Week4PHY215SP2020.pdf - 4 Newtonu2019s laws of motion I...

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4. Newton’s laws of motion I4.1ForceForces are what cause any change in the velocity of an object, according to Newton’s definition, aforce is that which causes an acceleration. There are two classes of forces, contact forces and fieldforces. Contact forces involve physical contact between two objects (for example, friction). Fieldforces act through empty space, and no physical contact is required (for example, gravitationalforces). Forces are vectors, so you must use the rules for vector addition to find the net force actingon an object. The forces are applied perpendicularly to each other, and the resultant (or net) force isthe hypotenuse.Figure 4.1: Vector nature of forces.4.2Newton’s first law and inertial framesAny reference frame that moves with constant velocity relative to an inertial frame is itself aninertial frame. A reference frame that moves with constant velocity relative to the distant stars isthe best approximation of an inertial frame. We can consider the Earth to be such an inertial frame,although it has a small centripetal acceleration associated with its motion.Newton’s first law states that in the absence of external forces, when viewed from an inertialreference frame, an object at rest remains at rest and an object in motion continues in motion with aconstant velocity. Newton’s First Law describes what happens in the absence of a force. It also tellsus that when no net force acts on an object, the acceleration of the object is zero.
34Chapter 4. Newton’s laws of motion I4.3Inertia and massThe tendency of an object to resist any attempt to change its velocity is called inertia, and mass isthat property of an object that specifies how much resistance an object exhibits to changes in itsvelocity. Masses can be defined in terms of the accelerations produced by a given force acting onthem:m1m2=a2a1(4.1)The magnitude of the acceleration acting on an object is inversely proportional to its mass.It is also important to distinguish mass and weight, as they are two different quantities. Weightis equal to the magnitude of the gravitational force exerted on the object, and it varies with location(for example, on Earth or on the Moon).4.4Newton’s second lawWhen viewed from an inertial reference frame, the acceleration of an object is directly proportionalto the net force acting on it and inversely proportional to its mass. Force is the cause of change inmotion, as measured by the acceleration. Algebraically,Â~F=m~a,(4.2)whereÂ~Fis the net force, and corresponds to the vector sum of all the forces acting on the object.Newton’s Second Law can be expressed in terms of vector components:ÂFx=max(4.3)ÂFy=may(4.4)ÂFz=maz.(4.5)The SI unit of force is the newton (N),1 N=1 kg.m/s2. The force that is exerted on a standardmass of 1 kg to produce an acceleration of 1 m/s2has a magnitude of 1 newton (abbreviated N).4.5Gravitational force

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