Wednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu11. Motion in two dimension• Maximum ranges and heights– Reference Frames and relative motion2. Newton’s Laws of Motion •Force•Mass• Newton’s Law of Inertia• Newton’s second law of motion• Newton’s third law of motionPHYS 1443 – Section 003Lecture #7Wednesday, Sept. 15, 2004Dr. Jaehoon YuToday’s Homework is #5, due 1pm next Wednesday Sept. 22!!Wednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu2Announcements• Quiz #2 Next Monday, Sept. 20– Will cover Chapters 1 – 4.6• e-mail distribution list: 37/47 of you have subscribed so far. – -3 points extra credit if not registered by midnight tonight– A test message will be sent Thursday for verification purpose• Please be sure to reply only to ME!!!• Remember the 1stterm exam, Monday, Sept. 27, two weeks from today– Covers up to chapter 6.– No make-up exams• Miss an exam without pre-approval or a good reason: Your grade is F.– Mixture of multiple choice and free style problemsWednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu3Maximum Range and Height• What are the conditions that give maximum height and range of a projectile motion?⎟⎟⎠⎞⎜⎜⎝⎛=gvhii2sin22θThis formula tells us that the maximum height can be achieved when θi=90o!!!⎟⎟⎠⎞⎜⎜⎝⎛=gvRiiθ2sin2This formula tells us that the maximum range can be achieved when 2θi=90o, i.e., θi=45o!!!Wednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu4Example for a Projectile Motion• A stone was thrown upward from the top of a cliff at an angle of 37oto horizontal with initial speed of 65.0m/s. If the height of the cliff is 125.0m, how long is it before the stone hits the ground? xivfy=278.2 250gt t−−=()80.92)250(80.942.782.782×−××−−±=tstst 4.10or 43.2=−=st 4.10=yivSince negative time does not exist.cosivιθ=65.0 cos37 51.9 /ms=× =Dsiniivθ=65.0 sin37 39.1 /ms=× =D125.0−=212yivtgt−29.80 78.2 250 0tt−−=BecomesWednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu5Example cont’d• What is the speed of the stone just before it hits the ground? yfv =v ===xixfvv• What are the maximum height and the maximum range of the stone? Do these yourselves at home for fun!!!siniivgtθ−=cosivιθ=yivgt−=22xf yfvv+=()2251.9 62.8 81.5 /ms+− =39.1 9.80 10.4 62.8 /ms−×=−65.0 cos37 51.9 /ms×=DWednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu6Observations in Different Reference FramesResults of Physical measurements in different reference frames could be differentObservations of the same motion in a stationary frame would be different than the ones made in the frame moving together with the moving object.Consider that you are driving a car. To you, the objects in the car do not move while to the person outside the car they are moving in the same speed and direction as your car is.OFrame Sr’O’Frame S’The position vector r’ is still r’ in the moving frame S’.no matter how much time has passed!!v0The position vector r is no longer r in the stationary frame S when time t has passed.tvrtr0')( +=v0trHow are these position vectors related to each other?Wednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu7Relative Velocity and AccelerationThe velocity and acceleration in two different frames of references can be denoted, using the formula in the previous slide:OFrame Sr’O’Frame S’v0v0tr'r=GGalilean transformation equation What does this tell you?The accelerations measured in two frames are the same when the frames move at a constant velocity with respect to each other!!!The earth’s gravitational acceleration is the same in a frame moving at a constant velocity wrt the earth.'drdt=G'v=G'dvdt=G0' , when is constantaa v=GG G0drvdt−GG0vv−GG0dv dvdt dt−GG0rvt−GGWednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu8ForceWe’ve been learning kinematics; describing motion without understanding what the cause of the motion is. Now we are going to learn dynamics!!Can someone tell me what FORCE is?FORCE is what cause an object to move.FORCEs are what cause any change in the velocity of an object!! The above statement is not entirely correct. Why?Because when an object is moving with a constant velocity no force is exerted on the object!!!What does this statement mean?When there is force, there is change of velocity. Force causes acceleration.What happens there are several forces being exerted on an object?Forces are vector quantities, so vector sum of all forces, the NET FORCE, determines the direction of the acceleration of the object.F1F2NET FORCE, F= F1+F2When net force on an object is 0, it has constant velocity and is at its equilibrium!!Wednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu9More ForceThere are various classes of forcesContact Forces: Forces exerted by physical contact of objectsExamples of Contact Forces: Baseball hit by a bat, Car collisionsField Forces: Forces exerted without physical contact of objectsExamples of Field Forces: Gravitational Force, Electro-magnetic forceWhat are possible ways to measure strength of Force?A calibrated spring whose length changes linearly with the force exerted .Forces are vector quantities, so addition of multiple forces must be done following the rules of vector additions.Wednesday, Sept. 15, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu10Newton’s First Law and Inertial FramesAristotle (384-322BC): A natural state of a body is rest. Thus force is required to move an object. To move faster, ones needs higher force.Galileo’s statement is formulated by Newton into the 1stlaw of motion (Law of Inertia):In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity. A frame of reference that is moving at constant velocity is called an Inertial FrameWhat does this statement tell us? • When no force is exerted on an object, the acceleration of the object is 0. • Any isolated object, the object that do not interact with its surrounding, is either at rest or moving at a constant velocity.• Objects would like to keep its current state of motion, as long as there is no force that interferes with the motion. This tendency is called the Inertia.Galileo’s statement on natural states of matter: Any velocity once imparted to a moving body will be rigidly maintained as long as the
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