Answer :
The angle of the incline must be approximately 18.8 degrees for the crate to slide with an acceleration of 5.93 m/s^2.
When the crate slides down the inclined surface, there are two main forces acting on it: the gravitational force (mg) and the frictional force (μmg) due to kinetic friction. The component of the gravitational force parallel to the incline is mgsinθ, where θ is the angle of the incline. The equation of motion for the crate along the incline can be written as:
mgsinθ - μmg = ma,
where m is the mass of the crate, g is the acceleration due to gravity, μ is the coefficient of kinetic friction, and a is the acceleration of the crate.
Rearranging the equation, we get:
gsinθ - μg = a.
Substituting the given values, g = 9.8[tex]m/s^2[/tex], μ = 0.167, and a = 5.93 [tex]m/s^2[/tex], we can solve for θ:
9.8sinθ - 0.167 * 9.8 = 5.93.
Simplifying the equation and solving for θ, we find:
θ ≈ 18.8 degrees.
Therefore, the angle of the incline must be approximately 18.8 degrees for the crate to slide with an acceleration of 5.93 m/s^2.
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