Assessment Physics Terms

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5/21/14Hooke’slawAssessment1. A certain spring with a free length of 10.0 cmhas a spring constant of k 500 N/m. Howmuch force does the spring exert if it isextended to a length of 12.0 cm?2. What is the required spring constant for aspring to support a 10.0 kg mass whiledeflecting only 14 cm?EquationsObjectives Calculate the force from a spring whengiven its spring constant and deflection. Calculate a spring constant given therequired force and deflection.Physics terms Hooke’s law spring constant extension compression deflection deformationSpringsHooke’s law:The free length of a springis its length without anyexternal forces applied.The force exerted by a spring is the negative of the product ofthe spring constant multiplied by the deformation of the spring.Fs1

5/21/14SpringsSpringsThe deformation x of thespring depends on howmuch force is exerted tostretch it or compress it.The free length of a springis its length without anyexternal forces applied.FsInvestigationFsThe deformation x is thelength in meters that thespring is extended ( x) orcompressed (-x).InvestigationPart 1: Extension and restoring forceIn Investigation 5B you willmeasure the force anddeformation of a stretchedspring. How are thesevariables related?The investigation is foundon page 150.1. Set up the equipment using thelooser spring.2. With the spring scale attached, markthe equilibrium position of thebottom of the spring on the ruledpaper as “0 N.”3. Pull down the spring scale by 1 N toextend the spring. Mark the newlocation of the end of the spring onthe ruled paper with a label “1 N.”InvestigationInvestigationPart 1: Extension and restoring forceQuestions for Part 14. Pull down the spring for forces of 2,3, 4, and 5 N. Mark the position ofthe end of the spring and label eachmark with the force.a. What is the slope of your graph?5. Remove the paper and measure thedistance x (in meters) of each pointfrom equilibrium.b. What physical quantity isrepresented by the slope ofyour graph? Why?c. In steps 4 and 5, what were theindependent, dependent, andcontrolled variables?6. Graph your data with deformation xon the horizontal axis.2

5/21/14Make inferences from the dataInvestigationQuestions for Part 1Part 2: Stiff and loose springsd. Use your graph to determinethe force the spring wouldexert at other deformations.1. Now substitute a “stiff” spring forthe “loose” one. Then set up theexperiment as before.2. Repeat the steps of stretching thespring scale to different forces.Record and graph your data.InvestigationHooke’s lawQuestions for Part 2Hooke’s law describes an“ideal” spring. It is a goodapproximation for real springs.a. When you stretch the stiff springby hand, how does it feel orrespond that is different from theloose spring?b. How does the extension of thestiff spring compare to that of theloose one for the same n(m)Notice the units: The deformation must be in meters!What is a spring constant?The spring constant k is aproperty of the spring itself.What is a spring constant?The spring constant tells youhow stiff the spring is. Stiff springs have highspring constants.The units of k :The spring constant tells you howmuch force F is needed to deformthe spring a distance x. Weak springs have lowspring constants.Which of these springs hasthe higher spring constant?3

5/21/14Test your knowledgeWhich has a higher spring constant:the rubber band or the spring in a carsuspension?Test your knowledgeWhich has a higher spring constant:the rubber band or the spring in a carsuspension?The car’s suspension springhas a higher spring constant.How do you know?Test your knowledgeWhich has a higher spring constant:the rubber band or the spring in a carsuspension?The car’s suspension springhas a higher spring constant.Measure k of a rubber band.Materials: Ruler, spring scale, #33 rubber band Hook one end of the rubber band over the zero end of a ruler. Straighten the rubber band to its free length.How do you know?It is much stiffer—ittakes more newtonsof force to stretch orcompress it.Measure k of a rubber band.Measure a different rubber bandMaterials: Ruler, spring scale, #33 rubber bandMaterials: Ruler, spring scale, #16 rubber band Stretch the rubber band 0.10 m (10 cm). A #16 rubber band is thinner than a #33. Calculate the spring constant:Predict: Will it have a higher or lower springconstant than a #33 band? Repeat the measurements and calculate aspring constant for the #16 rubber band.x 10 cm4

