189 (25%) Problem 1: A block of mass m # 4.5 kg is attached to a spring with spr

Question

189 (25%) Problem 1: A block of mass m # 4.5 kg is attached to a spring with spring constant k 950 N/m. It is initially at rest on an inclined plane that is at an angle of ?-29° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is = 0.18. In the initial position, where the spring is compressed by a distance of d 0.13 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. Randomized Variables me 45 kg k 950 N/m d 0.13 m Dtheexpertta.com k 0.18 g2 9/ 50% Part (a) What is the block's initial mechanical energy, EO in J? S0% Part (b) If the spring pushes the block up the incline, what distance, L in spring remains attached to both the block and the fixed wall throughout its motion. Grade Summary Potential er MienP cotanO asinO acos( atanO acotanO sinh0 0 O DegreesRadians Hint I give up Hintsi

Explanation / Answer

(A) mechanical energy = KE + gravitational PE + spring PE

= 0 + 0 + (950 x 0.13^2 / 2)

{ spring PE = k d^2 / 2}

= 8.03 J  

(B) Mechanical energy at final position,

KE = 0

gravt PE = m g L sin(theta)

spring PE = 0

energy dissipated = fk L = uk m g cos(theta) L

so from energy conservation,

8.03 = m g L sin(theta) + uk m g L cos(theta)

8.03 = (4.5 x 9.8) L ( sin29 + 0.18cos29)

L = 0.283 m

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