For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
Figure 1: Mass is intrinsic (amount of matter). Weight is extrinsic (force of gravity acting on that matter).
Let us return to the legend of Newton and the falling apple. From the study of statics, we know that the apple remains attached to the tree as long as the apple stalk is strong enough to support the weight of the apple.
As the apple grows, its mass increases. Eventually, the gravitational force (weight) exceeds the stalk's strength, and it snaps. But why does it fall? And what is the difference between the "stuff" inside the apple and the force pulling it down?
Advertisement
1. Mass vs. Weight: The Critical Distinction
In everyday language, we use "mass" and "weight" interchangeably. In engineering, confusing them causes catastrophic calculation errors.
Mass (m):
The amount of matter contained in a body. It is a measure of inertia (resistance to acceleration).
Unit: Kilograms (kg)
Weight (W):
The force exerted on a mass by a gravitational field.
Unit: Newtons (N) or Pounds-force (lbf)
The amount of matter contained in a body. It is a measure of inertia (resistance to acceleration).
Unit: Kilograms (kg)
Weight (W):
The force exerted on a mass by a gravitational field.
Unit: Newtons (N) or Pounds-force (lbf)
The Space Station Example:
Consider fruits grown inside an orbiting spacecraft. In that environment, objects are effectively weightless and float freely. However, they still possess mass. If an astronaut tried to shake a heavy floating pumpkin, it would still resist moving due to its inertia (mass), even though it has zero weight.
2. The Second Law: F = ma
When the apple separates from the tree, the downward force of gravity is no longer balanced by the tension in the stalk. There is a Net Force acting on the mass.
Newton formalized this relationship in his Second Law of Motion:
Figure 2: Force causes acceleration. The magnitude of that acceleration depends inversely on the mass.
F = m × a
This equation reveals two fundamental truths of mechanics:
- Direct Proportion: For a given mass, doubling the force will double the acceleration.
- Inverse Proportion: For a given force, doubling the mass will cut the acceleration in half.
Advertisement
3. Engineering Applications
Newton’s second law isn't just for falling apples. It is the backbone of dynamic analysis in mechanical design.
Figure 3: Calculating the torque required for a robot to accelerate a load requires F=ma (plus gravity).
Example: Sizing a Motor
When designing a conveyor belt or a robotic arm, you cannot simply calculate the static weight. You must calculate the force required to accelerate the load from a stop.
Engineering Calculation: Orientation Matters
Gravity always acts downwards, but how it opposes your motor depends on the direction of motion:
Gravity always acts downwards, but how it opposes your motor depends on the direction of motion:
- Vertical Lift (e.g., Elevator):
Force = (Mass × Gravity) + (Mass × Acceleration) - Horizontal Move (e.g., Conveyor):
Force = (Friction Coefficient × Mass × Gravity) + (Mass × Acceleration)
If you only design for gravity (static weight), your motor will stall or move too sluggishly to meet cycle time requirements.
Related: Newton's Three Laws Overview
Comments