AI Tutor
If you push an empty shopping cart with all your strength, it rockets down the aisle, but if you give that exact same shove to a stalled car, it barely creeps forward.
That difference comes down to how forces change an object's motion β€” governed by one of the most famous equations in physics.

The Law of Acceleration

In 1687, Isaac Newton published the Principia, where he formulated his second law to explain how planets orbit and why dropped apples speed up toward Earth.
Newton's second law states that the net force (the vector sum of all forces acting on an object, written as Ξ£F\Sigma F) equals the object's mass (mm) multiplied by its acceleration (aa).
Because force is a vector (a quantity with both magnitude and direction), an object only accelerates in the exact direction of the unbalanced net force.
What happens when multiple forces push, pull, and drag on an object at the exact same time?

Using Free Body Diagrams

A free body diagram is a simplified drawing where you represent the object as a single dot or box and draw every external force as an arrow pointing outward.
Let's look at a concrete problem: a worker pushes a 12Β kg12\text{ kg} tool chest horizontally across a rough concrete floor with an applied force of Fapp=60Β NF_{\text{app}} = 60\text{ N} to the right.
The floor pushes back with a friction force of Ff=24Β NF_f = 24\text{ N} to the left, while gravity (Fg=mg=120Β NF_g = mg = 120\text{ N}) and the upward normal force (FN=120Β NF_N = 120\text{ N}) act vertically.