With the given information, it is impossible to choose between the positive and

Question

With the given information, it is impossible to choose between the positive and negative solutions in part (b). Notice that the sum KE + PE, in part (c) equals the total energy E found in part (a), as it should (except for a small discrepancy due to rounding). Does doubling the initial displacement double the speed of the object at the equilibrium point? Explain. Yes, the maximum speed is directly proportional to the initial displacement. No, it multiplies the speed at the equilibrium point by Squareroot 2. No, it multiplies the speed at the equilibrium point by 4. No, the speed at the equilibrium point is unaffected. Use the worked example above to help you solve this problem. A 0.465 kg object connected to a light spring with a spring constant of 20.5 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 = J v_max = m/s (b) What is the velocity of the object when the displacement is 2.00 cm? plusminus m/s (c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm. KE = J PE_i = J For what values of x is the speed of the object 0.14 m/s? x = plusminus cm

Explanation / Answer

a) E = 0.5kx^2 = 0.5*20.5*(0.03)^2 = 9.225*10^-3 J

Now

E = 0.5mv_max^2

9.225*10^-3 = 0.5*0.465*v_max^2

v_max = 0.2 m/s

b) Conserving energy

E = 0.5*20.5*0.02^2 + 0.5*0.465*v^2

v = 0.1485 m/s

c) PE = 0.5*20.5*0.02^2 = 4.1*10^-3 J

KE = E - PE = 5.125*10^-3 J

Exercise

E = 0.5*20.5*x^2 + 0.5*0.465*0.14^2

x=0.02134m = 2.134 cm

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