Download Introductory Physics I: Lecture 4 - Scalars, Vectors, and Projectile Motion and more Study notes Physics in PDF only on Docsity! PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 4 • Scalars vs. Vectors • Vectors A: (Ax, Ay) or |A| & θ • Addition/Subtraction • Projectile Motion • X-direction: ax = 0 (vx = constant) • Y-direction: ay=-g • Parabolic trajectory Main points of last lecture Example 3.4c h D θ v0 The acceleration is smallest (in magnitude) at: a) A b) B c) C d) Same at all points Range Formula • Good for when yf = yi x = vi,xt y = vi,yt ! 1 2 gt 2 = 0 t = 2vi,y g x = 2vi,xvi,y g = 2vi 2 cos" sin" g x = vi 2 g sin2" Range Formula • Maximum for θ=45°R = vi 2 g sin2! Relative velocity
- Velocity always defined relative to reference frame.
Example 3.7 a) 5 mph b) 1 mph An airport walkway moves at 3 mph. A man walks at a leisurely pace of 2 mph. a) If he walks on the walkway in the same direction as the walkway, what is his speed as seen from the ground? b) If he walks on the walkway in the opposite direction as the walkway, what is his speed as seen from the ground? Relative velocity in 2-d • Sum velocities as vectors • velocity relative to ground = velocity relative to medium + velocity of medium. vbe = vbr + vre boat wrt river river wrt earth Boat wrt earth Example 3.9 An airplane is capable of moving 200 mph in still air. A wind blows directly from the North at 50 mph. The airplane accounts for the wind (by pointing the plane somewhat into the wind) and flies directly east relative to the ground. What is the plane’s resulting ground speed? In what direction is the nose of the plane pointed? 193.6 mph 14.5 deg. north of east Chapter 4 Forces and Motion What is a force? • Usually a push or pull • A Vector Fundamental Forces: 1. Strong Nuclear 2. Electromagnetic 3. Weak Nuclear 4. Gravity Newton’s Second Law • Acceleration is proportional to net force and inversely proportional to mass. r F! = m r a Units of Force • SI unit is Newton (N) • US Customary unit is pound (lb) • 1 N = 0.225 lb F = ma 1 N = 1 kg !m s2 Gravitational Force Weight = magnitude of Gravitational Force on an object near the surface of the Earth Galileo: weight mass ! r a = g " w = mg • Weight is different on surface of other planets/moons. • Mass is same everywhere. Defining the Object: Free-body Diagram • Newton’s Law uses the forces acting ON object • n and Fg act on object • n’ and Fg’ act on other objects Ignore rotational motion for now. Treat object as a particle. Definition of Equilibrium r F! = 0 Object is at rest or moving with constant velocity Example 4.1a A Ford Pinto is parked in a parking lot There is no net force on the Pinto A) True B) False Example 4.1d A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance) The force acting on the Pinto from the contact with the highway is vertical. A) True B) False Mechanical Forces • Gravity • Normal forces • Strings, ropes and Pulleys • Friction • Springs (later) Rules for Ropes and Pulleys • Force from rope points AWAY from object • (Rope can only pull) • Magnitude of the force is Tension • Tension is same everywhere in the rope • Tension does not change when going over pulley Approximations: Neglect mass of rope and pulley, neglect friction in pulley Example 4.4a 2) Which statements are correct? Assume the objects are static. T1 is _____ T2 cos(10o)=0.985 sin(10o)=0.173 A) Less than B) Equal to C) Greater than Example 4.4b 2) Which statements are correct? Assume the objects are static. T2 is ______ T3 cos(10o)=0.985 sin(10o)=0.173 A) Less than B) Equal to C) Greater than Example 4.4c 2) Which statements are correct? Assume the objects are static. cos(10o)=0.985 sin(10o)=0.173 A) Less than B) Equal to C) Greater than T1 is _____ Mg
