eloquent logic - work & energy

Legend

W	=	work
F	=	force
d	=	distance
KE	=	kinetic energy
PE	=	potential energy
v	=	velocity
a	=	acceleration

Wind blows against the sails, exerting a force and driving the boat forward. The boat accelerates and its KE increases.

Kinetic Energy

Kinetic Energy:

This is the energy objects possess because they are moving; also known as translational kinetic energy.

KE = 1/2 mv²
^{Work results when there is a change in KE in object.}
^{Example: object changes in its speed}

Here, we'll derive the formula, KE = 1/2 mv²
W_net = KE = 1/2 mv_f² - 1/2 mv_i²

W = Fd

and

F = ma

so,

W= mad

And from what we derived in vector kinematics section:

V_f² = V_i² + 2ad

Hence,

ad = 1/2 v_f² - 1/2 v_i²

And multiplying both sides by m yields:

W_net = 1/2 mv_f² - 1/2 mv_i²

^{We
define the kinetic energy of any object of mass m traveling at speed v as:}

KE = 1/2 mv²

When a baseball is thrown, it's kinetic energy changes. The baseball increases in speed. The force exerted by the pitcher acts over a distance on the ball.

Work & Energy

Potential Energy