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Compression and Speed of Spring

Please assist me with the attached 10 exam review problems.

Compression and speed of spring, acceleration of gravity, tension in a tightrope, speed of a wave

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01 This uses conservation of energy where the potential energy is converted to kinetic energy of motion. When the potential energy goes to zero the kinetic energy is at a maximum Potential energy is 1/2Kx^2 for the spring the kinetic energy of the mass is ½ m v^2. x for the compression is 6 cm or 0.06 m. K is 18.7 N/m and m is 0.47 Kg

so v^2 = 18.7 N/m x (0.06 m)^2/0.47 Kg = 0.143234043 srqrt gives 0.37 0.4 m/sec to 1 sig fig distance for compression was one sig fig.

02 The energy is conserved so total energy = potential + kinetic
the potential at 1.6 cm is ½ kx^2 for x = 0.016 m and the given k the total energy is for the 6 cm compression which is ½ k x^2 for x = 0.6 m and the given k
The kinetic energy is ½ m v^2 for the speed at the compression of 1.6 ...

Solution Summary

The solutions are explained with full calculations.