Chapter 5&6 Notes
Chapter 5&6 Notes PHSX 205-001
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This 8 page Bundle was uploaded by Rebeka Jones on Saturday October 15, 2016. The Bundle belongs to PHSX 205-001 at Montana State University taught by Dr. Greg Francis in Fall 2016. Since its upload, it has received 6 views.
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Date Created: 10/15/16
Chapter 5: Newton’s Laws The goal of mechanics is to take what is known about a system of objects and to there by determine what acceleration of each of those object will be. Principle of inertia – a body moving on a level surface will continue in th e same direction at constant speed unless disturbed Law I: Every body preserves in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed on it. All objects move at constant velocity: unless acted upon by an outside force Newton’s first law simply does not apply in a reference frame that is accelerating; it only applies in frames where it applies. So it is merely a definition. The reference systems where Newton’s first law applies are called inertial frames, and they are defined as those frames in which Newton’s first law applies. If you see all objects with no forces on them move at a constant velocity then you are in an inertial frame, and Newton ’s first law will work. *reference frames tied to the earth may be assumed to be an inert ial frame to high accuracy. The quantity of motion is the way to measure motion, arising as the product of mass and velocity. Now called momentum. Law II: The change in motion is always proportional to the applied force, and is made in the direction of the straight line in which that force is applied. ???? = ???????? ma is proportional to the force, not equal 2 The force unit is Newton 1 N = 1 kg x m/s Mass is a measure of an objects inertia of how difficult it is to accelerate the object – mas is scalar, it has no direction ???????????? ????????: ???? ▯▯▯ = ???????? Law III: To every action there is always opposed an equal and opposite reaction: or the mutual actions of two bodies are always equal, and directed to contrary parts. Easier version Law III: If an object exerts a force on a second object, the second object exerts an equal and opposite force back on the first object. The point of Newton’s 3 law is that forces always occur in pairs. When labeling forces use by,on subscripts Gravitational Force: W = mg *gravity acts on an object without anything touching the object Normal Force – can only arise when something is touching the object Friction Force – when the surface of the object is pulled along or is moving along another surface - Kinetic – when an object is in motion across the surface 2 - Static 0 what it takes to keep the object from moving Tension – created by strings, chains, cords, etc. Drawing a free body diagram should always be the first step in solving a problem involving Newton’s second law. Once we have identified the forces, we are able to apply Newton’s second law to the problem, Chapter Formulas ???? ▯▯▯ ???????????????????????? ???? ???????????????????????? ???????????? ∶ ???? ▯▯▯ = ???????? ???????? ???? ???? ???? = ???????? 3 Chapter 6: Forces Gravitational Force – Weight - The bigger the mass the small the acceleration The force of gravity of an object near the earth’s surface is really just a manifesto of a more general law. Newton found that any two objects with mass will attract each other with a gravitational force. ???????? ????▯= ???? ????▯ m,M are the masses of the two objects r is the distance between their centers -11 2 2 G is the universal constant = 6.67x10^ Nxm /kg Or more easily W = mg Mass – how difficult it is to accelerate an object, to speed it up or slow it down, or to shake it. Weight – the gravitational force exerted on that object and is proportional to the gravitational field strength g. *Gravitational force is an example of a non-contact force. Normal Force – when the surface of two bodies are in contact with each other, there are two ways they can push on each other. Once of those is called the normal force. It acts perpendicular to the surfaces of the objects. Whenever one solid object pushes on another solid object, a normal force will arise to oppose that push. There is no equation for normal force it is a force that arises from two objects exerting a force on each other. It is whatever it takes to keep the objects from falling through eachother. Friction Forces – acts parraell to the surface between the object exerting the force and the object experiencing the force. - Kinetic friction – two rough surfaces are sliding across each other – can be heard - Static friction – trying to move one rough surface across another rough surface, but friction force between them is great enough to keep the surfaces from sliding. Kinetic depends on two factors - How rough the two surfaces are - How tightly the two surfaces are pressed together. ???? = ???? ???? ▯ Static Friction The nooks and crannies of one surface are locked in the nooks and crannies of the other, It adjusts itself to be whatever magnit ude it has to have to keep the two surfaces from moving relative to each other. But there is a breaking point and it depends on the same stuff as kinetic. ????▯.▯▯▯ = ???? ???? ▯ *not a formula for the static friction but for the maximum value. The actual static friction force is found by Newton’s 2 law and the observation that the two surfaces are not moving relative to each other. *we general expect µ >µs k 2 Static friction can be acting on an object when that object is acceleration, Static friction must arise in a case where the acce leration of the object and that of the surface it is toughing are the same, so that the two surfaces are not scraping along each other. *if the plane is inclined, the gravitational force will be an exception. It will always point to the center of the earth regardless of the slant of the plane so it will typically have to be resolved into its components in the two directions. Tension – contact pull exerted by a rope, chain, or string. By Newton’s 3 law the object must also exert a tension force on the rope, chain, or string. Accelerating rope with some mass must have a different tension at the two ends of the rope of it would not be able to accelerate. Only in the limit of a negligible mass for the rope could the tension be the same through the rope. nd *always draw a free body diagram and use Newton’s 2 *no need to draw a free body diagram for massless things The tension in a massless string will simply always be the same on both ends. Elastic and Spring Forces – If a string is to provide a tension force, it must actually stretch a microscopic amount. It is also true that when a table hold something up it is compressed. Hooke’s law states that the force by which a material body resists deformation is proportional to the size of the deformation of the body. ????▯= ????∆???? 3 Fs is spring force Ds is the size of the deformation k is the spring constant which depends on the nature and geometry of the material *large spring constant means that a large force is achieved with little deformation Refrigerator Magnet Forces – because it is an attractive force, the direction of the magnetic force exerted by the refrigerator on the magnet must point directly toward the refrigerator. Can also invoke the 3 law to says that because the refrigerator can exert a magnetic force it must also be able to experience one. *a refrigerator can exert both a non-contact and magnetic pull on a magnet and a contact normal force push on the same magnet at the same time. Apparent Weight – a person’s weight is defined as the gravitational force exerted on him. However, if we stand on that same scale while accelerating in an elevator, we can get a reading on the scale that is different from our true weight. 2 law requires that a net force act in the direction of acceleration. This appears to change our weight. Centripetal Force – an object with uniform circular motion is always accelerating in a direction perpendicular to its velocity, toward the center of the circle. ???? ▯ ???? ▯ ???? 4 ???????? ▯ ???? ▯▯▯ = ???? ▯ ???? *centripetal force is not a force but a requirement on the forces Circular motion is the result of a force satisfying the centripetal requirement. Chapter formulas ▯▯ Gravity - ????▯= ???? ▯▯ and W = mg Kinetic Friction – ???? = ???? ▯ Static Friction - ????.▯▯▯ = ???? ???? ▯ ▯▯▯ Centripetal Requirement - ???? ▯▯▯ = ???? ▯ ▯ Spring Force - ???? = ????∆???? ▯ 5
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