Newton's third law of motion

From Mech
Jump to: navigation, search
QUICK PHRASES: action and reaction are equal and opposite

Definition

Newton's third law or Newton's third law of motion gives a relationship between the forces that two bodies exert on each other. It says that if body A exerts a force on body B, then body B exerts a force on body A, and further, that the forces are equal in magnitude and opposite in direction.

An important corollary of this formulation is that every force on a body is exerted by something. In other words, it isn't possible for an object to feel a force that isn't being exerted by anything.

Particular cases

Force types

Type of force Pair of bodies Directions of the action-reaction pair Magnitude of the action-reaction pair
Gravitational force Two masses that exert a gravitational force on each other. In most earthly situations, one of the bodies is the earth. On each body, in the direction toward the center of mass of the other body. Thus the force acts inward on both bodies along the line joining the centers of mass of the two bodies Gm_1m_2/r^2 where G is the gravitational constant, m_1, m_2 are the masses and r is the distance between the centers of mass
Normal force Bodies that share a surface of contact. On each body, the force acts in the outward direction along the surface of contact. The magnitude is determined to be such that the net relative acceleration along the direction perpendicular to the surface of contact is zero. It thus adjusts in response to the other forces being exerted on the bodies.
Static friction Bodies that share a surface of contact. On each body, the force acts in a direction parallel to the surface of contact, opposing the tendency of slippage of surfaces. The magnitude is determined so that the net relative acceleration of surfaces along the surface of contact is zero. It thus adjusts in response to the other forces being exerted on the bodies. There is, however, an upper limit: the limiting coefficient of static friction times the normal force magnitude.
Kinetic friction Bodies that share a surface of contact. On each body, the force acts in a direction parallel to the surface of contact, opposing the actual direction of slippage of surfaces. The magnitude is a fixed multiple of the normal force, where the constant of proportionality is the coefficient of kinetic friction and is determined by the nature of the surfaces in contact.
Tension An inextensible string and a body attached to one end of the string The string pulls the body inward; the body pulls the string outward. Determined from other constraints.

Concrete examples

Situation Pair of bodies Action-reaction pair What does Newton's third law tell us?
Any object close to the surface of the earth the object and the earth The gravitational force exerted by the earth on the object, and the gravitational force exerted by the object on the earth The two forces are equal in magnitude and opposite in direction. In other words, the "downward" force experienced by the object due to gravity has a corresponding "upward" force experienced by the earth. However, due to the huge mass of the earth, the resultant acceleration of the earth is too negligible to be noticed.
A block resting on a fixed horizontal floor the block and the floor the upward normal force exerted by the table on the block and the downward normal force exerted by the block on the floor The two forces are equal in magnitude and opposite in direction. The normal force adjusts in magnitude to counteract other forces, in this case gravitational forces, so the block experiences no net acceleration and remains stable (by Newton's first law of motion). The floor does not accelerate downward either, presumably because whatever mechanism is fixing it is also generating forces that counteract the downward force exerted by the block.
The earth and the moon the earth and the moon The gravitational force exerted by the earth on the moon, and the gravitational force exerted by the moon on the earth. The two forces are equal in magnitude and opposite in direction. The effect on the moon -- the moon orbiting the earth -- is more visible because the moon has less mass. The effect on the earth -- including tides -- is less salient because of the larger mass of the earth.

Misconceptions

Misleading action-reaction formulation

The law is often stated as action and reaction are equal and opposite where "action" refers to one of the forces and "reaction" refers to the other force. However, this formulation is misleading because it suggests that one of the forces happens first and the other force happens in response to it. This is incorrect. The correct formulation is that both forces occur together and are a pair, called an "action-reaction pair." Any physical phenomenon that causes a force also causes the corresponding reaction force.

For instance, if I push a wall, the wall pushes me back. In terms of human intention, I might say that I was the "cause" of the pair of forces, so the force I exert is the "action" and the force exerted by the wall is the "reaction" force. However, as far as physics is concerned, the role of the two forces is completely symmetric.

Larger objects and larger forces

One of the common misconceptions surrounding Newton's third law is that the larger object must exert the larger force. There are two possible sources of this misconception:

  1. The force exerted by the larger force has more of an effect on the smaller object than the force exerted by the smaller object. This is due to Newton's second law of motion, which says that the magnitude of acceleration experienced due to a given force is inversely related to the mass.
  2. It is true that if a smaller object were replaced by a larger object in a given setting, the larger object would exert more force than the smaller object. For instance, the forces exerted in a head-on collision of a light car and a heavy truck are greater than the forces exerted in a head-on collision of two cars. Newton's third law, in contrast, is comparing the forces between two objects within a given situation, rather than comparing across situations.

Normal "reaction" forces

Another common misconception is that forces that arise to cancel the effects of other forces are examples of Newton's third law. For instance, if a block is placed on a horizontal table, the table exerts an upward normal force on the block to counteract the downward gravitational force on the block.

The normal force and gravitational force do not form an action-reaction pair and do not illustrate Newton's third law. The simplest way of seeing this is that both forces act on the same object. Rather, the fact that they balance each other is due to Newton's first law of motion, which causes the normal force to adjust in magnitude to cancel the downward force exerted due to gravity.

Similar comments apply to static friction forces that arise to counteract external forces that would create a tendency for slipping.