MCAT Physics - Work and Energy

Energy

a system’s ability to do work or to make something happen; different forms have the capacity to perform differenet actions

Kinetic energy (KE)

energy of motion; associated with mass and speed

= ½mv²

joule (J)

SI unit of energy; equivalent to kg*m²/s²

Potential energy (U/V/PE)

energy that is associated with a given object;s position in space or other intrinsic qualities of the system

gravitational potential energy

depends on an object’s position with respect to the datum

PE = mgh (where h is relative to datum)

datum

ground or zero potential energy position

elastic potential energy

energy in a spring when stretched or compressed from equilibrium length

PE = ½kx² (k is the spring constant, x is the displacement)

spring constant (k)

a measure of the stiffness of the spring

Total mechanical energy (E)

the sum of an object’s potential and kinetic energies

E = KE + PE

first law of thermodynamics

energy is never created or destroyed, can only change forms; conservation

Conservative forces

path independent and that do not dissipate energy, associated with potential energies; If the change in energy around any round-trip path is zero—or if the change in energy is equal despite taking any path between two points—then the force is conservative.

ΔE = ΔPE + ΔKE = 0

e.g. gravitational, electrostatic

nonconservative forces

total mechanical energy is not conserved; transformed into another form of energy that is not accounted for in the equation; path dependent

W_{nonconservative} = ΔE = ΔU + ΔK

e.g. friction, air resistance, viscous drag

work

a process by which energy is transferred from one system to another; a measure of energy transfer

mechanical work

W = F·d = Fd cos θ

piston-cylinder

a cylinder filled with ideal gas has a piston that can control/change the pressure/volume of the container

P-V graphs

graphs that illustrate gas compression/expansion with volume on the x-axis and pressure on the y-axis; work is the area enclosed

isovolumetric/isochoric process

if volume stays constant as pressure changes, no work is done because there is no area to calculate

isobaric process

if pressure remains constant as volume changes, then the area under the curve is a rectangle of length P and width ΔV

W = PΔV

Power (P)

the rate at which energy is transferred from one system to another

P = W/t = ΔE/t

watt (W)

Si unit for power, equivalent to J/s

work-energy theorem

the net work done by forces acting on an object will result in an equal change in the object’s kinetic energy

W_net = ΔKE = KE_f – KE_i

mechanical advanatge

a measure of the increase in force accomplished by using a tool the ratio of magnitudes of the force exerted on an object by a simple machine to the force actually applied on the simple machine

MA = F_out/F_in

dimensionless

simple machines

designed to provide mechanical advantage

inclined plane, wedge, wheel and axle, lever, pulley, screw

inclined plane

make it easier to lift objects because they distribute the required work over a larger distance, decreasing the required force

pulley

a wheel on an axle or shaft enabling a taut cable or belt passing over the wheel to move and change direction, or transfer power between itself and a shaft

If the distance through which the displacement is achieved is greater than the displacement (an indirect path), then the applied force will be less than mg.

more = more mechanical advantage (decrease stension, divides effoet along more distance)

load

weight needed to be lifted

effort

force input

load distance

the height a load needs to be lifted too

effort distance

the displacement of the input force to reduce effort needed

efficiency

ability to conserve energy output to input; a measure of the amount of useful work generated by the machine for a given amount of work put into the system

Eff = W_out/W_in = (load)(load distance)/(effort)(effort distance) * 100%