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# study_guide_for_exam_2.pdf PHYS201012

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This 8 page Study Guide was uploaded by Udbluehen03 on Sunday October 16, 2016. The Study Guide belongs to PHYS201012 at University of Delaware taught by Gogoladze,Ilia in Summer 2016. Since its upload, it has received 107 views. For similar materials see Introductory Physics I in PHYSICS (PHY) at University of Delaware.

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Date Created: 10/16/16

NEWTON’S LAWS OF MOTION Force - A push and pull - Forces are what cause any change in the velocity of an object - A force is that which causes an acceleration - Vectors Classes of Forces - Contact forces o Involve physical contact between two objects - Field forces o Act through empty space. o No physical contact is required Fundamental Forces - Gravitational force o Between objects - Electromagnetic forces o Between electric charges - Strong force o Between subatomic particles (quarks, gluons) - Weak forces o Between subatomic particles Forces - A spring can be used to calibrate the magnitude of a force. - Doubling the force causes double the reading on the spring. - When both forces are applied, the reading is three times the initial reading. Mass - Measures the difficulty in accelerating an object - Inherent property of an object. - Independent of the object’s surroundings. - Independent of the method used to measure it. - SI unit: Kg Inertia - The resistance of any physical object to any change in its state of motion, including changes to its speed and direction. - It is the tendency of objects to keep moving in a straight line at constant velocity - it’s a property of all matter to resist changes it motion Newton’s First Law of Motion - An object at rest remains at rest as long as no net force acts on it - The law of Inertia: an object moving with constant velocity continues to move with the same speed and in the same direction as long as no net force acts on it - If the net force on an object is zero, its velocity is constant - When no force acts on an object, the acceleration of the object is zero - The First Law also allows the definition of force as that which causes a change in the motion of an object Newton’s Second Law of Motion - Unbalanced forces cause acceleration - Acceleration is proportional to force o The greater the force, the greater the acceleration - Acceleration is inversely proportional to mass o The greater the mass, the less the acceleration - ???? = ???????? - An object may have several forces acting on it; the acceleration is due to the net force o ∑ ???? = ???????? - ∑ ????is the net force - Newton’s II Law in terms of components o ∑ ????????= ???????? ???? o ∑ ????????= ???????? ???? o ∑ ????????= ???????? ???? - The SI unit of force is the newton (N). o 1 N = 1 kg·m / s Free-body diagrams A free-body diagram shows every force acting on an object. - Sketch the forces - Isolate the object of interest - Choose a convenient coordinate system - Resolve the forces into components - Apply Newton’s second law to each coordinate direction Newton’s Third Law of Motion Law of action and reaction - Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. - Rule to Identify Action and Reaction: o Action: object A exerts a force on object B o Reaction: object B exerts a force on object A - Action and reaction forces o One force is called the action force; the other force is called the reaction force o Are co-pairs of a single interaction o Neither force exists without the other o Are equal in strength and opposite in direction o Always act on different objects The Vector Nature of Forces: Forces in Two Dimensions - The easiest way to handle forces in two dimensions is to treat each dimension separately, as we did for kinematics. Mass vs. Weight - Mass and weight are two different quantities. - Weight is equal to the magnitude of the gravitational force exerted on the object. – - Weight will vary with location Weight - The weight of an object on the Earth’s surface is the gravitational force exerted on it by the Earth. - W = mg - SI unit: Newton - Because it is dependent on g, the weight varies with location - g, and therefore the weight, is less at higher altitudes APPLICATION OF NEWTON’S LAWS Forces of Friction - To slide one such surface across another requires a force larger enough to overcome the resistance of microscopic hills and valley bumping together. This is the origin of the force we call friction - When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion. - This is due to the interactions between the object and its environment. o This resistance is called the force of friction. - Force that slows down or stops motion. - Force that helps to start motion. - Problem-Solving Hints o Conceptualize Draw a diagram Choose a convenient coordinate system for each object o Categorize Is the model a particle in equilibrium? If so, ????F = 0 Is the model a particle under a net force? If so, ???????? = ma Kinetic friction - It is the friction encounter when surfaces slide against one another with a finite relative speed - Fk acts to oppose the sliding motion at the point of contact between the surfaces - The kinetic frictional force is also independent of the relative speed of the surfaces, and of their area of contact - The force of kinetic friction is proportional to the magnitude of the normal force, N o Fk = µkN - µk o coefficient of kinetic friction o always positive o typically, between 0 and 1 - the normal force is greater than the weight if someone