6 Mass, Weight & Newton’s Second Law
Resources
Video to Watch: Mechanical Universe: Episode 6 – Newton’s Law
Article to Read: Mathematicians solve age-old spaghetti mystery
Article to Read: Longest overhaul of scientific units since the French Revolution wins approval
Equations Introduced and Used for this Topic: (All equations can be written and solved as both scalar and vector)
- [latex]F = ma[/latex]
- [latex]w = mg[/latex]
Where…
- [latex]F[/latex] is force, measured in newtons (N)
- [latex]w[/latex] is weight (it is a force), measured in newtons (N)
- [latex]m[/latex] is mass, commonly measured in kilograms (kg), grams (g) or tonnes (t)
- [latex]a[/latex] is acceleration (deceleration is negative), measured in metres per second squared (m/s2)
- [latex]g[/latex] or [latex]a_g[/latex] is the acceleration due to gravity and varies from 9.78 m/s2 (equator) to 9.83 m/s2 (North or South Pole). The average value of gravity is taken to be either 9.80 m/s2 or 9.81 m/s2
Newton’s Laws of Motion
- Extra Help: A-Level Physics Tutor
- Article to Read: kilogram, ampere, kelvin and mole redefined
- Extra Help: Newton’s Laws
- Extra Help: The Meaning of Force
- Video to Watch: Newton’s 3rd Law of Force – Forklift Driver Causes an Entire Warehouse to Fall like Dominos
Sir Isaac Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666, when he was only 23 years old. Some twenty years later, in 1686, he presented his three laws of motion in the “Principia Mathematica Philosophiae Naturalis.”
Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally accepted as the definition of inertia. The key point here is that if there is no net force acting on an object (if all the external forces cancel each other out) then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. If an external force is applied, the velocity will change because of the force.
Newton’s second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. Newton also developed the calculus of mathematics, and the “changes” expressed in the second law are most accurately defined in differential forms. (Calculus can also be used to determine the velocity and location variations experienced by an object subjected to an external force.) For an object with a constant mass [latex]m[/latex], the second law states that the force ([latex]F[/latex]) is the product of an object’s mass and its acceleration [latex]a[/latex]:
[latex]F = m a[/latex]
Newton’s third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal force o