A Jar of Flies A bunch of flies are in a capped jar. You place the jar on a scale. The scale will register the most weight when the flies are a)   sitting on the bottom of the jar b)   flying around inside the jar c)   The weight of the jar is the same in both cases. Excerpted from Thinking Physics by Lewis Caroll Epstein Insight Press, 614 Vermont St., San Francisco, CA 94107-2636 www.appliedthought.com/InsightPress

The answer is: c. When the flies take off or land there might be a slight change in the weight of the jar, but if they just fly around inside a capped jar the weight of the jar is identical to the weight it would have if they sat on the bottom. The weight depends on the mass in the jar and that does not change. But how is a fly's weight transmitted to the bottom of the jar? By air currents, specifically, the downdraft generated by the fly's wings. But that downdraft of air must also come up again. Does the air current not exert the same force on the top of the capped jar as on the bottom? No. The air exerts more force on the bottom because it is going faster when it hits the bottom. What slows the air down before it hits the top? Friction. Without air friction the fly could not fly.

Newton’s Laws of Motion Free-Body Diagrams Normal, Tension and Friction Forces Newton’s Law of Universal Gravitation Weight

What is a force? Intuitively, we define force as a push or a pull. Physical contact is necessary for this to occur. Historically in physics, we also have non-contact or so-called action-at-a-distance forces. These are forces that act between objects with a distance separating the objects. Examples are gravity and electrical and magnetic forces. Physicists, including Newton, have always been uncomfortable with action-at-a-distance. The mechanism of force is not clear. The concept of an abstract field was classical physics solution to the question of action-at-a- distance. Modern physics’ solution is the concept of particle exchange (photons, mesons, gluons)

An Aside (theory?) The goal of modern physics (theoretical and experimental) is to try to develop a single theory for all forces observed in nature. In the last 50 years the effort has been to reduce into a single theory the four fundamental forces in nature -- electromagnetic force, strong nuclear force, weak nuclear force and the gravitational force. The “standard model” is the presently accepted theory for the strong nuclear force (QCD, quarks) and the electroweak force. The effort now is to combine gravity. The answer might by in the multidimensional (10 or 11 dimensions?) superstring theory where the fundamental particle is a string that mostly loop into itself except in 3 long range dimensions we observe.

What is mass? A measure of the amount of matter in an object. Mass that determines gravitational force is called gravitational mass. Mass that determines inertia or resistance to change in motion is called inertial mass. In classical physics, there is no fundamental reason why gravitational mass should be the same as inertial mass except for our choice of definitions of units. Most careful experiments show that they are equal. A postulate of special theory of relativity is the equivalence of gravitational and inertial mass, there is only one kind of mass. SI unit of mass is the kilogram (kg).

Newton’s First Law An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force. Question 1: The state of rest or motion can only be measured with respect to a frame of reference (and the coordinate system attached to it). In what frame of reference is Newton’s First Law valid or is it valid in all frames of reference? Question 2: Is force the same in all frames of reference?

Inertial Reference Frames Newton’s Laws are valid in “inertial” frames of reference. An inertial frame is one that moves with constant velocity relative to another inertial frame. An inertial frame is one that is not accelerated relative to another inertial frame. An inertial frame is one where Newton’s Laws are valid. “If an object, subject to no forces, does not move in a reference frame, that frame is inertial.” Isaac Newton: An inertial frame is one attached to the “fixed” or distant stars. Question: Is Newton’s Law an experimental law or simply a definition of force? This is a tough question.

Earth is an approximate inertial frame For motion that is localized and does not cover distances comparable to the size of the earth, the earth approximates an inertial frame. The earth is not really an inertial frame because it is rotating about its axis and revolving around the sun which is revolving around the Milky Way, etc., etc., etc. Rotating frames are accelerated. Fictitious forces such as centrifugal and Coriolis forces result from the non-inertial nature of the earth as a reference frame.

Newton’s Second Law When a net force SF acts on an object of mass m, the acceleration a that results is directly proportional to the net force and has a magnitude inversely proportional to the mass. The acceleration direction is the same as the direction of the net force. SI Unit of Force: kg·m/s2 = newton (N) In the “Imperial” or British-Engineering System or simply the fps system, force (weight) is a fundamental quantity defined by a standard object which has a weight of 1 pound where g=32.174 ft/s2. A mass of 1 slug is one that accelerates 1 ft/s2 when subjected to a 1 pound force.

