College Physics I: BIIG problem-solving method

Created Feb. 7, 2024 by C N Hiremath

Mechanics

  • The study of motion is kinematics, but kinematics only describes the way objects move, their velocity and their acceleration. It describes how something moves.
  • Dynamics considers the forces that affect the motion of moving objects and systems. It describes why something moves (the cause of motion).
  • Dynamics joins with kinematics to form mechanics. It is the general science of motion.

 

Modern Era

  • Newton’s laws of motion are the foundation of dynamics. These provide the principles under which nature functions. They are also universal laws in that they apply to similar situations on Earth as well as the space.
  • Issac Newton (1642-1727):  The development of Newton’s laws marks the transition from the Renaissance into the modern era.

 

Importance of Observation

  • The importance of observation and the concept of cause and effect were not always so entrenched in human thinking. This realization was a part of the evolution of modern physics from natural philosophy.
  • The achievements of Galileo, Newton, Einstein, and others were key milestones in the history of scientific thought.

 

History

  • Aristotle 384-322 BC concluded that the natural state of an earthly object is to be at rest.

Many natural philosophers proposed the nature of universe based largely on certain rules of logic.

  • Galileo: The natural state of an object, its behavior if free of external influences, is uniform motion with constant velocity. On frictionless surface, the motion continues forever! Limited to motion along horizontal surfaces!! He was instrumental in establishing observation as the absolute determinant of truth.  He discovered moons orbiting Jupiter and was punished!

 

Newton’s First Law of Motion : Inertia

  • A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force.

 

Mass

  • The property of a body to remain at rest or to remain in motion with constant velocity is called inertia.  Newton’s first law is often called the law of inertia.
  • The inertia of an object is measured by its mass.
  • Mass is a measure of the amount of matter in something.
  • Mass of an object is determined by the numbers of atoms and molecules of various types it contains.
  • Mass does not vary with location. It is measured in kilogram (kg).

 

Force

  • Force is a push or a pull. It has both magnitude and direction. Therefore, it is a vector quantity.
  • Forces can be added using vector addition or by trigonometric methods.

 

Free-body Diagram

  • Free-body diagram is used to illustrate all the external forces acting on a body.
  • The body is represented by a single point (or free body), and only those forces acting on the body from the outside are shown.

 

Newton’s Second Law of Motion

  • The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

a  =  Fnet  / m

This is often written in the more familiar form

Fnet   =  m a

  • The SI unit of force is called the newton(N) and is the force needed to accelerate a 1-kg system at the rate of 1m/s2.

1 N  =  1 kg ⋅ m/s2

  • Unit conversion:          1 N  = 0.225 lb
  • Problem (E4.1):  Suppose that the net external force (push minus friction) exerted on a lawn mower is 51 N parallel to the ground. The mass of the mower is 24 kg. What is its acceleration?       (2.1  kg m/s2 ) 

 

Weight

  • Weight is the gravitational force on a mass m.

w  =  m g

where, w is the downward force of gravity, and g is the acceleration of an object due to gravity.

  • Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g.
  • The acceleration due to gravity g varies slightly over the surface of Earth, so that the weight of an object depends on location and is not an intrinsic property of the object.
  • Problem (E4.2):  The rocket sleds, used for testing physiological effects, consisted of a platform that was mounted on one or two rails and propelled by several rockets. Calculate the magnitude of force exerted by each rocket, called its thrust T, for the four-rocket propulsion system. The sled’s initial acceleration is 49 m/s2, the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N.                                                                                             ( 26000 N ) 

 

Newton’s Third Law of Motion

  • Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.
  • Symmetry in nature forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law as “action-reaction,” where the force exerted is the action and the force experienced as a consequence is the reaction.
  • Newton’s third law has practical uses in analyzing the origin of forces and understanding which forces are external to a system.

 

Normal Force

  • If the force supporting a load is perpendicular to the surface of contact between the load and its support, this force is defined to be a normal force and here is given the symbol N.
  • This is not the unit for force N. The word normal means perpendicular to a surface.

 

Tension

  • A tension is a force along the length of a medium, especially a force carried by a flexible medium,

such as a rope or cable.

 

Real forces and Fictitious Forces

  • Real forces are those that have some physical origin, such as the gravitational pull.
  • Fictitious forces are those that arise simply because an observer is in an accelerating frame of reference.

 

Inertial frames

  • An inertial frame of reference is one in which all forces are real and, equivalently, one in which Newton’s laws have the simple forms.
  • The crucial factor in determining whether a frame of reference is inertial is whether it accelerates or rotates relative to a known inertial frame.

 

Applying Newton’s Second Law

  • If the acceleration is zero in a particular direction, then the net force is zero in that direction.

Fnet  =  0

  • Similarly, if the acceleration is nonzero in a particular direction, then the net force is

Fnet  =  m a 

 

Drag force

  • Drag force is a frictional force exerted by fluids, such as air or water.
  • The drag force opposes the motion of the object.
  • Problem (E4.7):  Suppose two tugboats push on a barge at different angles. The first tugboat exerts a force of 2.7×105 N in the x-direction, and the second tugboat exerts a force of 3.6×105 N in the y-direction.  If the mass of the barge is 5.0×106 kg and its acceleration is observed to be 7.5×10−2 m/s2, what is the drag force of the water on the barge resisting the motion?                    ( 75000 N ;  53º SW )  

 

The Four Basic Forces

  • The four basic forces are: the gravitational force, the electromagnetic force, the weak nuclear force, and the strong nuclear force.
  • In fact, nearly all of the forces we experience directly are due to only one basic force, called the electromagnetic force.
  • The gravitational force is the only force we experience directly that is not electromagnetic.
  • On a macroscopic scale, electromagnetism and gravity are the basis for all forces.
  • The nuclear forces are vital to the substructure of matter, but they are not directly experienced on the macroscopic scale.


BIIG: Problems & Solutions


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