PRACTICE ITUse the worked example above to help you solve this problem. A 0.545 kg object connected to a lightspring with a spring constant of 19.0 N/m oscillates on a frictionless horizontal surface.(a) Calculate the total energy of the system and the maximum speed of the object if theamplitude of the motion is 3.00 cm.E =Jm/sVmax=(b) What is the velocity of the object when the displacement is 2.00 cm?±m/s(c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm.KE =JJPES=EXERCISEFor what values of x is the speed of the object 0.14 m/s?x = ±cmHINTS: GETTING STARTED I I'M STUCK! STRATEGY The total energy of the system can be found most easily at the amplitude x = A, where thekinetic energy is zero. There, the potential energy alone is equal to the total energy. Conservation ofenergy then yields the speed at x = 0. For part (b), obtain the velocity by substituting the given value of xinto the time independent velocity equation. Using this result, the kinetic energy asked for in part (c) canbe found by substitution, as can the potential energy.SOLUTION(A) Calculate the total energy and maximum speed if the amplitude is 3.00 cm.E = KE + PEg + PES= 0 + 0 + ¹2kA² = ½(20.0 N/m)(3.00 x 10-² m)²= 9.00 × 10-³ JSubstitute x = A = 3.00 cm andk = 20.0 N/m into the equation for thetotal mechanical energy E.Use conservation of energy with x; = Aandxf= 0 to compute the speed of theobject at the origin.Substitute known values.(KE + PE + PE§); = (KE + PEg + PEs) f0 + 0 + 1₂kA² = 1/2mv²_1/2mv²Substitute into the equation for springpotential energy.VmaxmaxV == 9.00 × 10-³ J(B) Compute the velocity of the object when the displacement is 2.00 cm.v = ± √k/m(A² – x²)20.0 N/m0.500 kg(= ±0.141 m/s±1.80 x 10-² J0.500 kgmax= 1⁄2kx²+0+0PES= 4.00 × 10-³ J0.190 m/s(C) Compute the kinetic and potential energies when the displacement is 2.00 cm.Substitute into the equation for kineticenergy.=[(0.0300 m)² (0.0200 m-KE = 1/2mv² = 1/2(0.500 kg)(0.141 m/s)² = 4.97 × 10-³ J²])(20.0 N/m) (2.00 x 10-² m)²½

Name: PRACTICE ITUse the worked example above to help you solve this proble
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Description: PRACTICE ITUse the worked example above to help you solve this problem. A 0.545 kg object connected to a lightspring with a spring constant of 19.0 N/m oscillates on a frictionless horizontal surface.(a) Calculate the total energy of the system and

Given: The mass of the object: m=0.545 kg The spring constant: k=19.0 N/m

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Physics

Use the worked example above to help you solve this problem. A 0.545 kg object connected to a light spring with a spring constant of 19.0 N/m oscillates on a frictionless horizontal surface. (a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm. E = "max = J m/s (b) What is the velocity of the object when the displacement is 2.00 cm? ± m/s (c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm. KE = J PE, = J EXERCISE HINTS: GETTING STARTED I'M STUCK!

Use the worked example above to help you solve this problem. A 0.545 kg object connected to a light spring with a spring constant of 19.0 N/m oscillates on a frictionless horizontal surface. (a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm. E = "max = J m/s (b) What is the velocity of the object when the displacement is 2.00 cm? ± m/s (c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm. KE = J PE, = J EXERCISE HINTS: GETTING STARTED I'M STUCK!

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter16: Oscillatory Motion And Waves

Section: Chapter Questions

Problem 45PE: Suppose you have a 0.750kg object on a horizontal surface connected to a spring that has a force...

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