Consider the following situations:

• You and a friend are sitting on chairs with rollers.  You both have your feet off the ground and with your feet you push against your friend's chair.  Your friend starts moving away from you and you start moving away from your friend.  You both are accelerating.  The direction of your acceleration is opposite to the direction of your friend's acceleration.
• You both stretch out your hands and you grab your friend and pull him towards you.  He accelerates towards you and you accelerate towards him.  Again you both are accelerating.

What is happening is a consequence of Newton's third law.

For every force that an object exerts on a second object, there is a force equal in magnitude but opposite in direction exerted by the second object on the first object.  Forces are the result of interactions.

You pull on me, I pull on you.  If no other forces are present, I will accelerate towards you.  My acceleration has the magnitude of the force divided by my mass.  You will accelerate towards me.  Your acceleration has the magnitude of the force divided by your mass. 

Question:

You push against the table, the table pushes against you.  You accelerate away from the table.  Why is the table not accelerating away from you?

• If the table is on rollers, it will accelerate away from you.  If the table is very massive, the magnitude of its acceleration will be much smaller than the magnitude of your acceleration.  If it is not on rollers, then the force of static friction is also acting on it, and the vector sum of the two forces is zero.

Standing on a very slippery surface or on a skateboard, you throw a heavy object away from you in a northerly direction.  To do this, you have to exert a force on the object in the northerly direction.  The object exerts a force on you, which has equal magnitude but points towards the south.  You accelerate southward.

Newton's third law is also called the law of action and reaction.  For every action force, there exists a reaction force, equal in magnitude and opposite in direction.  The objects interact.

The action and reaction force always act on different objects.
Two forces acting on the same object, even if they have the same magnitude and point in opposite direction, never form an action-reaction pair.

Problem:

An apple with a 0.2 kg mass sits on a table in equilibrium.
(a)  What forces act on it?  Provide their magnitude and direction.
(b)  What is the reaction force to each of the forces acting on the apple?
(c)  What are the action-reaction pairs?

Solution:

• Reasoning:
  (a)  The forces acting on the apple are its weight W = mg = 1.96 N pointing down and the normal force provided by the table F_N = 1.96 N pointing up.  The net force acting on the apple is zero.
  (b)  The reaction force to W is a force F_WR = 1.96 N pointing up acting on the center of the Earth.  (The earth is pulling on the apple and the apple is pulling on the earth.)
  The reaction to F_N is a force F_NR = 1.96 N pointing down acting on the table.  (The table is pushing up on the apple, the apple is pushing down on the table.)
  (c)  The action-reaction pairs are W − F_WR and N − F_NR.

Action-reaction pairs are forces of equal magnitude and opposite direction that act on different object.  They never act on the same object.

Newton's 3rd law tells us that forces are interactions.  An object cannot exert a force on another object without feeling a reaction force itself.  The reaction force has the same magnitude and points in the opposite direction as the force the object exerts on the other object.  What and object does as a result of being acted on by a reaction force depends not only on the reaction force but on the net force acting on the object.  The net force is the sum of the reaction force and all the other forces acting on the object.

Newton's 3rd law is simple, forces are interactions.
Newton's second law is complicated, F_net = ma, because you need to know all the forces, and you need to add them as vectors. Only then can you figure out if the object accelerates, and if yes, how much and in which direction.

Examples of action-reaction pairs:

• Gun pushes on bullet --- bullet pushes back on gun  (recoil)
• Player throws ball forward by exerting a force with hand on ball --- ball pushes back on hand
• Student pulls on desk --- desk pulls on student  (This is how you can "pull" yourself forward.)
• Earth pull on person (gravity) --- person pulls on Earth

Examples of forces that have equal magnitude and opposite direction but are NOT action-reaction pairs.

