Module 8: Newton's Laws of Motion

Word Worksheet
PDF Worksheet

Learning Objectives

After reading this page, watching the videos and reviewing the exercises, you will be able to:

• Understand different types of forces.
• Know Newton's three laws of motion.
• Understand some of the subtleties of the three Laws.
• Apply the concepts of Newton's Laws to some dynamics problems.

Properties of Forces

• A force is a push or a pull.
• Force is a vector.
• Forces can be contact (e.g. friction) or long-range (e.g. electro-magnetic)
• Forces are the result of an interaction between objects.

An overview of the forces acting on a body in a mechanical system

Force of Gravity:

A long-range force. All masses attract each other with the Force of Gravity (given by $F_{G}={Gm_{1}m_{2} \over r^{2}}$ - you will see this in more detail later on).
Special case of a gravitational force (close to the surface of a planet): $|{\vec {F}}_{gravity}|=m\ g$, where m is the mass of the object and g is the local acceleration due to gravity. This is often called the weight ${\vec {w}}$. $\therefore |{\vec {w}}|=mg$.
The direction of the weight (force of gravity) is more or less towards the centre of the planet in question. Therefore you could write: ${\vec {w}}=-mg\ \mathbf {\hat {\jmath }}$, using a conventional coordinate system.
Note that weight is a force and is therefore measured in units of force, not units of mass.

Tension:

A Contact Force; Tension is caused by a restoring force acting between particles of thin long objects: rope, rod, beam, string, etc.
Note that a string always pulls, never pushes. The direction of the tension is always parallel to the string or rope.

Normal force:

A Contact Force; Normal force is caused by a restoring force acting between particles of surfaces; it is always perpendicular to the surface.
The normal force is real

Friction:

A Contact Force; Friction occurs when two surfaces are in contact. It is due to an interaction between surface particles of one object and surface particles of the second object. It opposes the sliding motion, or the attempted sliding motion of the two surfaces.
Air Friction (force of friction between an object and the air it is moving through) is called Drag.

Springs:

The sorts of springs you will be using can be compressed or extended. A compressed spring pushes back, an extended spring pulls. The restoring force of a spring is given by Hooke's Law : ${\vec {F}}_{spring}=-k{\vec {x}}$

Thrust:

The force associated with engines, driving an object such as a rocket forward.

Sometimes people talk about Applied Forces. Forces applied to an object can be classified under one of the above definitions.

Newton's Three Laws of Motion

Watch out for these misconceptions: We often test for whether you know these are incorrect!

Newton's First Law of Motion

"A body continues in a state of rest, or of uniform motion in a straight line, unless acted upon by an external force."

State of rest: The object has and keeps a zero velocity. = Static Equilibrium
Uniform motion: The object keeps a constant velocity (both magnitude and direction are constant).= Dynamic Equilibrium
No external force implies the net force (vector sum of forces) is zero:

$\Sigma {\vec {F}}={\vec {0}}$

We can rewrite the above Newton Law in a more meaningful way:
"If no net force acts on a body, the body's velocity cannot change; that is, the body cannot accelerate"

This means that Newton's first law is really a special case of the second law (see below).
Newton’s first law is based on the principle of inertia. The tendency of a body to resist a change in its state of motion is called inertia.

What Newton First Law story does this picture tell? Make sure you wear your seat belt.

Newton's Second Law of Motion

"The net force on a body is equal to the product of the body's mass and its acceleration or $\sum {\vec {F}}=m{\vec {a}}$"

Thus, the acceleration of a body is directly proportional to the net force acting on the body, and is inversely proportional to its mass.

Important Points about Newton's Second Law

1. Be careful: you will often hear Newton 2 quoted as F=ma. This is technically incorrect. It is the net force, resultant force, or sum of forces which results in acceleration $\sum {\vec {F}}$. The summation sign is important.
2. People sometimes say forces make things move. A common misconception is that the force is related to the velocity. Newton 2 states that the net force is related to the acceleration, that is to say the change in velocity.
3. Net force causes acceleration, not the other way around.
4. Newton 2 is still a vector equation. This means that the direction of the net force also gives the direction of the resultant acceleration.
5. Newton 2 gives the definition of the force unit: the Newton (N). $1\ Newton=1\ kg\times {\frac {m}{s^{2}}}=1\ {\frac {kgm}{s^{2}}}$
6. What is your definition of mass? You might say 'mass is how much matter you have'. A physicist, however, defines mass by how it accelerates given a certain net force. For example, a mass of 1 kg will accelerate with 1m/s/s with a net force of 1N.
   

This defines inertial mass. Why inertial mass is the same as gravitational mass, is still unexplained by physics. but remains a postulate of Einstein's General Relativity.

What is the difference between Mass and Weight?

Newton's Third Law of Motion

"When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction."
You will often see this written simply as:
"For every action there is an equal and opposite reaction."

However, the "When two bodies interact," part is very important. The action and reaction are always on different objects.
Forces always come in pairs, equal and opposite, acting on different objects.

Watch this video: The forces resulting from the interaction of the two players are always equal and opposite. What is different for the players is their masses, and therefore their accelerations. Note also that any object can have many different interactions, with many different objects, and that it is the net force on any particular object which determines its acceleration.
Action Reaction

In other words, if player $1$ applies a force on player $2$, then player $2$ applies an equal and opposite force on player $1$.
This could be written as:
${\vec {F_{12}}}=-{\vec {F_{21}}}$

• Focus on notation: The first subscript $1$ indicates the particle which exerts the force; the second subscript $2$ indicates the particle on which the force is exerted.

Watch the following video which describes Newton's third law as applied to the force of gravity. Keep your eye on the Speed Limit Sign in the background for a physics joke. Hint: c= speed of light.
Does the bigger object apply the bigger force?

The take home message is that in any force interaction, the forces are equal and opposite. However, the masses and accelerations can be different.
The force of the earth on you is equal to your weight. What is your gravitational force on the earth?

A common misconception

If you were asked "what is the reaction to your weight?", many students will say "it is the normal force".
Wrong!
Throw a ball out the window. It experiences a force of gravity, its weight (acting on the centre of mass of the ball). This is action of the earth on the ball. The reaction to this is the force of gravity from the ball on the earth. This reaction is equal to the ball's weight and could be said to be acting on the centre of mass of the earth.
The ball accelerates as it falls. What happens to the earth? The earth also experiences the force of gravity from the ball. It accelerates too, but because the mass of the earth is so much greater than that of the ball, the earth's acceleration is beyond miniscule.
For the ball sitting on the table, the weight interaction with the 'centre of the earth' is still there. But the ball also experiences a normal force from the table. This interaction comes from the atoms in the ball pushing on the table, and the atoms in the table reacting to this, pushing out from the table surface. This interaction is different from the force of gravity, and is a separate interaction.
The weight and normal force show up on the free body diagram of the ball, but they are the result of different action-reaction interactions with different objects.

Exercises

• [Applications Of Newton's Third Law]