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# Physics Online Notes from Readings 9/27 and 10/2 PHYS 23300 - 001

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This 4 page Class Notes was uploaded by Kiersten Notetaker on Sunday October 2, 2016. The Class Notes belongs to PHYS 23300 - 001 at Purdue University taught by Stephen M Durbin in Fall 2016. Since its upload, it has received 9 views.

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Date Created: 10/02/16

Physics 233 online notes based on readings from 9/27 and 10/2 Viscosity - Interaction of molecules in a fluid results in an internal friction that works to slow down the motion of neighboring layers of fluid. For example: Plate Keep the bottom plate at rest, and moving the top plate in the direction of the arrow with a constant velocity. Fluid Fluid is being pulled so that the amount Plate Not of deformation of the fluid changes moving perpendicular to the direction of the - At the top of the plate, the fluid moves with the plate - Some of the fluid at the bottom of the not moving plate will remain at rest - This sets up a gradient of velocity Rate of change with respect to space -The layers of fluid move past each other as shown - Those at the top of the fluid (near the top plate being actively moved) have the greatest velocity -Those at the bottom of the fluid (near the bottom plate held at rest) have the lowest velocity Equation (still using example above) - Both plates have an area (A) - Both separated by a thickness (Y) - We’re holding the bottom plate and moving the top with a constant velocity (u) Acceleration of the plate is determined by Newton’s 2 ndLaw: net appiscous M *p =F p p = F p + F fluid->p *Note* if there were no internal resistance, any force on top would continue to app speed up. If we apply F on the plate it will speed up but its velocity will increase more slowly until it reaches constant velocity. - when the plate reaches a steady speed, acceleration is zero. - this shows that the force we’re applying is equal and opposite to the viscous force. F is: viscous Proportional to the speed of the plate Proportional to the area of the plate Inversely proportional to the distance between the moving plate and the fixed plate - We use μ to represent viscosity of fluid Viscosity of fluid= u= μ*( ) Ax y F= force y A= area μ= viscosity of fluid u= constant velocity y= thickness - Dimensionality of viscosity= M o Has SI system uniLT kg/m-s o We use force a lot with this so we rearrange and incorporate Newtons: (N/m )*s - We also know about viscous forces on a sphere with radius (R) moving in a fluid: o Ffluid->sphere= -6piμRv viscous R= radius, v=velocity DRAG - When an object moves through a fluid it feels resistance to its motion: o The object is dragging the fluid with it and making the fluid slide along itself. The fluid shows viscosity. o It’s pushing the fluid in front of it, making the fluid in front go with the same speed as the object. This is called drag - The object exerts a force on the liquid in the direction of motion and the liquid pushes back in the opposite direction The cylinder will move Δx=vΔt Cylinder will sweep out all the molecules in a thin volume equal to the area of the circle*Δx V 2 2 -so Δv=piR Δx R Mass of molecules in this volume= the volume*density Δm = ρΔV Density Force equations for drag: F inertial=p∗g (pi∗R 2)v2 fluid →cylinder F ❑ =Ppi R v2 2 cylinder→ fluid So, The drag force that a fluid exerts on an object moving through it: - Opposes the motion - Is proportional to the density of fluid - Is proportional to the area being pushed through the fluid - Is proportional to the square of velocity of the object through the fluid Cdragis the drag coefficient - It’s determined by measurement but it’s usually close to 1 - USE THIS EQUATION FOR DRAG: inertialdrag 2 2 F fluid →cylindedragP (pi∗R v 2 Gravity - Weight is a force that can change an object’s velocity - We assume that the gravitational force on an object points down and is independent of position o This is referred to as flat earth gravity Flat Earth Gravity - Estimation excluding fast velocities, change in height, and change in position. - Ex: o Think of holding a ball and nothing is moving N N The F hand →ball ball →hand Object’s weight pushing down=upward normal force of the hand - Think of a large and small ball being dropped at the same time. They will hit the ground at the same time even though their masses are different. o The net force on an object is shared over the whole object - W E→A/m A constant independent of the object o (weight of the object divided by its mass= a constant independent of the object) - Constant independent of the object=g ❑ W E→ Am gA <- gravitational force equation W= weight E=earth m=mass - We mentioned above how weight is a force o The weight of an object is proportional to its mass o The constant g refers to gravitational field and is represented as 9.81N/kg Free Fall in Flat Earth Gravity - Gravitational force= weight - If the only force acting on an object is gravity we say it’s in free fall o Still has an initial velocity o Can be moving up or sideways and still be considered in free fall - We refer to free fall motion as projectile motion Δ x V x Shows that x motion had no acceleration so object Δt remains at whateer x-velocity it had when it was released V = Δ y y Δt y motion has a constant downward acceleration meaning y velocity is continuously changing ax=0 for x motion, average v= instantaneous (constant) velocity a =−g (vi+v f y for y mtion, average v= 2 Gravitational field o Gravitational force on an object of mass placed at that point is m*g, and the force vector points in the direction of that field vector - Force of gravity is proportional to the objects mass - The further we are from the center of the earth the weaker gravity is - The direction of the field is not the direction an object moves when it’s experiencing the forces of that field - The gravitational field doesn’t refer to the region of space where the gravitational force is significant o It refers to the set of vectors at each point in space - The gravitational field determines the gravitational force but the net force determines the acceleration - If an object is not moving and there are no other forces on it then it will accelerate in the direction of the arrow o If there are any other forces acting on it, it won’t accelerate in the direction of the arrow - Net force determines acceleration (Δv) o So, if the object already has a velocity, then the force of the arrow will point in the direction of the change in velocity not direction of velocity - If the ball is thrown in the direction Gravitation of the arrow, the field will push it al field down , but the direction of the motion of the ball won’t be in the direction of the field (The ball isn’t going to change its direction to move straight down like

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