pushes down on the bricks, and this would cause more friction, or less than the weight if the bricks are placed on an incline - the greater the µk, the greater the friction - the smaller the µk, the smaller the friction Static Friction µs) - Coefficient of friction does not depend to the mass and area, but frictional force does - f s,max= µ s N Tension - When you pull on a string or rope, it becomes taut. We say that there is tension in the string - The tension in a real rope will vary along its length, due to the weight of the rope - An ideal pulley is one that simply changes the direction of the tension but not magnitude of the tension - T = mg Connected Objects - When forces are exerted on connected objects, their accelerations are the same. - If there are two objects connected by a string, and we know the force and the masses, we can find the acceleration and the tension Hook’s Law - Hooke’s law for springs states that the force increases with the amount the spring is stretched or compressed - F = -kx - The constant k is called the spring constant and it is measured in ????/????. Uniform Circular Motion, Acceleration - A particle moves with a constant speed in a circular path of radius ???? with an acceleration. - The magnitude of the acceleration is given by 2 - ????⃗ = ???? ???? ???? - The centripetal acceleration,????⃗???? , is directed toward the center of the circle. - The centripetal acceleration is always perpendicular to the velocity Uniform Circular Motion, Force ⃗ - A force, ???? , is associated with the centripetal acceleration. - The force is also directed toward the center of the circle. - Applying Newton’s Second Law along the radial direction gives ???? 2 - ???????????? ???????? ???????? = ???? ???? - A force causing a centripetal acceleration acts toward the center of the circle. - It causes a change in the direction of the velocity vector. - If the force vanishes, the object would move in a straight-line path tangent to the circle Horizontal (Flat) Curve - Car in equilibrium in the vertical direction. - The force of static friction supplies the centripetal force. - Car in uniform circular motion in the horizontal direction - The maximum speed at which the car can negotiate the curve is: - ???? = √ µ ???????? - Note, this does not depend on the mass of the car. WORK AND KINETIC ENERGY Work Done by a Constant Force - The definition of work, when the force is parallel to the displacement o W = Fd - The meaning of the term work is distinctly different in physics than in everyday meaning. - Work is done on the system - SI unit; newton * m (nm) = Joules (J) - The sign of the work depends on the direction of the force relative to the displacement. o Work is positive when projection of onto is in the same direction as the displacement. o Work is negative when the projection is in the opposite direction - If the force is at an angle to the displacement - W = (Fcosθ)d = Fdcosθ Scalar Product of Two Vectors - The scalar product of two vectors is written as ???? ∙ ????⃗ o It is also called the dot product o ???? ∙ ???? = ABcosθ - θ is the angle between A and B - Applied to work, this means o W = Fdcosθ = ???? ∙ ???? ⃗ - The scalar product is commutative ⃗ ⃗⃗ ⃗⃗ ⃗ o ???? ∙ ???? = ???? ∙ ???? - The scalar product obeys the distributive law of multiplication o ???? ∙ (???? + ????) = ???? ∙ ???? + ???? ∙ ????) ⃗ Work - A force does no work on the object if the force does not move through a displacement. - The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application - Work is positive o ???? < 90° o ???? > 0 - Work is negative o ???? > 90° o ???? < 0 - Work is zero o ???? = 90° o ???? = 0 - If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force o ???? ????????????????????= (???? ????????????????????cos????)???? =???? ????????????????????????cos???? Kinetic Energy and the Work-Energy Theorem - When positive work is done on an object, its speed increases - When negative work is done, its speed decreases - Work-Energy Theorem o The total work done on an object is equal to its change in kinetic energy o ???? ????????????????????= ∆???? = ????????1 ????2 − ???????? ????2 2 2 - Kinetic Energy is the energy of a particle due to its motion o ???? = ???????? 1 2 2 - Here K is the kinetic energy, m is the mass of the particle, v is the speed of the particle Work Done by a Variable Force: A Spring - A model of a common physical system for which the force varies with position. - The block is on a horizontal, frictionless surface. - Observe the motion of the block with various values of the spring constant Spring Force (Hooke’s Law) - The force exerted by the spring is ???????? = − ???????? - ???? - is the position of the block with respect to the equilibrium position (???? = ????). - k is called the spring constant or force constant - k measures the stiffness of the spring Work Done by a Spring Force - The spring force is given by Hooke's law o ???? = −???????? ⃗ ???? - The negative sign represents that the force always opposes the displacement - This is a variable force (function of position) and it exhibits a linear relationship between ???? and ???? - For a spring along the ????-axis we can write o ???? =????−???????? - We can find the work by 1 2 1 2 o ???? = ???????? − 2???? ???? 2 ???? - For an initial position of ???? = ???? o ???? = − ???????? 1 2 ???? 2 - For an applied force where the initial and final kinetic energies are zero o ???? = ???????? ???? Power - Measure of how fast work is done - Power = work done/time interval - SI unit: J/s = watt, W

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