Learning Goal: To practice Problem-Solving Strategy Simple Harmonic Motion II: E

Question

Learning Goal: To practice Problem-Solving Strategy Simple Harmonic Motion II: Energy EXECUTE the solution as follows A child's toy consists of a spherical object of mass 50 g attached to a spring One end of the spring is fixed to the side of the baby's crib so that when the baby pulls on the toy and lets go, the object oscillates horizontally with a simple harmonic motion. The amplitude of the oscillation is 6 em and the maximum velocity achieved by the toy is 32 m/s. What is the kinetic energy K of the toy when the spring is compressed 3.2 cm from its equilibrium position? Part B What is the kinetic energy of the object on the spring when the spring is compressed 3 2 em from its equilibrium postion? Express your answer in joules using three signiticant figures. View Available Hintis) 0 Submit Incorrect; Try Again; 5 attempts remaining EVALUATE your an Part C What is the potential energy U of the toy when the spring is compressed 3.2 cm from its equilibrium position? Express your answer in joules using three significant figures. Submit

Explanation / Answer

equating the kinetic energy equation

1/2*m*v2max = 1/2*k*A2

solving for k, we get

k = m*v2max / A2

k = 0.05*3.22 / 0.062

k = 142.22 N/m (spring constant)

also, we have

1/2mv2f + 1/2kxf2 = 1/2mvmax2

solving for final kinetic energy (first term in the above equation), we get

Kfinal = 1/2mvmax2 (1 - xf2/ A2 )

Kfinal = 0.1832 joules ------------------ > answer to part B

Part C

P.E = 1/2KX2

P.E = 0.5*142.2*0.032

P.E = 2.2752 JOULES.

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