Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 1 PHYS 1441 – Section 001 Lecture #11 Monday, June 23, 2014 Dr. Jaehoon Yu Newton’s Law of Universal Gravitation Weightlessness Work done by a constant force Multiplication of Vectors Work-Kinetic Energy Theorem

Announcements Term exam #2 –In class this Wednesday, June 25 –Non-comprehensive exam –Covers CH 4.7 to what we finish tomorrow, Tuesday, June 24 –Bring your calculator but DO NOT input formula into it! Your phones or portable computers are NOT allowed as a replacement! –You can prepare a one 8.5x11.5 sheet (front and back) of handwritten formulae and values of constants for the exam  no solutions, derivations or definitions! No additional formulae or values of constants will be provided! Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 2

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Newton’s Law of Universal Gravitation People have been very curious about the stars in the sky, making observations for a long~ time. The data people collected, however, have not been explained until Newton has discovered the law of gravitation. Every object in the Universe attracts every other object 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 law mathematically? G is the universal gravitational constant, and its value is This constant is not given by the theory but must be measured by experiments. With G Unit? This form of forces is known as the inverse-square law, because the magnitude of the force is inversely proportional to the square of the distances between the objects. 3

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Ex. Gravitational Attraction What is the magnitude of the gravitational force that acts on each particle in the figure, assuming m 1 =12kg, m 2 =25kg, and r=1.2m? 4

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Why does the Moon orbit the Earth? 5

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Gravitational Force and Weight Since weight depends on the magnitude of gravitational acceleration, g, it varies depending on geographical location. The attractive force exerted on an object by the Earth Gravitational Force, FgFg Weight of an object with mass M is By measuring the forces one can determine masses. This is why you can measure mass using the spring scale. What is the SI unit of weight? N 6

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Gravitational Acceleration What is the SI unit of g? m/s 2 Gravitational acceleration at distance r from the center of the earth! 7

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Gravitational force on the surface of the earth: Magnitude of the gravitational acceleration on the surface of the Earth 8

Monday, June 23, 2014 Example for Universal Gravitation Using the fact that g=9.80m/s 2 on the Earth’s surface, find the average density of the Earth. Since the gravitational acceleration is Therefore the density of the Earth is Solving for MEME Solving for g PHYS , Summer 2014 Dr. Jaehoon Yu 9

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu There is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius. Satellite in Circular Orbits What acts as the centripetal force? The gravitational force of the earth pulling the satellite! 10

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Determine the speed of the Hubble Space Telescope orbiting at a height of 598 km above the earth’s surface. Ex. Orbital Speed of the Hubble Space Telescope 11

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Period of a Satellite in an Orbit Speed of a satellite Period of a satellite Square either side and solve for T2 This is applicable to any satellite or even for planets and moons. Kepler’s 3 rd Law 12

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu Geo-synchronous Satellites What period should these satellites have? Satellite TV Global Positioning System (GPS) The same as the earth!! 24 hours 13

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu In each case, what is the weight recorded by the scale? Ex. Apparent Weightlessness and Free Fall

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu At what speed must the surface of the space station move so that the astronaut experiences a push on his feet equal to his weight on earth? The radius is 1700 m. Ex. Artificial Gravity 15

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 16 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  Free Body Diagram M d  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!! Why? What kind?Scalar

Let’s think about the meaning of work! A person is holding a grocery bag and walking at a constant velocity. Are his hands doing any work ON the bag? –No –Why not? –Because the force hands exert on the bag, Fp,Fp, is perpendicular to the displacement!! –This means that hands are 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 due to that force!! What happened to the person? –He spends his energy just to keep the bag up but did not perform any work on the bag. Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 17

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 18 Work done by a constant force s

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 19 Scalar Product of Two Vectors Product of magnitude of the two vectors and the cosine of the angle between them Operation is commutative Operation follows the distribution law of multiplication How does scalar product look in terms of components? Scalar products of Unit Vectors =0

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 20 Example of Work by Scalar Product A particle moving on the xy plane undergoes a displacement d =(2.0 i +3.0 j )m as a constant force F =(5.0 i +2.0 j ) N acts on the particle. a) Calculate the magnitude of the displacement and that of the force. 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?

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 21 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 50.0 o for a distance s=75.0m. Does work depend on mass of the object being worked on?Yes 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?

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 22 Ex. 6.1 Work done on a crate A person pulls a 50kg crate 40m along a horizontal floor by a constant force F p =100N, which acts at a 37 o angle as shown in the figure. The floor is rough and exerts a friction force F fr =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? F G =-mg So the net work on the crate Work done on the crate by FGFG FpFp F fr Which force performs the work on the crate? FpFp F fr Work done on the crate by Fp:Fp: Work done on the crate by F fr : This is the same as F N =+mg Work done on the crate by FNFN

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 23 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 lowers it the same distance. The weight is raised and lowered at a constant velocity. Determine the work in the two cases. What is the angle between the force and the displacement? What does the negative work mean? The gravitational force does the work on the weight lifter!

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 24 The truck is accelerating at a rate of m/s 2. The mass of the crate is 120-kg and it does not slip. The magnitude of the displacement is 65 m. What is the total work done on the crate by all of the forces acting on it? Ex. Accelerating a Crate What are the forces acting in this motion? Gravitational force on the crate, weight, W or F g Normal force force on the crate, F N Static frictional force on the crate, f s

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 25 Ex. Continued… Lets figure out what the work done by each of the forces in this motion is. Work done by the gravitational force on the crate, W or F g Work done by Normal force force on the crate, F N Work done by the static frictional force on the crate, f s Which force did the work? Static frictional force on the crate, f s How? By holding on to the crate so that it moves with the truck!

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 26 Kinetic Energy and Work-Kinetic Energy Theorem Some problems are hard to solve using Newton’s second law –If forces exerting on an object during the motion are complicated –Relate the work done on the object by the net force to the change of the speed of the object M ΣF M s vivi vfvf Suppose net force ΣF ΣF was exerted on an object for displacement d to increase its speed from vi vi to vf.vf. The work on the object by the net force ΣF ΣF is Using the kinematic equation of motion Work Kinetic Energy Work done by the net force causes change in the object’s kinetic energy. Work-Kinetic Energy Theorem

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 27 When a net external force by the jet engine does work on an object, the kinetic energy of the object changes according to Work-Kinetic Energy Theorem

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 28 The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If a 56.0-mN force acts on the probe parallel through a displacement of 2.42×10 9 m, what is its final speed? Ex. Deep Space 1 Solve for v f

Monday, June 23, 2014PHYS , Summer 2014 Dr. Jaehoon Yu 29 A satellite is moving about the earth in a circular orbit and an elliptical orbit. For these two orbits, determine whether the kinetic energy of the satellite changes during the motion. Ex. Satellite Motion and Work By the Gravity For a circular orbit For an elliptical orbit No change!Why not? Gravitational force is the only external force but it is perpendicular to the displacement. So no work. Changes!Why? Gravitational force is the only external force but its angle with respect to the displacement varies. So it performs work.