A 5.0 kg block is placed on a 30 degree friction-less incline on the surface of earth. What will be the acceleration of the block?

The net force on the block parallel to the incline is

∑ F = -mg sin(θ) = ma

where m is the mass of the block, g = 9.8 m/s² is the acceleration due to gravity, θ is the angle the incline makes with the horizontal, and a is the acceleration of the block. Solving for a gives

a = -g sin(θ)

so the block would slide down the incline with acceleration

a = - (9.8 m/s²) sin(30°) = -4.9 m/s²

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