Weight - Force on an object by the earth The proverbial apple falls with an acceleration g downward because of the attraction of the earth. This force of gravity is the weight of the object. What is the weight in terms of m and g? Neglecting air resistance, the only force on the falling apple is the weight. Therefore, by Newton’s Second Law

Newton’s Third Law Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body. Note that the two forces are acting on different bodies and do not cancel each other out. Newton’s Third Law is sometimes called the Law of Action and Reaction.

Example of Action and Reaction In outer space there are no great forces from other objects as an astronaut pushes off a spacecraft. The only forces acting are action and reaction forces between the astronaut and the spacecraft. The astronaut pushes on the spacecraft; the spacecraft exerts an equal magnitude but opposite direction force on the astronaut. Thus there is only one force on the spacecraft and only one force on the astronaut. They move in opposite directions due to these forces.

Universal Gravitation, Gravity Newton’s Law of Universal Gravitation expresses the force of attraction between any two masses in the universe. A point mass, m1 exerts an attractive force on a second point mass, m2 proportional to the product of the masses and inversely proportional to the square of the distance between them. The force acts along the line joining the two point masses. The proportionality constant is called the universal gravitational constant, G = 6.673 x 10-11 N-m2/kg2.

Weight Weight is the force of gravitational attraction exerted by the earth on other bodies. Weight is always downward (locally over a small ‘flat’ area) or looking at a large scale, towards the center of the earth. If mE = earth’s mass, m is the mass of an object on the earth’s surface and RE is the radius of the earth If we can indirectly “weigh” the earth by measuring its size.

Normal Force Normal force is the reaction force exerted by a surface on an object due to the force exerted by the object on the surface. It is called “normal” force because it is always normal or perpendicular to the surface. W Free-Body Diagram FN

Free-Body Diagram Free-Body Diagram - a diagram of an isolated object (all other objects removed) and all the forces acting on the “free” object. It is important that there be a complete accounting of all forces including their directions. Forces acting on other bodies are not included. We apply Newton’s Laws on the Free Body.

Example: Apparent Weight in an Accelerated Frame Assume a is upward. In case (a) a = 0. (b) a is positive. (c) a is negative. (d) a = -g.

Apparent Weight - Solution FBD - Person Newton’s Second Law (upwards is positive) a FBD - Scale Force exerted by person (Newton’s 3rd Law) Scale records the force FN exerted by the person standing on it. What is the value of FN for cases (a) to (d)? FN Weight of scale WS Normal force exerted by floor (FN)F

Tension Force Reaction force in a string, cord, rope, cable and similar objects when applied forces pull on it tending to stretch the string, cord, etc. Think of a spring being stretched; it will pull back against the stretching force. The resistance of the spring to stretching is the tension force. Tension forces are transmitted along the length of the cord to the opposite end and is always “pulling back” in. For massless rope, tension is the same everywhere on the rope whether it is accelerated or not.

Force of Friction Friction is a force between two surfaces in contact directed parallel to the surface. Friction is due to attraction between the atoms at the points of contact. Friction when surfaces are not sliding is called static friction. Friction when the surfaces are sliding relative to each other is called kinetic friction.

Static Friction W Occurs between two surfaces in contact that tend to slide because of other forces acting. Is directed parallel to the surface and opposite the direction of possible motion. Has a magnitude that can vary from zero to a maximum value. The actual magnitude is what is necessary to maintain equilibrium. µS is a dimensionless quantity called the coefficient of static friction. FN

Kinetic Friction Force of friction between sliding surfaces. Has a constant magnitude that does not depend on the velocity of sliding. Has a magnitude less than the maximum static friction force. mk is a dimensionless quantity called the coefficient of kinetic friction. Its value is less than ms Both static and kinetic friction do not depend on the total surface area but only on the coefficient and the normal force. You would think that friction should depend on area. Actually it does but the critical area is the area of microscopic contact sites. The dependence on the normal force and coefficient is a macroscopic description of this dependence.

Relevant Sample Problems to be done in the next lecture - Applications of Newton’s Laws