is the Power Formula P = F × v?

Definition: This formula calculates mechanical power as the product of force and velocity.

Purpose: It helps determine the rate at which work is done or energy is transferred in mechanical systems.

2. Derivation of the Formula

The formula comes from the fundamental definitions:

Where:

• \( P \) — Power (Watts, W)
• \( F \) — Force (Newtons, N)
• \( v \) — Velocity (meters per second, m/s)
• \( W \) — Work (Joules, J)
• \( t \) — Time (seconds, s)
• \( x \) — Displacement (meters, m)

Explanation: Power is work per unit time. Since work is force times displacement (W = F×x), the time derivative gives us force times velocity.

3. Practical Applications

Examples:

• Calculating engine power output based on thrust and vehicle speed
• Determining electrical generator output from mechanical input
• Measuring human power output during cycling or rowing

4. Using the Calculator

Tips: Enter the force in Newtons and velocity in m/s. The calculator will compute power in Watts (1 W = 1 N·m/s).

5. Frequently Asked Questions (FAQ)

Q1: Why does power depend on both force and velocity?
A: Power measures how quickly work is done. High force at low velocity can do the same work as low force at high velocity, but at different rates.

Q2: What if the force and velocity aren't in the same direction?
A: Use the component of force in the direction of motion: \( P = F \times v \times \cos(\theta) \), where θ is the angle between them.

Q3: How does this relate to electrical power?
A: Electrical power (P=VI) is analogous - voltage (V) is like force, current (I) is like velocity.

Q4: What are typical values for human power output?
A: A person can sustain about 100W (0.13 hp) for hours, or 300-400W (0.4-0.5 hp) for short bursts.

Q5: How does this formula apply to rotational systems?
A: For rotation, \( P = \tau \times \omega \), where τ is torque (N·m) and ω is angular velocity (rad/s).