roblem 15.46 Correct A 150 g block hangs from a spring with spring constant 13 N

Question

roblem 15.46 Correct A 150 g block hangs from a spring with spring constant 13 N/m. Att-0 s the block is 21 cm below the equilibrium point and moving upward with a speed of 137 cm/s Part B What is the block's distance from equilibrium when the speed is 66 cm/s ? Express your answer to two significant figures and include the approp 0.2 Submit Incorrect Try Again; 3 attempts remaining Part C What is the block's distance from equilibrium at t 2.0s? Express your answer to two significant figures and include the appropri #Halue Units Submit

Explanation / Answer

w = sqrt(k /m) = sqrt(13 / 0.150) = 9.31 rad/s

v^2 = w^2 ( A^2 - x^2)

1.37^2 = 9.31^2(A^2 - 0.21^2)

A = 0.256 m

Now for v = 66 cm/s = 0.66 m/s

0.66^2 = 9.31^2 (0.256^2 - x^2)

x = 0.25 m Or 25 cm ........Ans(B)

(C) x = (0.256) cos(9.31 t + phi)

at t = 0 , - 0.21 = 0.256 cos(phi)

phi = 145 deg OR 225 deg

v = dx/dt = - 2.38 sin(9.31t + phi)

at t = 0, 1.37 = -2.8 sin(phi)

phi = 225 deg Or 3.93 rad

x = (0.256) cos(9.31t + 3.93)

t = 2 s

x = - 0.22 m Or 22 cm

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