A spring with a spring constant of 2000 N/m is compressed 10.0 cm on a horizonta

Question

A spring with a spring constant of 2000 N/m is compressed 10.0 cm on a horizontal surface. Then a 1.00 -kg object is attached to it and released. At the relaxed-length position of the spring, the mass leaves the spring and the table goes from very smooth to rough, with a coefficient of friction of 0.500. There is a wall 50 .0 cm away from the release point. Determine whether the mass will make it back to the spring after one bounce off the wall, assuming it rebounds elastically (no speed loss) off the wall. If it does make it to the spring, how far doe s it compress it? If it doesn't make it to the spring, where is its final location?

Explanation / Answer

energy stored in spring = (1/2) k x^2 = (1/2) * 2000* 0.10^2 = 10.0 Joules

work done by friction if block travels back to spring =

= u mg d = 0.5 * 1.00 * 9.8 * 1.00 = 4.90 Joules

SO YES, the block does return to the spring... the energy given to the block by the spring is greater than the energy the friction can take away. So the block still has 10.0 - 4.90 = 5.10 Joules of energy when it returns to the spring.

(b) the spring will then compress

energy = (1/2) k x^2

5.10 = (1/2) * 2000 * x^2

x = 0.0714 m = 7.14 cm

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