A spring of stiffness k is placed horizontally and a ball of mass m strikes the spring with a velocity v. Find the maximum compression of the spring. Take m = 5 kg, k = 500 N/m, v = 3m/s

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written 8.4 years ago by

teamques10 ★ 68k

• modified 4.5 years ago

engineering mechanics

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written 8.4 years ago by

teamques10 ★ 68k

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Given:-

$m=5kg \\ v=3m/s \\ k=500N/m$

To find:-

Maximum compression (x or $\delta $ )

Solution:-

Using work energy principle,

(Kinetic energy of ball) = (potential energy of compressed spring)

$\therefore \dfrac 12 mv^2= \dfrac 12 k\delta^2 \\ \delta =\sqrt{\dfrac mk} v \\ =\sqrt{\dfrac 5{500}}.3 \\ \delta =0.3m \Rightarrow Ans$

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