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(A) According to the law of conservation of energy,the kinetic energy of the body is converted into the elastic potential energy of the spring at maxi

Vedclass · Accepted Answer

$0.15$

Vedclass · Answer

(A) According to the law of conservation of energy,the kinetic energy of the body is converted into the elastic potential energy of the spring at maximum compression.Let $m = 0.5 \ kg$,$v = 1.5 \ m/s$,$k = 50 \ N/m$,and $x$ be the maximum compression.Kinetic Energy = Elastic Potential Energy$\frac{1}{2} mv^2 = \frac{1}{2} kx^2$$mv^2 = kx^2$$0.5 	imes (1.5)^2 = 50 	imes x^2$$0.5 	imes 2.25 = 50 	imes x^2$$1.125 = 50 	imes x^2$$x^2 = \frac{1.125}{50} = 0.0225$$x = \sqrt{0.0225} = 0.15 \ m$Therefore,the maximum compression is $0.15 \ m$.

$A$ body of mass $0.5 \ kg$ moves with a speed of $1.5 \ m/s$ on a smooth horizontal surface. It hits a massless spring with a force constant $k = 50 \ N/m$. What will be the maximum compression of the spring in $m$?

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