A 0.44-kg object connected to a light spring with a force constant of 22.4 N/m o

Question

A 0.44-kg object connected to a light spring with a force constant of 22.4 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. 0.28 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm/s (b) Determine the speed of the object when the spring is compressed 1.5 cm cm/s (c) Determine the speed of the object when the spring is stretched 1.5 cm. cm/s (d) For what value of x does the speed equal one-half the maximum speed? cm

Explanation / Answer

M=0.44kg k=22.4N/m

Apply law of conservation of energy

1/2kx^2=1/2mv^2.....eq 1

22.4×(0.4)^2÷0.44=v^2

v=0.285m/s

b)substitute for x =0.015m in eq 1

1/2×22.4×(0.015)^2=1/2 ×0.44×v^2

v=0.107m/s

C) when spring stretched by x=1.5cm velocity wil remain same as it is for compression i.e v =0.107m/s

d) max speed = 0.285 m/s

1/2×0.285=0.1425

1/2kx^2=1/2mv^2

22.4x^2=0.44×(0.1425)^2

x=1.99cm

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