PHYS 1443 – Section 003 Lecture #7AnnouncementMaximum Range and HeightNewton’s First Law and Inertial FramesMassNewton’s Second Law of MotionExample for Newton’s 2nd Law of MotionSlide 8Gravitational Force and WeightNewton’s Third Law (Law of Action and Reaction)Example of Newton’s 3rd LawWednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu1PHYS 1443 – Section 003Lecture #7•Newton’s Laws of Motion–Newton’s 2nd Law of Motion–Newton’s 3rd Law of Motion–The Force of Gravity–Freebody Diagrams•FrictionWednesday, Sept. 17, 2003Dr. Jaehoon YuToday’s homework is homework #4, due noon, next Wednesday!!Remember the first term exam on Monday, Sept. 29!!Wednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu2Announcement•Almost all of you have done e-mail. We only have five people not on the list. –I will send out a test message this afternoon Please reply if you receive the message.–-2 points if not done by this Friday•Can I speak to:–Robyn Barber, Mark Helms & James Mann after the class?Wednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu3Maximum Range and Height•What are the conditions that give maximum height and range of a projectile motion?gvhii2sin22This formula tells us that the maximum height can be achieved when i=90o!!!gvRii2sin2This formula tells us that the maximum range can be achieved when 2i=90o, i.e., i=45o!!!Wednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu4Newton’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 on natural states of matter: Any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of retardation are removed!!Galileo’s statement is formulated by Newton into the 1st law 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.Wednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu5MassMass: A measure of the inertia of a body or quantity of matter1. Independent of the object’s surroundings: The same no matter where you go.2. Independent of method of measurement: The same no matter how you measure it.1221aammThe same forces applied to two different masses result in different acceleration depending on the mass.The heavier an object gets the bigger the inertia!!It is harder to make changes of motion of a heavier object than the lighter ones.Note that mass and weight of an object are two different quantities!!Weight of an object is the magnitude of gravitational force exerted on the object. Not an inherent property of an object!!! Weight will change if you measure on the Earth or on the moon.Wednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu6Newton’s Second Law of MotionamFiiThe acceleration of an object is directly proportional to the net force exerted on it and is inversely proportional to the object’s mass. How do we write the above statement in a mathematical expression?xiixmaF Since it’s a vector expression, each component should also satisfy:From the above vector expression, what do you conclude the dimension and unit of force are?]][[ am]][[]][[][2LTMamForceThe dimension of force is The unit of force in SI is For ease of use, we define a new derived unit called, a Newton (N) yiiymaF ziizmaF lbssmkgN41/112]][[2LTM2/ smkg Wednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu7Acceleration Example for Newton’s 2nd Law of MotionWhat constant net force is required to bring a 1500kg car to rest from a speed of 100km/h within a distance of 55m?This is a one dimensional motion. Which kinetic formula do we use to find acceleration?What are given?Thus, the force needed to stop the car isxF hkmvxi/100 ifxxixfxxavv 222What do we need to know to figure out the force?Acceleration!! Initial speed:sm /28Displacement:mxxxif55Final speed:smvxf/0 ifxixfxxxvva222 22/1.7552/28smmsm Nsmkgmax42101.1/1.71500 Given the force how long does it take to stop a car?xxixfifavvxxx222 xxixfmavvm222 xxixfFvvm222•Linearly proportional to the mass of the car•Squarely proportional to the speed of the car•Inversely proportional to the force by the brakeWednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu8Acceleration Vector aF2F1Example for Newton’s 2nd Law of MotionDetermine the magnitude and direction of acceleration of the puck whose mass is 0.30kg and is being pulled by two forces, F1 and F2, as shown in the picture, whose magnitudes of the forces are 8.0 N and 5.0 N, respectively.xF110220xFComponents of F1Components of F2Components of total force F2/293.07.8smmFaxxMagnitude and direction of acceleration ayF1xF2yF2yF2/173.02.5 smmFayy 222/341729 sma 302917tantan 11xyaa2/1729 smjijaiaayx NF 0.460cos0.8cos11o NF 9.660sin0.8sin11o NF 7.420cos0.5cos22o NF 7.120sin0.5sin22o NFFxx7.87.40.421 xma NFFyy2.57.19.621 ymaWednesday, Sept. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu9Gravitational Force and WeightSince 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, Fg amFGWeight of an object with mass M isMggMFWGBy measuring the forces one can
View Full Document
Unlocking...