Applied Force Calculator

| Added in Physics

What is Applied Force?

Applied force is the force that you exert on an object to cause it to move or accelerate. In real-world scenarios, when you push or pull an object, not all of your effort goes into accelerating it. Some of the force is used to overcome friction between the object and the surface it's on. Understanding applied force is essential for engineers, physicists, and anyone working with mechanical systems.

The Applied Force Formula

The formula for calculating applied force when friction is present is:

[AF = (m \times a) - F_f]

Where:

  • AF is the applied force in Newtons (N)
  • m is the mass of the object in kilograms (kg)
  • a is the acceleration in meters per second squared (m/s²)
  • F_f is the frictional force in Newtons (N)

This formula accounts for the fact that friction opposes motion. The applied force must be enough to both accelerate the object and overcome the frictional resistance.

Calculation Example

Let's work through an example to see how this formula works in practice.

Given:

  • Mass = 15 kg
  • Acceleration = 3 m/s²
  • Frictional Force = 8 N

Step 1: Calculate mass times acceleration

[m \times a = 15 \text{ kg} \times 3 \text{ m/s}^2 = 45 \text{ N}]

Step 2: Subtract the frictional force

[AF = 45 \text{ N} - 8 \text{ N} = 37 \text{ N}]

Therefore, the applied force required is 37 Newtons.

Understanding the Components

Mass

Mass is the amount of matter in an object. Heavier objects require more force to achieve the same acceleration as lighter objects. This is why it's harder to push a loaded shopping cart than an empty one.

Acceleration

Acceleration is the rate of change of velocity. If you want an object to speed up quickly, you need to apply more force. The relationship between force and acceleration is direct and proportional.

Frictional Force

Friction is the resistance that one surface encounters when moving over another. It depends on the nature of the surfaces in contact and the normal force pressing them together. Common examples include:

  • Sliding friction when pushing a box across the floor
  • Rolling friction when a car tire moves on pavement
  • Air resistance when objects move through the atmosphere

Practical Applications

Understanding applied force is crucial in many fields:

  • Engineering: Designing motors, vehicles, and machinery that must overcome friction
  • Construction: Calculating forces needed to move heavy materials
  • Sports Science: Analyzing the forces athletes exert during performance
  • Robotics: Programming robots to apply the correct amount of force for tasks

Tips for Accurate Calculations

  1. Use consistent units: Make sure all your measurements are in compatible units before calculating
  2. Measure friction accurately: Frictional force can vary significantly based on surface conditions
  3. Consider static vs. kinetic friction: Static friction (starting motion) is typically higher than kinetic friction (maintaining motion)
  4. Account for all friction sources: In complex systems, friction may come from multiple points

Frequently Asked Questions

Applied force is the force you exert on an object, while net force is the sum of all forces acting on the object. When friction is present, the applied force must overcome friction to produce the net force that causes acceleration.

Frictional force opposes motion, so it works against the applied force. To achieve a certain acceleration, the applied force must account for both the force needed to accelerate the object (ma) and the force lost to friction.

When there is no friction (frictionless surface), the applied force equals mass times acceleration (F = ma). Simply enter 0 for the frictional force in the calculator.