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Force
- A push or pull.
- Capable of changing the state of motion of an object (that is, accelerating the object.)
Acceleration requires the application of some force.
- A vector quantity.
- Has magnitude and direction.
- Multiple forces must be added vectorally to get the sum.
- Measured in pounds, ounces, tons, newtons, dynes…
- Friction, tension, thrust, weight, drag, resistance are all forces.
NET Force
The (vector) sum of all forces acting on an object.
“No net force” or “net force = zero” means either,
1) no forces are acting at all, OR
2) the (vector) sum = zero.
Force Myths
Force of hand (or bat or racket or foot or…) stays with a thrown (or batted or hit or kicked or…)
object (while it’s in flight.)
Force is required to keep an object moving.
The force required to push an object along at a constant speed is greater than the retarding forces
(i.e., friction.)
Inertia is a force.
A force is a property of an object.
Air doesn’t exert a force.
Forces can exist in isolation. (Force fields.)
Greater speeds require greater forces for equal accelerations.
Newton’s Second Law of Motion AKA: The Law of Acceleration
If the net force on an object (of mass m) is not zero, then the object will accelerate in the direction of
that net force with a magnitude that is proportional to the net force and inversely proportional to the
mass of the object. Mathematically stated:
a=F/m
Most commonly remembered as:
F=ma
The “F” in the above equations is ALWAYS the NET force.
Maybe, think of NET force as the “extra” force applied beyond the amount needed to balance all
forces. If there is no “extra” force, there will be no acceleration and the object will either remain at
rest or continue straight-line motion at a constant speed.
Objects accelerate ONLY during the time that NET force is greater than zero. (Or only during times
there is an unbalanced force.)
Note the nature of the proportionalities in the a=F/m equation:
For example, if the force is doubled, the acceleration will be doubled. (directly proportional)
If the mass is doubled, the acceleration will be halved. (inversely proportional)
This equation tells us how we measure force:
- If the mass is measured in kg and the acceleration in m/s2, then force will have units of kg
m/s2 or newtons (N). (SI units)
- If the mass is measured in g and the acceleration in cm/s2, then force will have units of g
cm/s2 or dynes. (cgs units)
- If the mass is measured in slugs (yes! SLUGS!) and the acceleration in ft/s2, then force will
have units of slugs ft/s2 or pounds (lbs). (British units)
To compare newtons (something you may not be familiar with) to pounds (something you should be
familiar with!):
1 lb = 4.5 N
or
1 N = 0.22 lb
Mass versus Weight
Mass
- A measure of the amount of an object’s inertia.
- A measure of the amount of stuff in an object.
- A measure of an object’s resistance to acceleration.
- NOT a measure of the amount of space an object takes up. (That would be volume.)
- A scalar quantity.
- Independent of location/position.
- Depends on speed. (But only at very high, relativistic speeds.
It’s part of Einstein’s relativity ideas. Ignore this for now!)
- Proportional to the weight of an object.
- Measured in slugs (English) or kilograms (SI) or grams (metric) or tonnes (metric).
- Measured with a balance.
Weight
- A measure of the force of gravity on an object.
- A force.
- A vector quantity. The direction is downward!
- Depends on location/position.
- Depends on g. (Proportional to g.)
- Proportional to the mass of an object.
- Measured in pounds (English), newtons (SI), dynes, ounces, tons, etc…
- Measured with a spring scale.
Common usage: These two words are frequently interchanged, usually with no resulting confusion.
(See the label on just about any canned or packaged food item.)
Science usage: There is a critical, non-trivial distinction between these two words and concepts.
Failure to grasp that distinction will be detrimental to your success in related problems.
Newton’s Third Law of Motion AKA: The Law of Interaction
For every action…
(Don’t be confused with non-physics cases!)
If one object exerts a force on a second object, then the second object exerts an equal but oppositely
directed force on the first object.
Action/reaction forces are DIFFERENT forces on DIFFERENT objects. They NEVER cancel out.
Forces cannot exist in isolation. (A “force” field is not a force…)