Newton's Laws of Motion

From a physicist's point of view, it is difficult to teach the natural laws of force and motion first made famous by Isaac Newton:

1. An object at rest tends to remain at rest, and an object in motion tends to remain in motion (in a straight line) until acted upon by an outside force. This is also known as the law of inertia.

2. A change in state (rest, or motion) is called acceleration a, which is proportional to the net force F_net applied to the object from outside:
   F_net = m a.

   The proportionality "constant" m is what physicists call mass.

3. For every action (a force applied to an object from the outside) there is always an equal-and-opposite reaction (the object pushes back on whatever pushed on it).

It is usually best to allow the student to experience and experiment first and to then formulate questions. The purpose of this Web page is to summarize some important facts related to Newton's Laws, and to provide some suggestions on how to try them out yourself.

• An example of where Newton's First Law applies is the rolling of a shopping cart. The cart will not move until it is pushed. Once it is moving, however, it does not keep moving in a straight line without help from you. You might think that violates the First Law, but all is well once you consider friction. Friction is an outside force that acts to slow down the shopping cart, and to keep the cart moving you have to provide a counteracting pushing force. If there were no friction, the cart would indeed keep moving forever once it is in motion, without any help from you.
• Newton's Second Law essentially defines mass: it is the numerical size of an object's inertia; that intrinsic property of matter which makes it resist being accelerated. The more mass an object has, the less acceleration it will have when pushed or pulled by a given size of force. The amount of mass is a measure also of the quantity of matter that makes up an object. The more mass (more matter) in an object, the harder it is to get it moving and the harder it is to stop it once it is moving. All matter has mass, down to the subatomic level; energy (light, for example) is not matter and so has no mass. A fully-loaded shopping cart will have very small acceleration when given a moderate push (neglecting the effects of friction) compared with an empty shopping cart, which will respond readily to the same push -- gathering speed quickly. And the fully-loaded shopping cart is a lot harder to stop, so it hurts you more when it bumps into you!

  Weight is another type of force that can be exerted on an object from the outside. Other forces besides weight and friction are: push, pull, and normal (support from beneath). Weight (a.k.a. gravity) is the force of attraction between two masses when they occupy the same region of space (Sun and Earth, Earth and your body). It is an observed fact that the attractive force of gravity between the Earth and an object is proportional to the object's mass:

  weight = m g

  where the proportionality constant g is called the acceleration of gravity, and is found to depend on location (distance between the object and the Earth's center). The weight of an object can be varied (move to a higher altitude or move to a different planet) but the mass of an object is fixed.

  To experiment with the difference between mass and weight, try this:

  1. Support a ball from underneath, holding it above the floor at rest. You are supplying a force (called normal force) equal and opposite to the weight force (gravity) pulling down on the ball.
  2. Throw the same ball sideways (parallel to the floor) at various speeds, and notice that there is pressure (force) between your hand and the ball in proportion to the acceleration that you give to it. You are now sensing the ball's mass, its quantity of inertia. The inertia would still be there even if gravity were to somehow switch off; force would be required to move an object with mass.

  Unfortunately for us teachers, there is a tendency for non-scientists to use the terms weight and mass interchangeably. The unit of mass is the gram or kilogram; scales that provide readings in those units when an object is layed on them are not really measuring mass: they are measuring force needed to support against an object's weight. But because mass and weight are proportional, the readout has been "fudged" to calculate the mass from the weight. It is incorrect for a person to say that he/she "weighs 50 kilo's" (kilograms). The unit of weight is the Dyne or Newton (in the British system: mass is in slugs and weight is in pounds).

• Newton's Third Law essentially means that all forces come in balanced pairs. It is not possible for an object to receive a force out of nowhere; all pushes or pulls arise from an interaction between at least two bodies pushing or pulling on each other with equal and opposite forces. Take gravity for example: the weight of an apple is actually one of a pair of forces, with the counterpart force being an equal upward pull by the apple on the Earth. If an apple were dropped, the result would be that both the apple and the Earth would feel forces, and both would be accelerated (the Earth rises up to meet the apple!!). Of course, the masses (inertias) of the apple and Earth are so different that their acceleration values are not comparable.
  
  In the shopping cart example, it is not possible for you to push the shopping cart forward without also feeling a backward push by the shopping cart on you (you feel your skin of your hands being pressed toward you, right?). Assuming there is lots of friction between your shoes and the floor, that backward force is actually being applied to you and the Earth collectively; so while the cart accelerates forward, you and the Earth accelerate backwards. Of course, the Earth's acceleration is not noticeable due to the mass differences.

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