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2.5 Chapter summary

2.5 Chapter summary (ESBM3)

Presentation: 23K5

  • The normal force, \(\vec{N}\), is the force exerted by a surface on an object in contact with it. The normal force is perpendicular to the surface.

  • Frictional force is the force that opposes the motion of an object in contact with a surface and it acts parallel to the surface the object is in contact with. The magnitude of friction is proportional to the normal force.

  • For every surface we can determine a constant factor, the coefficient of friction, that allows us to calculate what the frictional force would be if we know the magnitude of the normal force. We know that static friction and kinetic friction have different magnitudes so we have different coefficients for the two types of friction:

    • \(\mu_s\) is the coefficient of static friction
    • \(\mu_k\) is the coefficient of kinetic friction
  • The components of the force due to gravity, \(\vec{F}_g\), parallel (\(x\)-direction) and perpendicular (\(y\)-direction) to a slope are given by: \begin{align*} {F}_{gx} & = {F}_g\sin(\theta)\\ {F}_{gy} & = {F}_g\cos(\theta) \end{align*}

  • Newton's first law: An object continues in a state of rest or uniform motion (motion with a constant velocity) unless it is acted on by an unbalanced (net or resultant) force.

  • Newton's second law: If a resultant force acts on a body, it will cause the body to accelerate in the direction of the resultant force. The acceleration of the body will be directly proportional to the resultant force and inversely proportional to the mass of the body. The mathematical representation is:\[\vec{F}_{net} = m\vec{a}\]

  • Newton's third law: If body A exerts a force on body B, then body B exerts a force of equal magnitude on body A, but in the opposite direction.

  • Newton's law of universal gravitation: Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them.\[F=G\frac{m_1m_2}{d^2}\]

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Physical Quantities
Quantity Unit name Unit symbol
Acceleration (\(a\)) metres per second squared \(\text{m·s$^{-1}$}\)
Distance (\(d\)) metre \(\text{m}\)
Force (\(F\)) Newton \(\text{N}\)
Mass (\(m\)) kilogram \(\text{kg}\)
Tension (\(T\)) Newton \(\text{N}\)
Weight (\(N\)) Newton \(\text{N}\)

Table 2.1: Units used in Newtons laws