Physics Principles of Physics

Transcription

1 Physics Principles of Physics Lecture 9 Chapter 6 February 5, 008 Sung-Won Lee Sungwon.Lee@ttu.edu Announcement I Lecture note is on the web Handout (4(or 6) slides/page) *** Class attendance is strongly encouraged and will be taken randomly. Also it will be used for extra credits. No Homework next week Announcements II First Exam /10 Tuesday 9: 30 am 10:50 am Chapter 1-5 Announcement III SI session by Reginald Tuvilla SI sessions will be at the following times and location. Monday 4:30-6:00pm - Holden Hall 106 Thursday 4:00-5:30pm - Holden Hall 106 Exams - Overview There will be 3 in-class exams and a final exam (see class Schedule for dates). The exams are closed book. You may bring one hand-written 3 by 5 index card with formulae, etc. Telephones, pagers, PDAs, ipod, iphone and other gizmos are not allowed. Exam Tips Total 10 problems some are easy and some are difficult to solve, but don t worry too much. Pattern of many problems in the exam are quite similar to the H.W. & examples in the text book. Please read the text book (lecture note too) carefully and solved the examples by yourself before you take the exam. Small calculator is needed.

2 Chapter 6 The Major Player of Dynamics Isaac Newton Gravitation & Newton s Synthesis Develops Calculus to explain the theory of Mechanics and Gravitation From his general statements on motion he develops calculus and shows that 1. 1) Planets follow elliptical motion. Gravity Near the Earth s Surface; Geophysical Applications ) They sweep out equal areas in equal time (conservation of angular momentum) 3. Satellites and Weightlessness 4. Kepler s Laws and Newton s Synthesis 5. Types of Forces in Nature If the force of gravity is being exerted on objects on Earth, what is the origin of that force? Newton s realization was that the force must come from the Earth. He further realized that this force must be what keeps the Moon in its orbit. 3) From universal gravity he derives Kepler s 3rd law Newton proposed that every object in the universe attracts every other object with a force that has the following properties: 1. The force is inversely proportional to the distance between the objects.. The force is directly proportional to the product of the masses of the two objects. F1 on = F on 1 = G m1m r [Universal gravitational constant] F1 = -F1 Newton looked at proportionality of accelerations between the Moon and objects on the Earth i.e. F acceleration (1/distance) The forces form a Newton s 3rd-Law action-reaction pair. Gravitation is a field force that always exists between two particles, regardless of the medium b/w them. Centripetal Acceleration The Moon experiences a centripetal acceleration as it orbits the Earth The force decreases rapidly as distance increase; consequence of the inverse square law Always distinguish between G and g G = universal gravitational constant It is the same everywhere g = acceleration due to gravity g = 9.80 m/s at the surface of the Earth g will vary by location Moon s Acceleration G vs. g

3 The Motion of the Moon Newton guessed that the acceleration of the moon in its orbit had the same origin as acceleration of an apple on the surface of the earth. The difference in accelerations results from the distance dependence of the gravitational force The acceleration of the Moon in its (nearly) circular orbit at distance r M = 60 is (independent of its mass) 6-1 Example 6-1: Can you attract another person gravitationally? A 50-kg person and a 70-kg person are sitting on a bench close to each other (0.5m). Estimate the magnitude of the gravitational force each exerts on the other. a M = v r M = r M = 4" r M T =.7 # 10 $3 m / s Universal gravitation predicts a M = g( /r M ) = g/3600 =.7e-3 m/s Quiz (3 min) Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth s center is twice that of satellite A. What is the ratio of the centripetal force of B to that of A? Question Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth s center is twice that of satellite A. What is the ratio of the centripetal force of B to that of A? 1/8 1/4 1/ F B /F A Since the only force is the gravitational force, it must scale as the inverse square of their distances from the center of the Earth. F B F A = GmM E r B GmM E r A = r A r = 1 B 4 6- Vector Form of Newton s Universal Gravitation 6- Vector Form of Newton s Universal Gravitation In vector form, If there are many particles, the total force is the vector sum of the individual forces: This figure gives the directions of the displacement and force vectors.

4 Surface Gravity Near the Earth s surface, the distance to the center of the earth is roughly constant for heights h which is small compared to the radius of the earth: F g = G M E m Experimentally, this is just as observed: F g = mg = ma m a = g h = m G M $ E " # % & = g Example What is the force of gravity exerted by the earth on a typical physics student? Typical student mass m = 55kg g = 9.8 m/s. F g = mg = (55 kg)x(9.8 m/s ) F g = 539 N" g = G M E = 9.81 m / s M The force that gravity exerts on any object is its Weight W = 539 N Gravity on another planet Solution The gravitational force on a person " of mass m by another object (for instance a planet) having mass M is given by: F = G Mm R E " Ratio of of weights = = ratio ratio of of forces: = G M Xm R X G M E m W X W E = F X F E = M " X M E # $ R X % & ' W x /W E X W X " 1 % = 300 W E # $ 0& ' =.75 Finding g from G Variation of g with Height The magnitude of the force acting on an object of mass m in free fall near the Earth s surface is mg This can be set equal to the force of universal gravitation acting on the object g above the Earth s Surface If an object is some distance h above the Earth s surface, becomes + h This shows that g decreases with increasing altitude As r -> ", the weight of the object approaches zero The acceleration due to gravity varies over the Earth s surface due to altitude, local geology, and the shape of the Earth

5 Decrease of g with Distance g= FM on m GM = m r Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth s gravity altogether. Artificial satellites launched at different speeds. This minimum speed is called the escape speed Objects in orbit are said to experience weightlessness. They do have a gravitational force acting on them, though The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness. Satellites and Weightlessness More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly: Fig shows some examples of free fall or apparent weightlessness, experienced by people on Earth for brief moments. (a) An object in an elevator at rest exerts a force on a spring scale equal to its weight; F = w-mg = 0, w=mg (b) In an elevator accelerating upward at g, the object s apparent weight is 1 times larger than its true weight; F = w mg = ma, w = mg + ma, w=3/g, where a = g (a) In a freely falling (a=-g) elevator, the object experiences weightlessness : the scale reads zero; w = mg + ma = mg + m(-g) = 0