Use the equation mg sin A = umg cos A to determine the angle at which a waxed wood block on an inclined plane of wet snow begins to slide. Assume the coefficient of friction, u, is 0.17.
To determine the angle at which the waxed wood block on an inclined plane of wet snow begins to slide, we can use the equation:
mg sin A = umg cos A
where:
- m is the mass of the wood block
- g is the acceleration due to gravity
- A is the angle of inclination of the plane
- u is the coefficient of friction
To simplify the equation, we can cancel out the mass and acceleration due to gravity:
sin A = u cos A
Now we can substitute the given coefficient of friction, u = 0.17, into the equation:
sin A = 0.17 cos A
To solve for A, we can rearrange the equation:
sin A / cos A = 0.17
Using the trigonometric identity tan A = sin A / cos A, we get:
tan A = 0.17
Now we can take the inverse tangent of both sides to find the angle A:
A = tan^(-1)(0.17)
Using a calculator or a trigonometric table, we find:
A ≈ 9.96 degrees
Therefore, the angle at which the waxed wood block on an inclined plane of wet snow begins to slide is approximately 9.96 degrees.