WORKPOWER

ENERGY& MOMENTUM

WORK What do you think of when you hear the

word “work”? WORK happens when a FORCE moves

an object through a DISTANCE. W = F * d Work is measured in Newton meters

(Nm) or Joules (J) Work is a scalar quantity

Force

Distance

F and d have to be parallel to each other – if a force is perpendicular to a distance then that force is not the cause of the work done

WORK - CONTINUED

WORK - CONTINUED Forces exterted at an angle: Only the vector component parallel to the distance

moved does the work

Since work is (F)(d) and one force we deal with is Fg (force of gravity) and Fg = mg then

W could = (mg)d

F

Fx

W = F cos Θ d

WORK PROBLEM

500 N

4 m

8 m

To get the 500 N block to the top takes the same amount of WORK whether you lift straight up or push it up the ramp.

The FORCE to lift anything is its WEIGHT Fg = mgW = Force x distanceLifting Work = (500 N) (4m) = 2000 Nm or 2000J

Slide up ramp work = F x d (up the ramp) 2000 J = F (8m)

F = 250 N

I doubled the distance so the force is halved

SIMPLE MACHINES An inclined plane is a simple machine. Simple machines allow us to do the

same amount of work with less force (effort)

Simple machines include: Inclined planesLeversScrewsWedgePulleyWheel & axle

POWER Power = rate that work is done

P = work/time (J/s)= Watt (W) A 100 Watt light bulb puts out 100 J of

NRG per sec 1 horsepower = 746 Watts 1kW = 1000 W P = work/time = (Fd)/t or Fv Force might be Fg which = mg so P =

(mgd)/t

ENERGY Energy is the ability to do work Forms of energy:

Solar, electrical, mechanical, thermal, chemical, nuclear, hydroelectric, light, sound, wind, potential, kinetic, electromagnetic, etc.

Chemistry – focused on thermal, chemical and nuclear energy

Physics – 1st semester focuses on mechanical, kinetic, and potential energy – 2nd semester will focus on electrical, magnetic, thermal, sound, and light energy

TYPES OF ENERGY Mechanical Energy:

Energy which is possessed by an object due to its motion or its stored energy

ME = KE + PE As a car rolls down a hill it loses PE and gains KE

Kinetic Energy: Energy of a moving object

KE = ½ mv2

KE and mass are directly related if mass is doubled, KE doubles

KE and v2 are exponentially related If v2 doubles, KE quadruples If v2 triples, KE x 9

TYPES OF ENERGY - CONTINUED Potential Energy

energy of position, shape, or formPosition example: an object at the top of a

hill or cliff or table that has the potential to fall from a height

Shape example: a spring has (stored) potential energy to snap back into shape

Form example: a rubber band, a snap bracelet, a bow to shoot an arrow

TYPES OF ENERGY - CONTINUED Gravitational Potential Energy (GPE)

potential (stored) energy due to a location relative to a reference level.

Assume reference is found or floor unless otherwise stated.

GPE = Mass x acceleration due to gravity x height above or below reference GPE = mgh

TYPES OF ENERGY - CONTINUED Elastic Potential Energy (EPE)

Potential energy of an elastic object that is stretched or compressed

The spring or rubber band or bow string has to be able to go back to its original shape and size

EPE = ½ x spring constant (stiffness) x distance stretched (ls - lr)2

EPE = ½ kd2 (NM or J)

CONSERVATION OF ENERGY Law of Conservation of Energy – energy

cannot be created nor destroyed, only changed in form

In other words, numerically, total energy will remain constant.

Mechanical energy = sum of kinetic and potential energiesME = KE + GPE + EPEConservation of energy

Etop (GPE = 75 J, KE =0) = Ebottom (GPE =0, KE = 75 J)

GPEt + KEt = GPEb + KEb

CONSERVATION OF ENERGY Pendulum

GPE max

KE = 0

Loses GPEGains KE

HalfwayGPE =

KE

GPE max

KE = 0

CONSERVATION OF ENERGY Roller Coaster – starts high so we have

lots of PE GPE = mgh

V=0 KE=0GPEmax = 100J

Losing GPE because h is lowerIf GPE = 60JThen KE = 40J

Gaining KEV increasing

GPE = 0JKE = 100J

GPE = 50JKE = 50J

WORK-ENERGY THEOREM If you do WORK on an object, you

change its (kinetic and potential) energy.Work = Δ E

If I lift books from the deskDo I do work?Was there a force applied in the direction of

an object’s movement?Did I change the GPE (gravitational

potential energy) of the book? The KE (kinetic energy)?

WORK-ENERGY THEOREM FORMULAS If work = change in KE

Fd = KEf – KEi

Fd = ½ mv2f – ½ mv2

i

If work = change in GPE Fd = mghf – mghi

Fd = mgΔh

If work = change in EPEFd = ½ kd2

f – ½ kd2i

MOMENTUM AND IMPULSE MOMENTUM is the product of the mass

of an object times its velocityp = mv

Momentum is a vector quantity – its direction is the same as its velocity

The IMPULSE given to an object is the product of the time and the average of force which acts upon an object. I = Ft = Δp = Δmvm1v1 + m2v2 = m1v1

’ + m2v2’

NEWTON’S 2ND LAW & IMPULSE In the simple case of constant

acceleration from rest and a constant time (tf – ti)a = F/mv = a(tf – ti ) = [F (tf – ti)]/mp = mv = F (tf – ti)

An impulse produces a change in momentum that is equal to the impulse in magnitude and in direction

The standard (SI) unit of momentum is 1 kg·m/s

CONSERVATION OF MOMENTUM The total momentum (vector sum) of a

system of massive objects changes only if an outside force acts on the system

Internal forces between the objects can redistribute the total momentum but cannot change the total

Total momentum is represented with a capital P

Calculation of total momentum:P = p1 + p2 + … + pN

Pf – Pi = Fext(tf – ti)

COLLISIONS Before, during, and after a collision

between two or more massive objects that move free from friction or other external forces, the sum of their momenta is constant.

2- and 3-dimentional collisions can be analyzed in the same way as 1-dimentional collisions.