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How far will a spring of spring constant 7.0 N/m be compressed if a 1.3 kg mass runs into the end...

Question:

How far will a spring of spring constant 7.0 N/m be compressed if a 1.3 kg mass runs into the end of it at 2.2 m/s?

Spring Restoring Force:

When a force is applied to the spring in order to compress the spring or stretch the spring than a restoring force is set up by the spring in the direction opposite to the applied and equal to the product of spring constant and the deflection of the spring.

Answer and Explanation:

Given

Spring constant of the spring is {eq}k=7\ N/m {/eq}

Mass of the object is {eq}m=1.3\ kg {/eq}

The velocity of the object is {eq}v=2.2\ m/s {/eq}

Now from the conservation of energy :

{eq}K.E=P.E_s\\ \frac{1}{2}mv^2=\frac{1}{2}kx^2\\ 1.3\times (2.2)^2=7\times x^2\\ x^2=0.898\\ x=0.94\ m {/eq}

Thus, the compression of the spring is 0.94 m


Learn more about this topic:

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