Forces and Motion

This chapter covers what matter is, the forces that act on it, and how Newton’s laws describe its motion.

Matter

Definitions

Matter

A physical substance that has mass and takes up space (volume).

Mass

The measure of the amount of matter in an object

Weight

The specific force of gravity acting on an object

Weight is a force acting on the mass of an object. Weight changes based on gravity, but mass never does. So if you went to the moon, your mass would stay the same, but you would weigh less because the moon has a lower gravity than Earth does.

Let’s talk more about other forces.

Forces

Definitions

Force

A push or a pull on an object

Gravity

An attractive force between masses.

Friction

A force that opposes the motion of objects that touch.

Compression

A pushing force that squeezes an object

Tension

Pulling force

Net force

The combined result of all forces acting on an object, found by adding the forces with their directions: forces in opposite directions subtract, so 10 N left and 4 N right make 6 N left.

Sidenote

Types of friction

Friction comes in four types: static (keeps a resting book from sliding off a slightly tilted table), sliding (slows a box pushed across the floor), rolling (acts on bicycle tires as they turn), and fluid, including air resistance (what you feel when you stick your hand out a car window).

Forces can be balanced or unbalanced. Unbalanced forces (a nonzero net force) change an object’s motion: they speed it up, slow it down, or change its direction. Balanced forces (net force of zero) leave its motion unchanged, so the object stays at rest or keeps moving at a constant speed in a straight line. Force is governed by Newton’s laws.

Equilibrium

Definitions

Equilibrium

Equal forces are opposing, resulting in a net force of zero. An example is a balanced tug-of-war.

Center of gravity

The point on an object where its weight is evenly balanced in every direction.

An object stays upright as long as its center of gravity is supported. Tip it too far, and the center of gravity moves outside its base, and the object falls over. This is why a loaded moving truck is more likely to tip on a turn than an empty one: cargo stacked high raises the center of gravity, so a smaller lean on a turn is enough to move it outside the wheels’ base. Objects with a low center of gravity and a wide base are the most stable.

Newton’s laws

Newton’s 1st law: inertia

An object at rest stays at rest, and an object in motion keeps moving the same way, unless a force acts on it. This resistance to change is called inertia.

Newton’s 2nd law: F = ma

Acceleration is equal to the net force divided by mass. An unbalanced force results in a change of motion. In other words, the greater the force, the greater the acceleration of the object. The greater the mass of the object, the harder it is to accelerate. (Acceleration is covered in more detail in the Motion section below: it’s the rate at which velocity changes.)

Let’s look at an example.

Example: Newton’s 2nd law

A $10$ kilogram box is pushed with a net force of $20$ newtons (assume no friction). What is its acceleration?

$F=ma$

$20=10\times a$

Divide both sides by $10$: $a=20÷10=2$

Answer: 2 m/s²

ASVAB questions like this one are usually built so the numbers divide evenly, so a quick mental division is often all the math you need.

Newton’s 3rd law: action and reaction

Whenever one object exerts a force on a second, the second object exerts an equal and opposite force on the first. These forces act on different objects and do not cancel out.

For example, if you jump up, you are pushing down on the ground (action) with the same force the ground is pushing up at you (reaction), causing you to launch into the air.

Motion

To describe motion, we need a frame of reference - the viewpoint used to measure an object’s direction and amount of motion. For example, a passenger in a moving car has a different frame of reference (the car) than someone standing on the sidewalk (the street), even though the same motion is happening.

Distance vs. displacement

Distance is the total length of a path.

Displacement is the straight-line distance and direction from an object’s starting point to its ending point.

For example, if you walk $100$ meters down a hallway and back, your distance is $200$ meters, but your displacement is zero because you ended up where you started

Speed and velocity

Speed is the distance an object travels per unit of time. On a distance-time graph, the slope represents speed.

Velocity is speed in a given direction.

A car traveling $60$ miles per hour north has both a speed and a direction, so that describes velocity, not just speed.

Acceleration

Acceleration is the rate at which velocity changes: speeding up, slowing down, or changing direction. It’s measured in meters per second per second (m/s²).

Momentum

The product of mass and velocity. If a grocery cart and a marble are moving at the same speed, the cart has more momentum because it has more mass.