I need the answer for B Part A Problem 10.72 What is the maximum compression of

Question

I need the answer for B

Part A Problem 10.72 What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. A 11 kg box slides 4.0 m down the frictionless ramp shown in the figure(Fioure 1) then collides with a spring whose spring constant is 230 N/m Asmar= 1.6 m Submit My Answers Give Up Correct Significant Figures Feedback: Your answer 1.62 m was either rounded differently or used a different number of significant figures than required for this part. Figure 1 -of! Part B At what compression of the spring does the box have its maximum speed? Express your answer to two significant figures and include the appropriate units. 4.0 m Submit MYAnswers Give Up Incorrect; Try Again; 5 attempts remaining

Explanation / Answer

Given

mass of box m = 11 kg, sliding down the incline is 4.0 m , with angle of inclination is theta= 30 degrees

spring constant k = 230 N/m

Part A , maximum compression is Ds max = 1.62 m,

mg sin theta*xi = mg sin theta*xf + 0.5*k*x^2

11*9.8*4*sin30 = 11*9.8 *x*sin 30+0.5*230*x^2 ==> x = -1.62 m

Paart B

we know that the box will have max speed or max kientic energy at equilibrium position (wher the net force =0)

so the force at maximum displacement is

Fx = -kx -mg sin theta

equating Fx = 0

0 = -kx - mg sin theta

kx = mg sin theta

x = mg sin theta /k

x = 11*9.8 sin 30 /(230) m

x = 0.2343 m

so here x = -0.2343 m

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