PHYS 1441 – Section 501 Lecture #8Newton’s Law of Universal GravitationMore on Law of Universal GravitationWork Done by a Constant ForceExample of Work w/ Constant ForceKinetic Energy and Work-Kinetic Energy TheoremExample for Work-KE TheoremWork and Energy Involving Kinetic FrictionExample of Work Under FrictionWork and Kinetic EnergyPotential EnergyGravitational Potential EnergyExample for Potential EnergyElastic Potential EnergyConservative and Non-conservative ForcesMore Conservative and Non-conservative ForcesConservative Forces and Potential EnergyConservation of Mechanical EnergyExample for Mechanical Energy ConservationExample 6.8Work Done by Non-conservative ForcesExample for Non-Conservative ForceEnergy Diagram and the Equilibrium of a SystemGeneral Energy Conservation and Mass-Energy EquivalencePowerEnergy Loss in AutomobileLinear MomentumLinear Momentum and ForcesWednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu1PHYS 1441 – Section 501Lecture #8Monday, June 28, 2004Dr. Jaehoon Yu•Work done by a constant force•Kinetic Energy and Work-Energy theorem•Power•Potential Energies gravitational and elastic•Conservative Forces•Mechanical Energy ConservationWednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu2Newton’s Law of Universal GravitationPeople have been very curious about the stars in the sky, making observations for a long time. But the data people collected have not been explained until Newton has discovered the law of gravitation. Every object in the Universe attracts every other objects with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.How would you write this principle mathematically?21221rmmFg1110673.6GG is the universal gravitational constant, and its value isThis constant is not given by the theory but must be measured by experiment.With G21221rmmGFgUnit?22/ kgmN This form of forces is known as an inverse-square law, because the magnitude of the force is inversely proportional to the square of the distances between the objects.Wednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu3It means that the force exerted on the particle 2 by particle 1 is attractive force, pulling #2 toward #1.More on Law of Universal GravitationConsider two particles exerting gravitational forces to each other.Gravitational force is a field force: Forces act on object without physical contact between the objects at all times, independent of medium between them.1222112ˆrrmmGF The gravitational force exerted by a finite size, spherically symmetric mass distribution on a particle outside the distribution is the same as if the entire mass of the distributions was concentrated at the center.m1m2rF21F1212ˆrTwo objects exert gravitational force on each other following Newton’s 3rd law.Taking as the unit vector, we can write the force m2 experiences as12ˆrWhat do you think the negative sign mean?gFHow do you think the gravitational force on the surface of the earth look?2EERmMGWednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu4xyWork Done by a Constant ForceWork in physics is done only when the SUM of forces exerted on an object caused a motion to the object.MFFree Body DiagramMdgMFGNFFWhich force did the work?WForce FHow much work did it do?What does this mean?Physical work is done only by the component of the force along the movement of the object.Unit?N m�Work is energy transfer!!( )cosF d q�ur ur (for Joule)J=Wednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu5Example of Work w/ Constant ForceA man cleaning a floor pulls a vacuum cleaner with a force of magnitude F=50.0N at an angle of 30.0o with respect to East. Calculate the work done by the force on the vacuum cleaner as the vacuum cleaner is displaced by 3.00m to East.Does work depend on mass of the object being worked on?MF0MdWJW 13030cos00.30.50 Yes!Why don’t I see the mass term in the work at all then?It is reflected in the force. If the object has smaller mass, it would take less force to move it the same distance as the heavier object. So it would take less work. Which makes perfect sense, doesn’t it? cosdFWednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu6Kinetic Energy and Work-Kinetic Energy Theorem•Some problems are hard to solve using Newton’s second law–The forces exerting on the object during the motion are very complicated.–Relate the work done on the object by the net force to the change of the speed of the object.MFMdvivfSuppose net force F was exerted on an object for displacement d to increase its speed from vi to vf. The work on the object by the net force F isW = tvvdif 21aWDisplacement AccelerationWWork221mvKE Kinetic EnergyWorkThe work done by the net force caused change of object’s kinetic energy. dma tvvtvvmifif 21222121ifmvmv tvvif222121ifmvmvifKEKEKEcosFd q =( )cos 0ma d =( )ma dWednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu7Example for Work-KE TheoremA 6.0kg block initially at rest is pulled to East along a horizontal, frictionless surface by a constant horizontal force of 12N. Find the speed of the block after it has moved 3.0m.Work done by the force F isFrom the work-kinetic energy theorem, we knowW =Since initial speed is 0, the above equation becomes MFMdvi=0vfW =221fmvW fv =Solving the equation for vf, we obtain 2 21 12 2f imv mv-2Wm=2 363.5 /6.0m s�=cosF d q =ur ur( )12 3.0cos 0 36 J� =Wednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu8Work and Energy Involving Kinetic Friction•Some How do you think the work looks like if there is friction?–Why doesn’t static friction matter?MMdvivfFriction force Ffr works on the object to slow down The work on the object by the friction Ffr isfrW =The final kinetic energy of an object, taking into account its initial kinetic energy, friction force and other source of work, isFfrKED =fKE =t=0, KEiFrictionEngine workt=T, KEfBecause it isn’t there while the object is moving.( )cos 180frF d =frF d-frF d-iKEW+�frF d-Wednesday, Mar. 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu9Example of Work Under FrictionA 6.0kg block initially at rest is pulled to East along a horizontal surface with
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