Newtonian Force Calculator (F=ma)

Force (Newton)

Knowing how much force is needed to move objects is crucial information in many daily applications; In racing, cars are engineered to require minimal force to achieve maximum speed. When lifting weights, we often want to know how much force is needed to pick up bar- and dumbbells. Roller coasters are designed to generate specific accelerations that create the sensation of G-forces. These are all examples of Newton's second law of motion.

We all have experienced this law in action. When pushing a closet forward, the force needed to move the closet is greater than when trying to move a toy car. Note that moving something from rest requires acceleration.

Newton's second law explains the relationship between the force, mass and acceleration. Newton came up with the following formula to explain the relationship:

• F = the force, with Newton (N) as the unit of measurement
• m = the mass of the object in kilograms (kg)
• a = the acceleration of the object in meters per second squared (m/s²)

Sometimes you may see:

Here, g represents the acceleration due to gravity on Earth, which is approximately 9.81 m/s².

The formula implies that 1 Newton of force is equal to 1 kg * m/s². More simply 1 Newton is the force required to accelerate a mass of 1 kilogram at 1 meter per second, per second. An acceleration of 1 m/s² means that every second the object will move 1 m/s faster. This may be confusing because the object may not reach a speed of 1 meter per second immediately. That's because acceleration is measured at a single point in time, not over a duration.

This equation explains why race car engineers aim to make vehicles as lightweight as possible. Accelerating a 1700 kg car at 6 m/s² requires a force of 1700 * 6= 10200 N, while the same acceleration of a 800 kg car requires a force of 800 * 6= 4800 N. Therefore, the same engine can accelerate a lighter car more quickly!

Example

You are holding a cupcake weighing 102 grams. What is the force required to hold the cupcake in the air? Note that gravity on Earth exerts an acceleration of approximately 9.81 m/s², commonly denoted as g

m = 102 g = 0.102 kg

a = 9.81 m/s²

F = m * a = 0.102 * 9.81 = 1 N

You thus must exert an upward force of 1 Newton to hold the cupcake in the air.