A 1.0 kg box moves back and forth on a horizontal frictionless surface between t

Question

A 1.0 kg box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.6 cm , and then is released from rest. (Sorry, I do not know how to include the figure provided in Mastering Physics. There is a frictionless surface where there is a box in between 2 springs. The spring on the left hand side is k= 32 N/cm, while the spring on the right hand side is k= 16 N/cm).

Part A: By how much will the box compress the weaker spring? Express your answer using two significant figures. l = ? cm
Part B: What is the maximum speed the box will reach? Express your answer using two significant figures. vmax = ? m/s

Explanation / Answer

(A) Applying energy conservation,

initial PE + KE = final PE + KE

{ Spring PE = k x^2 /2 }
(32 x 10^2 N / m ) (0.046 cm)^2 / 2 + 0 = (16 x 10^2 N/m) (x^2) /2 + 0

x = 0.065 m OR 6.5 cm ........Ans

(B) APplying energy conservation again ,

KE will be max when spring PE = 0

(32 x 10^2) (0.046^2)/2 = 1 V^2 /2 + 9

v =2.60 m/s

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