Quick help with physics force problem. easy points?

Question

A 250kg crate is placed on an adjustable inclined plane. If the crate slides down the incline with an acceleration of 0.7m/s^2 when the incline angle is 25 degrees, then what should the incline angle be for the crate to slide down the plane at constant speed?

Answer 1

Looking at a FBD of the crate, using down the plane parallel to it as positive, the forces are:

gravity parallel to the inclined plane:

sin(th)*m*g
friction
-cos(th)*m*g*u

from the problem statement:
.7=sin(25)*g-cos(25)*g*u

solving for u
(.7/g -sin(25))/(-cos(25))=u
u=.388

now set the angle so that
0=sin(th)-cos(th)*u
tan(th)=u
th=atan(u)
=21.2 degrees

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