A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is:

Question

G1 Physics · Accepted Answer

Image The block of mass 5 kg descends through a vertical height: h = 10 sin30° = 5 m The 2 m horizontal portion before the spring is smooth. During compression x of the spring, friction acts on the rough surface: f = μmg = 0.5 × 5 × 10 = 25 N Using work-energy theorem from release to maximum compression: mgh - fx - ½kx² = 0 5 × 10 × 5 - 25x - ½(100)x² = 0 250 - 25x - 50x² = 0 2x² + x - 10 = 0 Solving: x = 2 m