Newton’s Second Law: Forces, Friction, Mass, Weight, and Acceleration

Ch. 04 – Newton’s Second Law

3.1 Forces

Force is defined as a push or pull. According to Newton’s Second Law, forces cause changes in velocity (speeding up, slowing down, or changing direction).

• Acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

$\text{Acceleration of an object} = \frac{\text{Net force on the object}}{\text{Mass of the object}}$

$\vec{a} = \frac{\vec{F}_{\text{net}}}{m}$

3.2 Friction

The force of friction occurs when solid surfaces slide (or tend to slide) over one another. Friction always acts in the direction opposite to motion.

• Static friction: Acts when an object is at rest.

• Kinetic (sliding) friction: Acts when an object is sliding on a surface.

Friction is independent of speed and surface area of contact (for most solid surfaces). It depends mainly on the nature of the surfaces and the normal force between them.

• Example: A sliding object experiences sliding (kinetic) friction, while a stationary object experiences static friction.

Graph: The relationship between frictional force and applied force shows that static friction increases up to a maximum value, after which kinetic friction takes over and remains constant.

3.3 Mass and Weight

Quantity	Definition	Units	Location Dependence	Variable
Mass	The quantity of matter in an object; a measure of inertia or sluggishness that an object exhibits in response to any effort made to start, stop, or change its state of motion.	kg	Independent	m
Weight	The force upon an object due to gravity.	N	Dependent	$F_g$ or $w = mg$

The amount of acceleration depends not only on the net force but also on the mass being pushed:

$\text{Acceleration of an object} = \frac{\text{Net force}}{\text{Mass of the object}}$

$a = \frac{F_{\text{net}}}{m}$

3.4 Newton’s Second Law

The acceleration of an object is directly proportional to the net force $F_{\text{net}}$ acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.

$a = \frac{F_{\text{net}}}{m}$

3.5 Free Fall (acceleration is $g$)

When the force of gravity is the only force acting on an object (i.e., when friction such as air resistance is negligible), we say the object is in free fall.

• All objects in free fall accelerate downward at the same rate, regardless of their mass.

• The force of gravity ($F_g$) is the weight, so the mass is doubled and the force is also doubled, resulting in the same acceleration $g$.

Example: The force of gravity on a rock is huge, but its mass is also large. The force of gravity on a feather is tiny, but its mass is also tiny. The ratio of force to mass is always $g$.

3.6 Non-free Fall (acceleration is less than $g$)

Free-fall always happens in a vacuum. However, when an object falls through the air, the air exerts a force, called air drag or air resistance, which opposes the motion of the object.

• As speed increases, air resistance increases.

• The direction of air resistance is always opposite to motion.

Terminal speed (or terminal velocity) is the speed at which the force of air resistance equals the weight of the object, resulting in zero acceleration (constant velocity).

• At terminal speed: $F_{\text{air resistance}} = F_g$

• Acceleration: $a = 0$

Example: A skydiver jumps from a plane. As speed increases, air resistance increases until it balances the force of gravity, and the skydiver falls at terminal velocity.

Terminal velocity increases for objects with greater mass or smaller surface area (less air resistance).

Check: If two skydivers of different mass jump from the same height with the same size parachutes, which parachutist reaches the ground first? The heavier one, because they reach a higher terminal velocity.