Distinguish weight from mass, calculate weight using Fg = mg, and describe the normal force and friction as the contact forces that act on objects on a surface (MA STE Introductory Physics, Motion and Forces).

What this topic is asking

Before you can draw forces or apply $F = ma$, you need to know the everyday forces and what each does. The Massachusetts Introductory Physics MCAS expects you to distinguish weight from mass, calculate weight with $F_g = mg$, and describe the normal force and friction, the two contact forces that act when an object sits on or slides along a surface. This grounds the cause-and-effect reasoning of the whole module.

Mass and weight

The distinction is one of the most tested ideas in the module. Mass is an intrinsic property: a $6$ kg box is $6$ kg on Earth, on the Moon, or in deep space. Weight depends on the local gravity: that same box weighs about $60$ N on Earth (where $g = 10$ m/s squared) but only about $10$ N on the Moon (where gravity is roughly one sixth as strong). So the question "would you weigh less on the Moon?" has the answer yes, while "would your mass change?" has the answer no.

The reference-sheet equation is

where $F_g$ is the weight (a force in newtons), $m$ is the mass in kilograms, and $g$ is the acceleration due to gravity. This is just Newton's second law applied to gravity, since a freely falling object has acceleration $g$.

The normal force

The normal force is why a book on a table does not fall through it: the table pushes up with a force equal to the book's weight. If you press down on the book, the normal force increases to support the extra push; if something lifts part of the weight, the normal force decreases. The normal force is always perpendicular to the surface, so on a ramp it points out of the slope, not straight up.

Friction

Friction is the contact force that resists the relative sliding of two surfaces. It always acts opposite to the direction of motion (or the direction the object is trying to move). Friction is why a sliding crate slows and stops once you stop pushing, and why you can walk without slipping. It depends on how rough the surfaces are and on how hard they are pressed together (the normal force): rougher surfaces and heavier objects produce more friction.

On the MCAS, friction is usually given as a number to include in the net force. A box pushed forward with $40$ N against $10$ N of friction has a net force of $30$ N. At constant velocity, friction exactly balances the push, so the net force is zero.

Try this

Q1. A $2.0$ kg object rests on a level bench. Take $g = 10$ m/s squared. State its weight and the normal force. [2]

• Cue. Weight $= mg = (2.0)(10) = 20$ N down; normal force $= 20$ N up (they balance).

Q2. State the direction of friction on a car braking to a stop while moving forward. [1]

• Cue. Backward, opposite to the car's motion.