Newton’s laws of motion - University of North Florida



Newton’s laws of motion

THEORY

Isaac Newton formulated his three laws of motion in the 1600’s. These form the foundation for understanding motion in the everyday world. Two new concepts appear: force and mass.

Definitions

( Force ( a push or a pull, measured in units called Newtons.

( Mass ( the amount of resistance to acceleration (inertia) a body offers

Alternatively, mass is a measure of the amount of matter a body contains.

Mass has units of kilograms.

Here are the three laws of motion,

Law of inertia: Law One

I.

A particle moves in a straight line with constant speed if no net force acts on it. That is,

Σ F = 0 ( v = constant.

Most famous equation in physics: Law Two

If a net force acts on a particle of mass m then the particle accelerates,

Σ F = Fnet = m a.

Law of action-reaction: Law Three

If particle two exerts a force on particle one, F12 , then particle one exerts a force on particle two, F21. These forces are equal in magnitude but opposite in direction,

F12 = -F21 .

Comments

( We will expend a considerable amount of time getting to understand these laws since they are the heart of classical mechanics. Much about these laws is counter-intuitive, only because we live in a region of space where gravity exists and therefore, friction is important.

( What does ΣF mean?

This is the (vector) sum of all of the forces that on the particle in question.

To do this sum it is very important to be clear about what you are calling the system under study.

( The laws imply the effect of a force is to cause acceleration.

Some important forces

( Weight

One of the most important forces we will encounter is weight. The weight of a particle is the force on the particle by the earth. If weight is the only force then according to Newton’s second law,

FW = m g.

We have made use of the fact that (near earth and neglecting friction) all bodies have an acceleration of magnitude, g.

( Elastic force

Another important force is the elastic force a spring exerts on a particle attached to it,

Fel = -kx (Hooke’s Law)

Here k is a measure of the stiffness of the spring called the spring constant and x gives the distance from equilibrium, the stretch or compression.

( Friction

Finally, the importance of the frictional force will be addressed. When a body is at rest it can experience static friction, if the body is moving across a surface the friction is called kinetic friction. If both cases the friction is proportional to the “normal” force acting on the body by the surface it is placed on. The laws of friction will be presented in class.

APPLICATIONS

In class we will take up a number of applications of these laws:

mass on an inclined plane

pulling on a mass with a rope (tension)

masses attached to each other over a pulley (Atwood’s machine)

elevator problem

A general scheme of solving such problems will now be introduced, what I call THE NEWTON’S LAW RECIPE:

|Step One |

|Define the system and draw the free-body diagram for the system, possibly using Newton’s third law. |

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|Step Two |

|Choose a coordinate system and resolve the force vectors along the coordinate axes. |

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|Step Three |

|Use Newton’s second law in component form to obtain the equations of motion and then solve the equations for the |

|unknowns in terms of the knowns. |

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|As in all physics problems, make sure the units work out and as the final step, make sure your final answer seems |

|reasonable. |

Examples [in class]

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