Unit 4 - Work, Energy, and Power

Definition of Work

• A scalar quantity that can be described as the product of a force and the distance through which it acts in the direction of the force.
• The SI unit of work is the joule (J)
• $$W_x = F_x * d_x$$
• From Wikipedia

Definition of Energy

• The kinetic energy of an object is the energy which it possesses due to its motion
• The SI unit of work is the joule (J)
• $$E_{kinetic} = \frac{1}{2}mv^2$$
• From Wikipedia

Definition of Potential Energy

• The potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system
• The SI unit of work is the joule (J)
• $$U_{gravity} = mgh$$

Conservation of Energy

• $$E_{final} = E_{initial} - E_{lost}$$
• Losses can be due to friction and the heat generated.

Definition of Power

• Power is the rate at which energy is transferred, used, or transformed
• The SI unit of power is the watt (W), which is equal to one joule per second
• $$P = \frac{W}{\Delta{t}}$$
• From Wikipedia

Friction and Energy Dissipated

• Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other
• From Wikipedia

General Equations of Force & Potential Energy

Dimension	Small Distances	Large Distances
Force	mg	$(G*M1*M2)/r^2$
Potential Energy	mgh	$(G*M1*M2)/r$

Conservative Force vs Force

• If we have a conservative force, then (PE-a + KE-a) = (PE-b + KE-b)
• PE + KE = Mechanical Energy
• Gravity is a conservative force as is a spring force.
• Friction is not a conservative force because it is dependent on the route taken.
• One route could be longer than another resulting in more frictional work.
• From MIT Professor Lewin
• Useful constants with General Gravity equation
• G constant = 6.674 * 10^-11
• Radius  of the earth = 6.4 * 10^6 meters
• Mass of the earth = 5.97 * 10^24 kilograms
• Also in another lecture by MIT Professor Lewin, he takes up the subject of Power and our ongoing "Energy Crisis".