(7%) Problem 10: A block of mass rn = 1.5 kg is attached to a spring with spring
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(7%) Problem 10: A block of mass rn = 1.5 kg is attached to a spring with spring constant k = 510 N/m. It is initially at rest on an inclined plane that is at an angle of = 21° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is ,-0.12. In the initial position, where the spring is compressed by a distance of d= 0.12 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero 0 Randomized Variables m=1.5kg k = 510 N/m d=0.12 m = 21° Pk= 0.12 ©theexpertta.com 50% Part (a) What is the block's initial mechanical energy, EO in J? × 50% Part (b) If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion Grade Summary Deductions Potential 0% 100%Explanation / Answer
a) initial mechanical energy E0 = 1/2 k d2
= 1/2 * 510 * 0.122
= 3.67 J
b) W = delta PE + delta KE + delta PEspring
-muk m g L = -m g L sin theta + 1/2 k(L2 - d2)
-0.12 * 1.5 * 9.8 * L = -1.5 * 9.8 * L sin 21 + 1/2 * 510(L2 - 0.122)
-1.764 L = -5.27 L + 255(L2 - 0.122)
3.506 L = 255 L2 - 3.672
L = 0.127 m
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