Answer :
Final answer:
To find the angle at which a 42.0 kg crate slides down an incline due to gravity with an acceleration of 5.96 m/s^2 given a coefficient of kinetic friction of 0.227, we use physics equations of motion, friction and gravity. These calculations yield an answer of θ = 44.2 degrees. This means the incline should be set at an angle of 44.2 degrees for the crate to slide at the required acceleration.
Explanation:
To find the angle of the incline in which a crate slides due to gravity with a specified acceleration, we will use physics equations related to motion, friction, and gravity.
We know that the acceleration due to gravity, g, is 9.81 m/s^2, the given mass of the crate, m, is 42.0 kg and coefficient of kinetic friction, µk, is 0.227. The crate slides at 5.96 m/s^2.
The frictional force that opposes motion is µk*m*g*cosθ but the net force acting on the crate is m*g*sinθ - µk*m*g*cosθ = m*a. By dividing through by m*g, and rearranging, we get: sinθ - µk*cosθ = a/g.
Solving this for θ using the given values of a, g, and µk yields the answer, θ = 44.2 degrees, which is the angle of the incline for the crate to slide with the specified acceleration.
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