A 0.250-kg block is placed on a light vertical spring $k = 5.00 \times 10^3 \text{ N/m}$ and pushed downwards, compressing the spring 0.100 m.

# A 0.250-kg block is placed on a light vertical spring $k = 5.00 \times 10^3 \text{ N/m}$ and pushed downwards, compressing the spring 0.100 m.

393k points

A 0.250-kg block is placed on a light vertical spring $k = 5.00 \times 10^3 \text{ N/m}$ and pushed downwards, compressing the spring 0.100 m.  After the block is released, it leaves the spring and continues to travel upwards.  What height above the point of release will the block reach if air resistance is negligible?

A 0
bhdrkn

389.5k points

The potential energy contained in a spring is:

$PE_s = \frac{1}{2}k x^2$

The potential energy of the spring at its lowest point, is turned into gravitational potential energy at it's highest point.  Therefore,

$\frac{1}{2}k x^2 = mgh \,\,\, \to \,\,\, h=\frac{k x^2}{2gm} = \frac{(5.00 \times 10^3 \, N/m)(0.100 \, m)}{2(9.8 \, m/s^2)(0.250 \, kg)} = 102 \, meters$

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