A 250-kg crate is placed on an adjustable inclined plane. If the crate slides down the incline with an acceleration of 0.25 m/s² when the incline angle is 25 $\degree$, then what should the incline angle be for the crate to slide down the plane at constant speed? Note: g = 9.8 m/s². A) 12 $\degree$ B) 21 $\degree$ C) 24 $\degree$ D) 29 $\degree$

Question

Quizplus · Accepted Answer

The crate will slide down the plane at constant speed when the force of gravity pulling the crate down the plane is equal to the force of friction opposing the motion. The force of gravity is given by Fg = mg sin(theta), where m is the mass of the crate, g is the acceleration due to gravity, and theta is the angle of the incline. The force of friction is given by Ff = mu*mg cos(theta), where mu is the coefficient of friction. For the crate to slide down the plane at constant speed, we must have Fg = Ff, or mg sin(theta) = mu*mg cos(theta). Solving for theta, we get theta = arctan(mu). Plugging in the given values, we get theta = arctan(0.25) = 14.04 degrees.

A 250-Kg Crate Is Placed on an Adjustable Inclined Plane °\degree°

A 250-Kg Crate Is Placed on an Adjustable Inclined Plane $\degree$