please show steps and equations used I), (II) A mass m = 0.70 kg slides along th

Question

please show steps and equations used

I), (II) A mass m = 0.70 kg slides along the x-axis of a horizontal frictionless surface with speed v 2.2 m/s. It runs into a re- laxed spring oriented along the x-axis. This spring had previous- ly been observed to stretch by 3.8 cm when it was oriented vertically with the mass suspended from it. (a) What is the max- imum compression of the spring when the mass runs into it? 23 (b) The mass rebounds as a result of having compressed the spring. What is its velocity when it leaves contact with the spring?

Explanation / Answer

a)

Spring Constant

K=Mg/x=0.7*9.8/0.038=180.5 N/m

By Conservation of energy

(1/2)MV2=(1/2)KXmax2

0.7*2.22=180.5*Xmax2

Xmax=0.137 m or 13.7 cm

b)

since there is no loss of energy

V=2.2 m/s

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