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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 cm and the maximum velocity achieved by the toy is 3.2 m/s . What is the kinetic energy K of the toy when the spring is compressed 5.1 cm from its equilibrium position?

Respuesta :

Answer:

0.07103 J

Explanation:

[tex]v_m[/tex] = Maximum velocity = 3.2 m/s

m = Mass of object = 50 g

x = Compression of spring = 5.1 cm

A = Amplitude of oscillation = 6 cm

[tex]\omega[/tex] = Angular speed

The maximum velocity is given by

[tex]v_m=\omega A\\\Rightarrow \omega=\frac{v_m}{A}\\\Rightarrow \omega=\frac{3.2}{0.06}\\\Rightarrow \omega=53.33\ rad/s[/tex]

Kinetic energy of the spring is given by the expression

[tex]K=\frac{1}{2}m\omega^2(A^2-x^2)\\\Rightarrow K=\frac{1}{2}0.05\times 53.33^2(0.06^2-0.051^2)\\\Rightarrow K=0.07103\ J[/tex]

The kinetic energy of the toy when the spring is compressed is 0.07103 J