Transcript lecture two
1.4: Simple Types of Motion: Having the initial conditions(initial position and initial velocity), what is the distance and speed at later time? a. No Motion: V=0 and a=0 v x a t t t b. Constant Velocity: (Uniform Motion) Constant speed in certain direction. Object covers equally distances in equally times x Slope=rise/run =v v a t t c. Constant Acceleration: Object changes its velocity at fixed rate. t x a v Motion up 9.81 Motion down t t t t=4s t=3s V=0m/s V=9.81m/s X=78.5m X=73.5m t=2s V=19.6m/s X=58.8m t=1s V=29.4m/s X=34.2m t=0 V=39.2m/s X=0 -9.81 Since the v-t relationship is linear vave=(vintial+v)/2 Vave=x/t=x/t at X=vavet=(vintial+v)t/2 v Solving for vintial Solving for vfinal vintial x=(vintial+vintial+at)t/2 x=(v+v-at)t/2 t X=vintialt+at2/2 X=vt-at2/2 V=vintial+at a=v/t=v-vintial/t v v vintial x The position,the velocity and the acceleration for a car starts at rest, Resting accelerates for an interval, then moves t with constant velocity,and then brakes with negative acceleration to rest again. Resting v a t a>0 a=0 a=0 a<0 a=0 t Relative Acceleration! Newton’s laws: What causes the motion? Force: A push or a pull acting on a body Units of force: Newton, dyne,..etc. 1 Newton: is the force when acts on a particle of mass 1kg, the particle gain acceleration 1m/s2. 1 Dyne: is the force when acts on a particle of mass 1g, the particle gain acceleration 1cm/s2. 1N=1kg1m/s2 1 dyne=1g1cm/s2 Q: Show that 1N=105dyne? m Weight: The force due to gravity. Q:A person has weight 500N on the earth, what is his weight on Fg=w the moon? Location – mass –weight Earth 1kg 9.8N Moon 1kg 1.6N c M Space 1kg 0N w w Friction: resistance force for the relative motion. Static friction: when there is no Dynamic friction: When there is a motion. relative motion. Isaac Newton: (1642-1727) His three laws of motion first appeared in his book called Principia. 2.2 Newton’s First Law of motion: A body remains at rest or moves in a straight line at a constant speed unless acted upon by a force. The force laws Environment Force body Acceleration F The laws of motion Newton’s laws F1 F1 At rest or moving with uniform velocity F2 Ftotal F2 Particle initially at rest: the particle will start move Kinetic friction when the external force is greater than the N (static)friction force. N Fk F w fs w w Particle initially is moving: 1.constant net force in its direction of motion: Particle accelerate 2.constant net force opposite to its direction of motion: Particle decelerate 3.constant net force perpendicular to its direction of motion: Uniform circular motion Centripetal force 2.3 Inertial mass and gravitational mass: g doesn't depend on mass Pisa Galileo 1600’s 2.4 Newton’s Second law of motion: The acceleration of an object is directly proportional to the net force acting on the object, and inversely proportional to the mass of the object. F m m F m a F a/2 2F m m a 2a m m F a/3 3F F =ma The total external force acting on a particle equals Its mass times its resultant acceleration. 3a m m a1/m aF Inertial mass and gravitational mass Revisited F=ma, m is the inertial mass W=mg, m is the gravitational mass Since F=w in the free fall and a=g then the inertial mass and the gravitational mass are equal. Thank You How the idea occurred to Einstein: “I was sitting in a chair in the patent office in Bern when all of a sudden A thought occurred to me: If a person falls freely he will not feel his own Weight. I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.”