The maximum speed of the object is 1.33 m/s.
The law of conservation of energy states that energy can neither be created nor destroyed. It can only be converted from one energy form to another.
The mass of the object = 195g = 0.195 kg
Force constant =76.5 n/m
The object is pulled 6.75 cm to the right of equilibrium i.e. A = 6.75 cm = 0.0675 m
The maximum speed of the object is determined using the law of conservation of energy.
[tex]\omega=\sqrt{\frac{k}{m}}[/tex]
[tex]\omega=\sqrt{\frac{76.5}{0.195}}[/tex]
[tex]\omega=[/tex] 19.8 rad/s
The maximum speed of the spring block system is given by A[tex]\omega[/tex].
Hence, the maximum speed = A[tex]\omega[/tex] = 19.8 x 0.0675 = 1.33 m/s.
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The complete question is -
A 195 g object is attached to a spring that has a force constant of 76.5 n/m. the object is pulled 6.75 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. Calculate the maximum speed of the object.
