A 2.5 kg box that is sliding on a frictionless surface with a speed of 11 m/s ap

Question

A 2.5 kg box that is sliding on a frictionless surface with a speed of 11 m/s approaches a horizontal spring. The spring has a spring constant of1800 N/m .

If one end of the spring is fixed and the other end changes its position, how far will the spring be compressed in stopping the box?

Express your answer using two significant figures. (in m)

How far will the spring be compressed when the spring is partially compressed and the box’s speed is reduced to half of its initial speed?

Express your answer using two significant figures. (in m)

Explanation / Answer

part A
KE of box = 0.5 * 2.5 * 11^2 = 151.25 = energystored in spring = 0.5 * 1800 * d^2

900 d^2 = 151.25
d = 0.41 m = the spring be compressed in stopping the box

part B
KE of box = 0.5 * 2.5 * 5.5^2 = 37.8 = energystored in spring = 0.5 * 1800 * d^2

900 d^2 = 37.8
d = 0.205 m = the spring be compressed when the box’s speed is reduced to half of its initial speed

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