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A block of mass m is placed on a horizontal track of negligible friction. The mass is pushed against a spring and released (the mass is not attached to the spring). The block then slides up a rough incline plane of coefficient of kinetic friction μ and angle θ = arctan⁡(3/4). Assuming the spring constant is k = 18 mg/h, what distance must the spring be compressed so that the block's maximum height is h? Express your result in terms of the given quantities and any numerical and physical constants.

A block of mass m is placed on a horizontal track of negligible friction. The mass is pushed against a spring and released (the mass is not attached to the spring). The block then slides up a rough incline plane of coefficient of kinetic friction μ and angle θ = arctan⁡(3/4). Assuming the spring constant is k = 18 mg/h, what distance must the spring be compressed so that the block's maximum height is h? Express your result in terms of the given quantities and any numerical and physical constants.

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A block of mass m is placed on a horizontal track of negligible friction. The mass is pushed against a spring and released (the mass is not attached to the spring). The block then slides up a rough incline plane of coefficient of kinetic friction μ and angle θ = arctan ⁡ ( 3 4 ) . Assuming the spring constant is k = 18 m g / h , what distance must the spring be compressed so that the block's maximum height is h ? Express your result in terms of the given quantities and any numerical and physical constants.

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