Physics: Chapter 5 Notes PDF

Lecture PowerPoints Chapter 5 Physics: Principles with Applications, 6th edition Giancoli © 2005 Pearson Prentice Hall Th...

Lecture PowerPoints Chapter 5 Physics: Principles with Applications, 6th edition Giancoli © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.  Chapter 5 Circular Motion; Gravitation  Units of Chapter 5 Kinematics of Uniform Circular Motion Dynamics of Uniform Circular Motion Highway Curves, Banked and Unbanked Nonuniform Circular Motion Centrifugation Newton’s Law of Universal Gravitation  Units of Chapter 5 Gravity Near the Earth’s Surface; Geophysical Applications Satellites and “Weightlessness” Kepler’s Laws and Newton’s Synthesis Types of Forces in Nature 5-1 Kinematics of Uniform Circular Motion Uniform circular motion: motion in a circle of constant radius at Instantaneous velocity is always 5-1 Kinematics of Uniform Circular Motion To determine the direction of acceleration, examine the Change in Velocity (Δv) over a very small region of the circular path. More evident as the limit is taken 5-1 Kinematics of Uniform Circular Motion Looking at the change in velocity in the limit that the time interval becomes infinitesimally small, we see that (5-1) 5-1 Kinematics of Uniform Circular Motion This acceleration is called the centripetal, or radial, acceleration, and it points towards the center of the circle. 5-2 Dynamics of Uniform Circular Motion For an object to be in uniform circular motion, there must be a net force acting on it. We can see that the net force must be inward by thinking about a ball on a string: 5-2 Dynamics of Uniform Circular Motion We already know the acceleration, so can immediately write the force: (5-1)  5-2 Dynamics of Uniform Circular Motion There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome. If the centripetal force vanishes, the object flies off tangent to the circle. 5-2 Dynamics of Uniform Circular Motion When a car goes around a curve, there must be a net force towards the center of the circle. If the road is flat, that force is supplied by friction. 5-2 Dynamics of Uniform Circular Motion If the frictional force is insufficient, the car will tend to move more nearly in a straight line, as the skid marks show.  5-2 Dynamics of Uniform Circular Motion As long as the tires do not slip, the friction is static. If the tires do start to slip, the friction is kinetic, which is bad in two ways: 1. The kinetic frictional force is smaller than the static. 2. The static frictional force can point towards the center of the circle, but the kinetic frictional force opposes the direction of motion, making it very difficult to regain control of the car and continue around the curve.  5-2 EXAMPLE A 1200 kg car executes uniform circular motion around a track of radius 60m. If the car goes once around in 30 seconds, without slipping, determine the force of static friction on the car. Determine the maximum speed of the car, before it slips (skids out). (µs=0.32) Solution Solution (pt 2)  5-2 EXAMPLE In a 1901 circus performance, Allo “Dare Devil” Diavolo introduced the stunt of riding a bicycle in a loop- the-loop (Fig.). Assuming that the loop is a circle with radius R = 2.7 m, what is the least speed v Diavolo could have at the top of the loop to remain in contact with it there? SOLUTION 5-3 Highway Curves, Banked and Unbanked Banking the curve can help keep cars from skidding. In fact, for every banked curve, there is one speed where the entire centripetal force is supplied by the horizontal component of the normal force, and no friction is required. SOLUTION 5-4 Nonuniform Circular Motion If an object is moving in a circular path but at varying speeds, it must have a tangential component to its acceleration as well as the radial one.  Example A race car starts from rest & reaches a speed of 35 m/s in 11s while moving on a circular track of radius 500m. Assuming constant tangential acceleration, find: 1. Magnitude of the Tangential Acceleration 2. Radial Acceleration as the instant when v=15m/s 3. The magnitude of the Total Acceleration at that same instant. Solution  5-4 Nonuniform Circular Motion This concept can be used for an object moving along any curved path, as a small segment of the path will be approximately circular. 5-5 Centrifugation A centrifuge works by spinning very fast. This means there must be a very large centripetal force. The object at A would go in a straight line but for this force; as it is, it winds up at B.  