5. A 5.4 kg block is projected by a spring up a plane that is inclined at 31° with the horizontal. The spring has a spring constant of 1800 N/m and is initially compressed 0.23 m. Assume there is no change in height and no friction while the spring is in contact with the block. a) How far up along the plane does the block go if the plane is frictionless? b) How far up along the plane does the block go if the coefficient of kinetic friction between the block and the plane is 0.44? c) If the block in part b) then slides back down against the frictional force, what is the block's speed when it reaches the original projection point?
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The potential energy in the spring is given by: \[ PE_{\text{spring}} = \frac{1}{2} k x^2 \] where \( k = 1800 \, \text{N/m} \) and \( x = 0.23 \, \text{m} \). \[ PE_{\text{spring}} = \frac{1}{2} \times 1800 \times (0.23)^2 \] Show more…
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