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Physics Notebook of Ian Beardsley
F=ma M=mv v=x/t
F=Force M=momentum m=mass v=velocity x=distance t=time a=acceleration
M=mv=m(x/t) a=dv/dt a(dt)=dv v=at v=dx/dt dx/dt=at dx=at(dt) x=(1/2)at^2
…x=x_0+vt+(1/2)at^2
int[x^n] 0 to x =(x^(n+1))/(n-1) and (d/dx)x^n=nx^(n-1)
K=kinetic energy U=potential energy C=constant
K=(1/2)mv^2 U=mgy h=height
K+U=C mgh=mgy+(1/2)mv^2 or (1/2)m(v_0)^2=U+K where v_0=initial velocity
Work=W= and U=-W
Thus work is the distance traveled or moved by the component of the force in that direction, and potential energy is the
negative of the work. Use the definition for work and the chain rule for derivatives to show that kinetic energy (energy of
motion) is as given above. The chain rule is:
…dv/dt=(dv/dx)(dx/dt)
A ball rolling on an incline will stay in motion until it attains the same height on another incline facing the first,
even if the inclinations of the two inclines are not the same. If there is no second incline, the ball will never attain the
original height and will therefore continue to roll forever, unless otherwise acted on by a force, like friction. For every
force there is an equal but opposite reaction, for the action pushes in the opposite direction, and these forces, action and
reaction must be equal in magnitude, for to not split the energy in half between the energy of action and that of reaction
would not conserve energy.
Notice that:
mgh=(1/2)m(v_0)^2
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