* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 5 PHYSICS 201 PHYSICS 201 (sections 521-525) ( )
Survey
Document related concepts
Lunar theory wikipedia , lookup
Electromagnetism wikipedia , lookup
Introduction to general relativity wikipedia , lookup
Mechanics of planar particle motion wikipedia , lookup
Equivalence principle wikipedia , lookup
Coriolis force wikipedia , lookup
Lorentz force wikipedia , lookup
Fictitious force wikipedia , lookup
Artificial gravity wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Centrifugal force wikipedia , lookup
Centripetal force wikipedia , lookup
Transcript
Lecture 5 PHYSICS 201 ((sections 521-525)) Instructor: Hans Schuessler e po a y Alexandre e a d e Kolomenski oo e s Temporary: http://sibor.physics.tamu.edu/teaching/phys201/ Projectile j Motion The horizontal and vertical parts of the motion behave p independently This iis why Thi h vectors t with ith th their i x and dy components is a convenient way of description! We will ill use se the same approach for dynamic problems as well! Ball Dropping • Analyze Vertical and Horizontal separately!!! • ay = g (downwards) (d d ) • ax = 0 – Constant for Both directions!!! Vx = 0 Vx>0 A weird consequence Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically! Main laws of dynamics: Newton’s laws •Discovered and formulated several fundamental laws of physics. •Created related fields of mathematics. Isaac Newton (1642-1727) Chapter 4: Newton’s Newton s Laws Force • First of all what is force? • How many forces can act on a body? • Is it a scalar or a vector? Mass • What is mass? Resistance to the force? • “Resistance” • Vector or scalar? Before we start What is a Force? Vector quantity, that can initiate a motion. • Examples: E l – Push – Pull – Slap – Gravity – Others? Examples • Example of non-zero net forces? – Friction: Causing a moving block to come to rest – ((Net force causes acceleration in the negative direction) – Gravity: making a ball fall • Example off zero net force f – Car just sitting on the pavement • No N acceleration, l ti mustt be b no nett force f – Spaceship in outer space • Nothing to slow it down down… constant velocity Newton’ss First Law Newton “A body acted on by a zero net force moves with constant velocity (which may be zero) zero), i.e. it moves with zero acceleration” In other words… Without a Force there is no change in the state of the motion => an acceleration is zero and the velocity is constant But this holds only in special reference frames (systems of coordinates) : inertial systems (to a good approximation the one related to Earth IS such a system) For instance,, in rotating g reference systems y this statement is not valid Force is a Vector! When several forces, need d to t add dd up allll th the fforces ((vectors) t ) to t find fi d the Net (or total) force. Example: inertial and non inertial frames of reference Newton’ss Second Law Newton “If If a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The acceleration is directly proportional to the net force and inversely proportional to the mass of the body.” a F m In other words... To cause an acceleration ( h (change velocity) l it ) requires i a Force An alternative formulation of the 2nd Newton Newton’ss law: The net force vector is equal to th mass off the the th object bj t times ti the th acceleration of the object. j Mass Mass characterizes inertial properties of an object and for a given object this quantity is a constant. Newton’ss Second Law Newton • Now need to translate English into Math: – Net forces cause the velocity to change This Thi iis a VECTOR equation ti Vector Equation F m a : F x ma x , F y ma y Same equation presented in components Reminder: Pulling a tanker Given: T1=T Gi T2, D, D R R, m a-? 2T1cos 30o +D- R =ma m The Law of Gravity Units 1 kg Force: F=ma, 1 Newton, 1N=1kg·1m/s 1N=1kg 1m/s2 Mass: 1 N is the amount of force that gives the acceleration of one o e meter ete pe per seco second d squa squared ed to a body with a mass of 1 kilogram. Example: Force to stop a car What constant net force is required to bring a car of mass m to rest from a speed of V within a distance of D? V0 = V V=0 X0 = 0 XF = D Getting to Newton’s Third Law How does one apply a force? • Applying a force requires another object! –A hammer exerts a force on a nail –However, H th the nailil acts t on th the hammer with a reaction force (this is what stops the hammer)! Newton’s Third Law “Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force (reaction).” OR “To To every action there is an equal and opposite reaction. (counter action)” Example Skater pushes on the wall. The wall pushes back that’s why back, she moves off with some nonzero speed! d! Weight and normal force (the force component perpendicular to the surface that the surface exerts on an object) Weight: mg Without reaction from supporting surface the object j will fall with Acceleration of gravity. Difference: weight and mass weight is a vector, directed toward the center of the Earth Earth, measured in N N. Mass is a scalar quantity measured in kg of mass. (weight) Examples FGround on the Person - FPerson on the Ground Force exerted by the person on the ground is equal and opposite it tto th the fforce exerted t d by the ground on the person. She pushes on the ground d and d the th ground d PUSHES her forward (especially when the motion starts!!!). t t !!!) Also vertical forces: weight reaction from the ground upward. FN W=mg Newton’s 3d law is very general: action and reaction via field (gravitational, electric, etc.) also is valid, not only contact forces! The Law of Gravity Analysis of forces: free body diagram Problem: pulling a box Forces mg=100 N Note: FN is less than mg The Law of Gravity Free body diagram: Action of surrounding objects is replaced with the forces they exert. Problem: weight, normal force and a box mg=98.0 mg=98 0N a-? FN-? The Law of Gravity Free body diagram Free body diagram is the main approach to solve dynamics problems, when different objects interact with each other. Action of surrounding objects is replaced with the forces they exert. If there are several interacting objects such a diagram should be drawn for each of them them. Free body di diagram ffor a block on a surface f with ith friction F.B.D. Dynamic equations: The Law of Gravity Motion of 2 blocks No friction, force F F F.B.D.-? F.B.D. ? F The Law of Gravity Problem: Apparent Weight (FN) F.B.D. ? y Fnet = FN – mg = m a The Law of Gravity Weightlessness F.B.D. ? The Law of Gravity •Thanks for your attention!