High School

This time, we have a crate with a mass of 42.0 kg on an inclined surface, with a coefficient of kinetic friction of 0.227. Instead of pushing the crate, you let it slide down due to gravity.

What must the angle of the incline be for the crate to slide with an acceleration of 5.96 m/s²?

A. 44.2 degrees
B. 49.1 degrees
C. 39.3 degrees
D. 63.8 degrees

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.

Learn more about Physics of Motion here:

https://brainly.com/question/13966796

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