Physics 1220, Week 6 Notes
Physics 1220, Week 6 Notes PHYS1220
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This 11 page Class Notes was uploaded by Jennifer Asselin on Saturday September 17, 2016. The Class Notes belongs to PHYS1220 at Clemson University taught by Pooja Puneet in Summer 2016. Since its upload, it has received 7 views. For similar materials see Physics with Calculus I in PHYSICS (PHY) at Clemson University.
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Date Created: 09/17/16
Chapter 6 Textbook Outline 6-1 Newton’s Laws in a messy World Ø This brief section talked about the forces that will alter the results of Newton’s Laws in the real world 6-2 Friction and the Normal Force Revisited Ø Friction: force acting on two surfaces when they are rubbed together; can be reduced but never fully eliminated o Without friction, we would not be able to walk on the ground, drive a car, or pet a dog o Friction is what holds up a box if you push it directly into a wall and have nothing below it to support the box; it is the component parallel to the wall o The normal force is the component of force pointing directly in the wall Ø Friction is caused by the edges of each objects actually being jagged instead of a smooth surface o Real contact areas are the jagged parts of each surface that actually tough o Apparent contact areas are the gap of air in between the contact areas o Polishing down a surface to make it more smooth will actually increase the magnitude of the friction force because it will increase the amount of contact are o You can slightly reduce friction between two very polished surfaces if you sprinkle some powder between them o Two extremely polished, clean surfaces pushed against one another in a vacuum can bond and become stuck together due to the high amount of contact area; this bond is called a cold bond Ø Friction acted differently depending on if the two objects are at rest, slide past one another, or roll over each other Ø Macroscopic: large scale; observing system as a whole Ø Microscopic: small scale; focusing on small components of a system 6-3 A Model for Static Friction Ø Static friction: results when an object is at rest with respect to a surface with which it is in contact; the force is parallel to the surface o If an object is not accelerating, the static friction force is balanced by the vector sum of any other forces that are applied to the object Ø The force of friction has a maximum, and cannot hold all objects in place Ø In a system where a box is at rest on a table, and a pulley with weight on the end of the rope hangs freely off the edge of the table will eventually pull the box toward the edge of the table when enough weights are added to the end of the rope to overcome to force of static friction o This can be mathematically represented by: ! !,!"# = ! ! ! where ! !s the coefficient of static friction and depends on the smoothness of each surface (it is a positive scalar value) Ø Experiments have shown that the magnitude of the apparent contact force does not affect the magnitude of static friction force because the effective contact are depends on the magnitude of the normal force o The friction of a rectangular box on its side will be the same magnitude of the friction on the bottom of the box if it is flipped upright Ø A heavy stationary box in the bed of a truck will exert a friction force in the direction the truck is moving o This is what keeps the box from sliding out of the truck 6-4 Kinetic and Rolling Friction Ø Kinetic Friction is a force parallel to the surface an object is sliding across; it point in the opposite direction of the motion Ø Like static friction, kinetic friction must be related to the number of molecular bonds that form between the two surfaces (contact areas) Ø This is represented by the equation: ! = ! ! , w! !e ! is a ! unitless, scalar constant unique to each surface pairing o Note: this is not a vector equation Ø According to Newton’s Second Law, the sum of all forces acting on a single object is equal to the mass of that object time the acceleration of that object: ! = !! ! ! o You can solve for variable in a problem by knowing this relationship o It is valid only when working with components in the same direction, so the sum of the vectors in the y-direction is equal to the mass time the acceleration in the y-direction only Ø Rolling Friction is the friction associated with the rolling motion of one object against the surface; it is weaker than kinetic and static friction o It has a similar mathematical equation: ! =!! ! ! ! Ø Moving Friction refers to both kinetic and rolling friction, but not static friction (because there is no motion with static friction) 6-5 Drag and Terminal Speed Ø Drag Force is the resistive force that occurs when an object moves in a fluid medium such as air or water Ø Moving friction and drag are called resistive forces because they work to resist motion Ø Like friction, drag is a macroscopic effect generated by many microscopic interactions Ø Drag force depends on the density of the medium and are object perpendicular to the direction of motion Ø Equations for drag: o For small objects moving slowly through air or large objects mobbing through water: ! = !!! o Magnitude of blunt objects moving at high speeds through the air: ! = ! ! ! ! ! , where C is the Drag Coefficient, ! which is a unitless number found experimentally between 0.4 and 1.0, and A is area Ø Terminal Speed (! ): t!e point in free fall when the magnitude of upward drag force equals an objects weight and the object stops accelerating o The object continues to move downward at constant speed o This is the highest speed the object can reach !!" o ! ! ! ! ! o In a vacuum, any two objects will land with the same velocity at the same time, but drag force does not allow that to happen in the world around us 6-6 Centripetal Force Ø Newton’s Second Law tells us there must be a net force on an object that makes it accelerate Ø In uniform circular motion, this net force will point into the center of the circle and is called centripetal force !! o The magnitude of centripetal force is: ! = ! ! o In polar coordinates, the vector can be expressed: !! !!= −! ! ! o This force is not generated by the circular motion; it is required for circular motion Ø If the total force on a particle is constant and perpendicular to its velocity, the particle undergoes uniform circular motion Ø If the force is not perpendicular, the motion is called nonuniform circular motion o The speed of the particle change because the total force has a component parallel to the velocity o We break down the total force vector into components that are parallel and perpendicular to the velocity vector § Parallel component: is the tangential component § Perpendicular component is the centripetal component because is points toward the center of the motion (circle) o The magnitude od the centripetal force (! ) an! the centripetal acceleration (! )!are the same as in uniform circular motion, but in nonuniform motion these quantities are not constant: !! § ! =!! ! !! § ! =! !
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