Chapter 5EnergyForms of Energy Mechanical Focus for now May be kinetic (associated with motion) or potential (associated with position) Chemical Electromagnetic NuclearSome Energy Considerations Energy can be transformed from one form to another The total amount of energy in the Universe never changes Essential to the study of physics, chemistry, biology, geology, astronomy Can be used in place of Newton’s laws to solve certain problems more simplyWork Provides a link between force and energy The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacementWork W = F ∆x This equation applies when the force is in the same direction as the displacement F and ∆x are in the same directionWork General W = (F cos θ)∆x F is the magnitude of the force ∆x is the magnitude of the object’s displacement θ is the angle between F and ∆xWork, cont. This gives no information about The time it took for the displacement to occur The velocity or acceleration of the object Work is a scalar quantityUnits of Work SI Newton • meter = Joule N • m = J J = kg • m2/ s2 US Customary foot • pound ft • lb no special nameWork exampleWork is done by gravityW = (mg cosθ) dMore About Work The work done by a force is zero when the force is perpendicular to the displacement cos 90° = 0 If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each forceMore About Work, cont. Work can be positive or negative Positive if the force and the displacement are in the same direction Negative if the force and the displacement are in the opposite directionWhen Work is Zero Displacement is horizontal Force is vertical cos 90° = 0Work Can Be Positive or Negative Work is positive when lifting the box Work would be negative if lowering the box The force would still be upward, but the displacement would be downwardWork, Final Work doesn’t happen by itself Work is done by something in the environment, on the object of interest The forces are constant Varying force will be discussed laterPositive & Negative WorkW > 0, velocity increasesW < 0Velocity decreasesWork and Dissipative Forces Work can be done by friction The energy lost to friction by an object goes into heating both the object and its environment Some energy may be converted into sound For now, the phrase “Work done by friction” will denote the effect of the friction processes on mechanical energy alonevfrWfr= − fr ∆xExample - Work µs =0.2, µk=0.1, Wfr=?30o15 N1 kg2 mWfr= − fr ∆x = µkN ∆xN = mg – F sin30o= (1)(10) – 15(0.5) = 2.5 N Wfr= − (0.1)(2.5)(2) = − 0.5 JKinetic Energy Energy associated with the motion of an object Scalar quantity with the same units as work Work is related to kinetic energy2mv21KE =Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy Speed will increase if work is positive Speed will decrease if work is negativenet f iW KE KE KE= − = ∆Work and Kinetic Energy An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest The moving hammer has kinetic energy and can do work on the nailTypes of Forces There are two general kinds of forces Conservative Work and energy associated with the force can be recovered Nonconservative The forces are generally dissipative and work done against it cannot easily be recoveredConservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points The work depends only upon the initial and final positions of the object Any conservative force can have a potential energy function associated with itMore About Conservative Forces Examples of conservative forces include: Gravity Spring force Electromagnetic forces Potential energy is another way of looking at the work done by conservative forcesNonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. Examples of nonconservative forces Kinetic friction, air drag, propulsive forcesFriction Depends on the Path The blue path is shorter than the red path The work required is less on the blue path than on the red path Friction depends on the path and so is a non-conservative forcePotential Energy Potential energy is associated with the position of the object within some system Potential energy is a property of the system, not the object A system is a collection of objects interacting via forces or processes that are internal to the systemWork and Potential Energy For every conservative force a potential energy function can be found Evaluating the difference of the function at any two points in an object’s path gives the negative of the work done by the force between those two pointsGravitational Potential Energy Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth’s surface Objects interact with the earth through the gravitational force Actually the potential energy is for the earth-object systemWork and Gravitational Potential Energy PE = mgy Units of Potential Energy are the same as those of Work and Kinetic EnergyfigravityPEPEW−=Work-Energy Theorem, Extended The work-energy theorem can be extended to include potential energy: If other conservative forces are present, potential energy functions can be developed for them and their change in that potential energy added to the right side of the equation( ) ( )nc f i f iW KE KE PE PE= − + −Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen for each problem The choice is arbitrary since the change in the potential energy is the important quantity Choose a convenient location for the zero reference height Often the Earth’s surface May be some other point