Wednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 1 PHYS 1441 – Section 002 Lecture #13 Wednesday, Oct. 20, 2010 Dr. Jaehoon Yu • Motion in Resistive Force • Work done by a constant force • Scalar Product of the Vector • Work with friction • Work-Kinetic Energy Theorem • Potential EnergyAnnouncements • 2nd non-comprehensive term exam – Date: Wednesday, Nov. 3 – Time: 1 – 2:20pm in class – Covers: CH3.5 – what we finish Monday, Nov. 1 • Physics faculty research expo today Wednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 2Wednesday, Oct. 20, 2010 3 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuWednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu Reminder: Special Project • Using the fact that g=9.80m/s2 on the Earth’s surface, find the average density of the Earth. – Use the following information only • The gravitational constant • The radius of the Earth • 20 point extra credit • Due: Wednesday, Oct. 27 • You must show your OWN, detailed work to obtain any credit!! G = 6.67 × 10−11N ⋅ m2kg2 RE= 6.37 × 103km4Wednesday, Oct. 20, 2010 Motion in Resistive Forces Medium can exert resistive forces on an object moving through it due to viscosity or other types frictional properties of the medium. These forces are exerted on moving objects in opposite direction of the movement. Some examples? These forces are proportional to such factors as speed. They almost always increase with increasing speed. Two different cases of proportionality: 1. Forces linearly proportional to speed: Slowly moving or very small objects 2. Forces proportional to square of speed: Large objects w/ reasonable speed Air resistance, viscous force of liquid, etc PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 5Wednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 6 x y Work Done by a Constant Force A meaningful work in physics is done only when the net forces exerted on an object changes the energy of the object. M F θ"Free Body Diagram M d θ"Which force did the work? Force How much work did it do? What does this mean? Physically meaningful work is done only by the component of the force along the movement of the object. Unit? Work is an energy transfer!! F∑( )⋅ d=Why? What kind? ScalarLet’s think about the meaning of work! • A person is holding a grocery bag and walking at a constant velocity. • Is he doing any work ON the bag? – No – Why not? – Because the force he exerts on the bag, Fp, is perpendicular to the displacement!! – This means that he is not adding any energy to the bag. • So what does this mean? – In order for a force to perform any meaningful work, the energy of the object the force exerts on must change!! • What happened to the person? – He spends his energy just to keep the bag up but did not perform any work on the bag. Wednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 7Wednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 8 Work done by a constant force = F cosθ( )s F ⋅sWednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 9 Scalar Product of Two Vectors • Product of magnitude of the two vectors and the cosine of the angle between them A⋅ B≡• Operation is commutative A⋅ B= ABcosθ=• Operation follows the distribution law of multiplication A⋅ B• How does scalar product look in terms of components? A= Axi∧+ Ayj∧+ Azk∧ B= Bxi∧+ Byj∧+ Bzk∧ A⋅ B= Axi∧+ Ayj∧+ Azk∧⎛⎝⎜⎞⎠⎟⋅ Bxi∧+ Byj∧+ Bzk∧⎛⎝⎜⎞⎠⎟• Scalar products of Unit Vectors A⋅ B= ABcosθ BAcosθ= B⋅ A A⋅ B+ C( )==0 + A⋅ CWednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 10 Example of Work by Scalar Product A particle moving on the xy plane undergoes a displacement d=(2.0i+3.0j)m as a constant force F=(5.0i+2.0j) N acts on the particle. a) Calculate the magnitude of the displacement and that of the force. d= F=b) Calculate the work done by the force F. Y X d F Can you do this using the magnitudes and the angle between d and F? F⋅ d= F⋅ d= FdcosθWednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 11 Ex. Pulling A Suitcase-on-Wheel Find the work done by a 45.0N force in pulling the suitcase in the figure at an angle 50.0o for a distance s=75.0m. Does work depend on mass of the object being worked on? = 45.0 ⋅ cos50( )⋅ 75.0 = 2170JYes Why don’t I see the mass term in the work at all then? It is reflected in the force. If an object has smaller mass, it would take less force to move it at the same acceleration than a heavier object. So it would take less work. Which makes perfect sense, doesn’t it? F∑( )⋅ d= F∑( )cosθdWednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 12 Ex. 6.1 Work done on a crate A person pulls a 50kg crate 40m along a horizontal floor by a constant force Fp=100N, which acts at a 37o angle as shown in the figure. The floor is rough and exerts a friction force Ffr=50N. Determine (a) the work done by each force and (b) the net work done on the crate. What are the forces exerting on the crate? WG=FG=-mg So the net work on the crate Wnet=Work done on the crate by FG Fp Ffr Which force performs the work on the crate? Fp Ffr Wp=Work done on the crate by Fp: Work done on the crate by Ffr: Wfr=This is the same as Wnet= FG⋅x = −mg cos −90( )⋅x = 0J Fp⋅x = Fpcos37⋅x = 100 ⋅ cos37⋅ 40 = 3200J Ffr⋅x = Ffrcos180⋅x = 50 ⋅ cos180⋅ 40 = −2000J WG+ Wp+ Wfr= 0 + 0 + 3200 − 2000 = 1200 J( ) F ⋅x( )∑= ( ) FG⋅x + Fp⋅x + Ffr⋅xFN=+mg WN= FN⋅x = mg cos 90⋅x = 100 ⋅ cos 90⋅ 40 = 0JWork done on the crate byFN WN+ FN⋅x +Wednesday, Oct. 20, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 13 Ex. Bench Pressing and The Concept of Negative Work A weight lifter is bench-pressing a barbell whose weight is 710N a distance of 0.65m above his chest. Then he
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