02 Dynamics

Force and mass

• The great genius Issac Newton postulated the existence of something called “Force” (a vector) and “mass” (a scalar) - to describe the differing effects of the same effort on different objects. He said: let us say that all objects have “mass” - with lighter objects having lower mass. Then, F/m = a. Or F = ma. Aka Newton’s second law of motion.
  • A corollary: In the absence of a force, there is no acceleration and no change in velocity. This is Newton’s first law of motion.
  • Momentum vector := mv. Then force is rate of change of momentum.
• Net force acting on a body can be determined by adding the incident forces just like any other vector. Likewise, one can decompose a force as a sum of forces along various dimensions.

Reaction force

• To explain rebounds and such, Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. Forces thus always occur in pairs.
• This results in the “conservation of momentum” in a closed system. Total of momentum of all bodies in a system remains constant (as internal forces and changes in momentum cancel each other out).

Curved motion

Net force acting on an object in a curved path can be divided up into two perpendicular components - tangential to the path (aka centrifugal force), and one perpendicular to the path (aka centripetal force).

Centripetal force = $F_c=m{a}_c=m{v}^2/r$ ($a_c$ was derived separately in kinepatics page.)

Work

Work $w={\int }_a^{b}fds$. When work is done to a body, energy is said to be transferred to the body.

Kinetic energy change

$w={\int }_{t_a}^{t_b}mavdt={\int }_u^{v}mvdv={\displaystyle \frac{m(v^2-u^2)}{2}}$.

This ${\displaystyle \frac{m{v}^2}{2}}$ value is taken to be the final “kinetic energy”, after the work was applied. The initial kinetic energy is taken to be ${\displaystyle \frac{m{u}^2}{2}}$

Potential energy change

Potential energy change = change in capacity to do work. Example: Work done in lifting an object of mass m for distance s against force F results in change in potential energy $Fs=mas$.

energy, power. The law of conservation of energy.

Potential and keinetic energy. Heat. Escape velocity.