5/21/14Springs in parallelSprings in seriesMaterials: Ruler, spring scale, two #16 rubber bandsMaterials: Ruler, spring scale, two #16 rubber bands Combine 2 rubber bands in parallel (side by side ). Combine 2 rubber bands in series by loopingone onto the other one.Predict: Will the combination have a higheror lower spring constant than one alone?Predict: Will the combination have a higheror lower spring constant than one alone? Repeat the measurements and calculate thespring constant for this parallel combination.Hooke’s law Repeat the measurements and calculate thespring constant for this series combination.Hooke’s lawWhat is the meaning of theminus sign in Hooke’s law?What is the meaning of theminus sign in Hooke’s law?The force exerted by the springis in the opposite direction fromthe (m)The meaning of the minus signFsWhen the deformation x is in thepositive direction, the force Fsexerted by the spring is in thenegative )The meaning of the minus signFsWhen the deformation x is in thenegative direction, the force Fsexerted by the spring is in thepositive direction.5

5/21/14Exploring the ideasEngaging with the conceptsSet the force tozero and solve forthe deformation.Click thisinteractivecalculator onpage 149.What happens?010DeformationEngaging with the conceptsEngaging with the conceptsSet the force tozero and solve forthe deformation.Enter a deformationof 0.5 m.What is the force?What happens?At zero force thespring is at its freelength and thedeformation is zero.010100Engaging with the conceptsForceEngaging with the conceptsEnter a deformationof 0.5 m.Enter a deformationof 0.5 m.What is the force?What is the force?-5 NWhy is it negative?0.50Deformation-F x-5 N-5010Why is it negative?0.50ForceBecause the springforce F pulls in theopposite direction ofthe stretch, x.-50100.50Force6

5/21/14Engaging with the conceptsEngaging with the conceptsEnter a deformationof -0.5 m.Enter a deformationof -0.5 m.What is the force?What is the force?-x F 5 N100.50ForceCalculating the spring constantExamine this graph offorce versus deflection.Force vs. deflection.The force created bythe spring nowpushes to the left.10ForceForce vs. deflection.What is the slope of thisgraph?What physical quantity isrepresented by the slope?Calculating the spring constantExamine this graph offorce versus deflection.Force vs. deflection.What is the slope of thisgraph?What physical quantity isrepresented by the slope?0.50Calculating the spring constantExamine this graph offorce versus deflection.What is the slope of thisgraph?5riserunExtending Hooke’s lawConsider this question: A bowling ball rests on a table.The table pushes up on the ball with a normal forceexactly equal to the ball’s weight.riseHow does the table “know” how much force to push with?runThe slope is the spring constant,k: the force the spring exertsper meter of stretch.7

5/21/14Real objectsReal objectsReal objects deflect under applied forces, just like springs.The table acts like a spring. Its “spring constant” determineshow much the table deflects under any given force.It continues to deflect until forces come to equilibrium.Real objectsTypes of springsFor small deflections, the relationship is approximated by Hooke’s law.Real springs come in many different types.Hooke’s law can be used to describe the forceexerted by all kinds of springs.AssessmentAssessment1. A certain spring with a free length of 10.0 cm has a springconstant of k 500 N/m. How much force does the springexert if it is extended to a length of 12.0 cm?1. A certain spring with a free length of 10.0 cm has a springconstant of k 500 N/m. How much force does the springexert if it is extended to a length of 12.0 cm?F -kx - (500 N/m) (0.02 m) -10 newtons2. What is the required spring constant for a spring tosupport a 10 kg mass while deflecting only 14 cm?8

5/21/14Assessment1. A certain spring with a free length of 10.0 cm has a springconstant of k 500 N/m. How much force does the springexert if it is extended to a length of 12.0 cm?F -kx - (500 N/m) (0.02 m) -10 newtons2. What is the required spring constant for a spring tosupport a 10 kg mass while deflecting only 14 cm?Weight mg (10 kg)(9.8 N/kg) 98 N downSince the mass is at rest with Fnet 0 N, then Fspring must be 98 N up.From Hooke’s law, k - F/x -(98 N) / (-0.14 m) 700 N/m9

Hooke’s law describes an “ideal” spring. It is a good approximation for real springs. Hooke’s law The spring constant k is a property of the spring itself. What is a spring constant? The units of k : The spring constant tells you how much force F is needed to deform the spring a di

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