• Earth pulls object down against the floor --- normal force pushes person up and prevents person from sinking into the floor  (Both forces act on same object.)
• Person 1 is pushing object to the left --- person 2 is pushing object to the right, but object stays at rest  (Both forces act on same object.)
• Car moves with constant velocity.  Motor pulls car forward --- friction points in the backward direction  (Both forces act on same object.)

External link:  Physics of Football - Newton's Third Law of Motion - YouTube

Embedded Question 2

A device used since the 1940s to measure the kick or recoil of the body due to heart beats is the "ballistocardiograph".   What physics principle(s) are involved here to measure the force of cardiac contraction?  How might we construct such a device?

Discuss this with your fellow students in the discussion forum!

Embedded Question 3

Suppose that you are holding a cup of coffee in your hand. Identify all forces on the cup and the reaction to each force.

Discuss this with your fellow students in the discussion forum!

Tension and compression

Assume two opposing teams and an opposing team are pulling on a rope in opposite directions.  Is there a net force on the rope?

If the rope is accelerating in the direction of one of the teams, then there is a non-zero net force.  F = ma.  The net force is the vector sum of the force of gravity and the forces exerted by the two teams.
The opposing team, since the rope starts accelerating in their direction.

If the rope is not accelerating, even so each team is pulling as hard as it can then there is no net force acting on the rope.  However, there is tension in the rope.  Tension results from different forces acting on different parts of the body.  Tension can break things.  A pure force, i.e. the same force acting on all parts of the body, cannot break things.
If instead of pulling on the rope the two teams push on a heavy rock, but the rock does not move, then again the net force on the rock is zero.  However, now the rock is under compression.

The tension T is a scalar.  It is defined as the magnitude of the force with which the stretched rope pulls on whatever it is attached to.  This force is often denoted by T.  The direction of T depends on which end of the rope is being considered.

The net force acting on an object is always the vector sum of all forces acting on an object.  The object's acceleration is in the direction of this net force and has magnitude a = (net force/object's mass).

Tension happens with extended object.  Two forces act on the object at different points, pulling in opposite direction.  The net force is zero of the two forces have equal magnitudes.
Internal "contact forces keep the object from breaking apart, but the object is under tension.  It usually stretches a small amount, and if the tension becomes too large, it breaks.
Compression also happens with extended object.  Two forces act on the object at different points, pushing in opposite direction, squeezing the object.

Problem:

A 15-lb block rests on the floor.  (Note: lb is a unit of force, the weight of the block is 15 lb.)
(a)  What force does the floor exert on the block?
(b)  If a rope is tied to the block and run vertically over a pulley and the other end is attached to a free-hanging 10-lb weight, what is the force exerted by the floor on the 15-lb block?
(c)  If we replace the 10-lb weight in part (b) with a 20-lb weight, what is the force exerted by the floor on the 15-lb block?

Solution:

• Reasoning:
  (a)  The block is at rest the net force is zero.  The weight of the block is 15 lb downward.  The floor must therefore exert a force 15 lb upward.
  (b)  The block is still at rest.  The weight is 15 lb downward, the rope pulls with 10 lb upward due to the tension in the rope.  The floor must therefore exert a force 5 lb upward.
  (c)  The weight is 15 lb downward, the rope pulls with 20 lb upward due to the tension in the rope.  The block will accelerate upward, since the net force is upward.  The block is not pushing on the ground, and the ground is not pushing back.  The ground exerts zero force on the block.

Problem:

Two blocks, one sitting on a table and the other heavier one hanging over its edge, are connected by a light string as shown in the figure.   Which force makes the block on the table accelerate, the tension in the string or the weight of the hanging block?   Write down an expression for the acceleration a.

Solution:

• Reasoning:
  The blocks accelerate together, the acceleration a is the same for both blocks.
• Details of the calculation:
  (1) m₁g - T = m₁a
  (2) T = m₂a.  The tension in the string makes the block on the table accelerate.
  
  Insert (2) into (1).
  m₁g - m₂a = m₁a
  Solve for a.
  a = m₁g/(m₁ + m₂)