Step inside the ground floor of a tall skyscraper and you “weigh” a little bit less …..how come? 5-6 Newton’s Law of Universal Gravitation 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.  5-6 Newton’s Law of Universal Gravitation The gravitational force on you is one-half of a Third Law pair: the Earth exerts a downward force on you, and you exert an upward force on the Earth. When there is such a disparity in masses, the reaction force is undetectable, but for bodies more equal in mass it can be significant.  5-6 Newton’s Law of Universal Gravitation Therefore, the gravitational force must be proportional to both masses. By observing planetary orbits, Newton also concluded that the gravitational force must decrease as the inverse of the square of the distance between the masses. In its final form, the Law of Universal Gravitation reads: (5-4) where 5-6 Newton’s Law of Universal Gravitation The magnitude of the gravitational constant G can be measured in the laboratory. This is the Cavendish experiment.  g VALID FOR POINT MASSES Our approximation –PROXIMITY – SYMMETRY  5-7 HOW DO YOU MASS THE EARTH? We can relate the gravitational constant to the local acceleration of gravity. We know that, on the surface of the Earth: Solving for g gives: (5-5) Now, measuring g and knowing the radius of the Earth, the mass of the Earth can be calculated: 5-7 Gravity Near the Earth’s Surface; Geophysical Applications The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.  Example Find the net force on a 1.5x106 kg asteroid that is positioned half way between the Earth and the moon. Then, find it’s acceleration. Mearth=5.98x1024kg Mmoon = 7.35x1022 kg Avg Dist E-to-M= 3.84x108 meters Solution  5-8 Satellites and “Weightlessness” 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.  5-8 Satellites and “Weightlessness” The satellite is kept in orbit by its speed – it is continually falling, but the Earth curves from underneath it.  5-8 Satellites and “Weightlessness” 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.  5-8 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:  Example: Orbital Motion A satellite of mass m orbits the earth (mass ME) at a height h above the earth’s surface. The radius of earth is given as RE. Determine the speed of the satellite in terms of m, ME, RE, & h.  Example: Orbital Motion The earth orbits once around the sun 365.25 days. Assuming a nearly circular orbit, determine the orbital speed (v) of the earth? Also determine earth’s centripetal acceleration (aR). M E  5.98E 24 kg M S  1.99E 30 kg E  S Distance  149.6E9 m 5-9 Kepler’s Laws and Newton's Synthesis Kepler’s laws describe planetary motion. 1. The orbit of each planet is an ellipse, with the Sun at one focus.  5-9 Kepler’s Laws and Newton's Synthesis 2. An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times.  5-9 Kepler’s Laws and Newton's Synthesis The ratio of the square of a planet’s orbital period is proportional to the cube of its mean distance from the Sun. 2 4 2 3 T  r GM star 5-9 Kepler’s Laws and Newton's Synthesis Kepler’s laws can be derived from Newton’s laws. Irregularities in planetary motion led to the discovery of Neptune, and irregularities in stellar motion have led to the discovery of many planets outside our Solar System.  5-10 Types of Forces in Nature Modern physics now recognizes four fundamental forces: 1. Gravity 2. Electromagnetism 3. Weak nuclear force (responsible for some types of radioactive decay) 4. Strong nuclear force (binds protons and neutrons together in the nucleus)  5-10 Types of Forces in Nature So, what about friction, the normal force, tension, and so on? Except for gravity, the forces we experience every day are due to electromagnetic forces acting at the atomic level.  REVIEW GIVENS: s Determine the Radius=R minimum speed Static Coefficient  = s required for the rider not to fall. Solution  Summary of Chapter 5 An object moving in a circle at constant speed is in uniform circular motion. It has a centripetal acceleration There is a centripetal force given by The centripetal force may be provided by friction, gravity, tension, the normal force, or others.  Summary of Chapter 5 Newton’s law of universal gravitation: Satellites are able to stay in Earth orbit because of their large tangential speed.