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A 103.8kg wood block is resting on a wooden floor. You can push a maximum of 1061.5 N on the block without moving it. If you continue to exert this push force once the block starts to move, find the magnitude of its acceleration (in m/s2 )? ( Coefficent of Kinetic friction between wood blocks is 0.3)

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MathPhys

Answer:

7.286 m/s²

Explanation:

Let's say P is the applied force and F is the force of friction.  Remember that friction is the product of normal force and the coefficient of friction (F = Nμ).

Apply Newton's second law in the y direction:

∑F = ma

N − mg = 0

N = mg

Apply Newton's second law in the x direction:

∑F = ma

P − F = ma

P − Nμ = ma

Substitute and solve for a:

P − mgμ = ma

a = (P − mgμ) / m

Given P = 1061.5 N, m = 103.8 kg, g = 9.8 m/s², and μ = 0.3:

a = (1061.5 − 103.8×9.8×0.3) / 103.8

a = 7.286 m/s²