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NEWTON’S LAWS OF MOTION
First Law: The Law of Inertia. When all external influences on a particle are removed, the particle moves with constant velocity. [This velocity may be zero in which case the particle remains at rest.]
Second Law: The Law of Acceleration. When a force F acts on a particle of mass m , the particle moves with instantaneous acceleration a given by the formula
where the unit of force is implied by the units of mass and acceleration.
Third Law: The Law of Interaction. When two particles exert forces upon each other, these forces are (i) equal in magnitude, (ii) opposite in direction, and (iii) parallel to the straight line joining the two particles.
Definition of Terms:
Inertia – is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion (including a change in direction).
Inertial Reference Frame – is a frame of reference that describes time and space homogeneously (uniform in structure), isotropically (uniform in all directions), and in a time-independent manner. The reference frame where Newton’s Laws of Motion are valid is the inertial reference frame.
Mass – is a scalar property of a physical system or body, giving rise to (i) the phenomena of the body's resistance to being accelerated by a force – inertial mass; and (ii) the strength of its mutual gravitational attraction with other bodies – gravitational mass. Instruments such as mass balances or scales use those phenomena to measure mass. The SI unit of mass is the kilogram (kg).
Force – is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or a flexible object to deform, or both. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
UNITS
Any consistent system of units can be used. The standard scientific units are SI units in which the unit of mass is the kilogram , the unit of length is the meter , and the unit of time is the second. The unit of force implied by the Second Law is called the newton , and written N. In the Imperial system of units, the unit of mass is the pound, the unit of length is the foot, and the unit of time is the second. The unit of force implied by the Second Law is called the poundal. These units are still used in some industries in the US, a fact which causes frequent confusion.
Classification of forces I. Field Forces
- Weight or Gravitational Force, W or FG – is a force that attracts the body directly toward a nearby astronomical body; in everyday circumstances, that astronomical body is the earth. The force is primarily due to an attraction, called gravitational attraction, between the astronomical body and any object nearby. 𝐖 = m𝐠
where g is the acceleration due to gravity.
- Electromagnetic Force (or Lorentz Force) – is the force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B , then it will experience a force
𝐅 = 𝑞(𝐄 + 𝐯 × 𝐁).
- Strong Nuclear Force – is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). The strong force is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves. The (aptly named) strong interaction is the "strongest" of the four fundamental forces. 4. Weak Nuclear Force – is due to the exchange of the heavy W and Z bosons. Its most familiar effect is beta decay (of neutrons in atomic nuclei) and the associated radioactivity. The word "weak" derives from the fact that the field strength is some 1013 times less than that of the strong force. Still, it is stronger than gravity over short distances.
II. Contact Forces – reactionary forces (in the atomic domain, it is mostly result of electromagnetic interaction)
- Normal Force , N or FN – is due to repulsive forces of interaction between atoms at close contact. When their electron clouds overlap, Pauli repulsion (due to fermionic nature of electrons) follows resulting in the force which acts in a direction normal to the surface interface between two objects. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever
This yields both the tangential force which accelerates the object by either slowing it down or speeding it up and the radial (centripetal) force which changes its direction.
- Spring Force or Elastic Force , Fs – acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If Δ x is the displacement, the force exerted by an ideal spring equals: 𝑭 = −𝑘∆𝑥⃑ where k is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to the applied load.
Fictitious Force ( Pseudo force, phantom force, d’Alembert force or inertial force )
- Centrifugal force – is the apparent force that draws a rotating body away from the center of rotation. It is caused by the inertia of the body as the body's path is continually redirected. It acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame.
- Coriolis force – acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame.
- Euler force (azimuthal force or traverse force) – is the fictitious tangential force that is felt as a result of any radial acceleration.
APPLICATION OF NEWTON’S SECOND LAW OF MOTION
Newton’s Second Law relates the forces acting on an object to its acceleration. Kinematics is often used to relate an object’s acceleration to its changing velocity and position.
Problem-Solving Strategy
The following procedure is recommended when dealing with problems involving the application of Newton’s Second Law: Draw a simple, neat diagram of the system. Isolate the object of interest (represent it by a point) and draw the forces acting on the object in the free body diagram (FBD). FBD is a diagram showing all external forces acting on the object. Do not include forces exerted by the object on its surrounding. For systems containing more than one object, draw separate FBD for each object. Establish convenient coordinate axes for each object and find the component of the forces along these axes. Solve for the unknowns. You must have as many independent equations as the number of unknowns.
SAMPLE PROBLEMS
- A 7.0 kg body and 5.0 kg body are suspended at the end of the cord that passes over a mass less, friction less pulley as shown on the right. a.) What is the acceleration of the system? b.) What is the tension in the chord?
- An unbalanced force of 50 N acts on an object weighing 100 N. What acceleration is produced?
- A constant horizontal force of 40 N acts on a body on a smooth horizontal surface. The body starts from rest and is observed to move 100 m in 5 s a.) What is the mass of the body? b.) If the force ceases to act at the end 5s, how far will the body move in the next 5 s?
- An elevator with a mass of 2000 kg rises with an acceleration of 1 m/s^2. What is the tension in the supporting cable?
- A 100 g mass lies on a frictionless table and a cord is attached to one end as shown. The cord passes over a mass less, frictionless pulley at the edge of the table while a 10 g mass hangs at the other end. Find a.) The acceleration, and b.) The tension in the cord.
- Two inclined planes are arranged as shown. The two bodies, 8N and 10N are tied at the ends of a cord that passes over a massless, frictionless pulley. Find a) The acceleration of the system, and b) The tension in the cord.
- A traffic light, weighing 100N, hangs from a cable tied to two other cable fastened to a support as shown in the figure on the right. Find the tension in the three cables.
- A block slides down a smooth plane having an inclination of 15°. If the block starts from the rest at the top and the length of the incline is 2m, find a) The acceleration of the block b) Its speed when it reaches the bottom of the inclined plane
- A box weighing 100N starts to move across a horizontal surface when a horizontal force of 25N is applied to it, but a force of only 20N is needed to keep it moving in uniform motion. a) What are the coefficients of static and kinetic friction? b) If the force is not applied horizontally but in a direction 30^0 above the horizontal, find the force applied for static and kinetic cases.
