Question

A block of mass m = 4.5 kg is attached to a spring with spring constant k = 710 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 25° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μ_k=0.18. 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. 

Part (a) What is the block's initial mechanical energy, E₀ in I?

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.

Answer 1

B)

Using law of conservation of energy,

5.11 = (0.5 x 710 x Y^2) + (4.5 x 9.8 x (0.12 + Y) sin(25) + 0.18 x 4.5 x 9.8 (0.12 + Y) cos(25)

5.11 = 355 Y^2 + 18.64 Y + 2.24 + 7.19 Y + 0.86

355 Y^2 + 25.83 Y - 2.01 = 0

Y = 0.047 m

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