Suppose a smooth glass-top table is tilted slowly. The angle, A, at which a glass plate on the table begins to slide is 43º. Use the equation mg sin A = umg cos A to determine the coefficient of friction, u.
A)0.43
B)0.22
C)0.90
D)0.93
tanA=mu
tan 43 = either c, or d. grab your calculator.
To determine the coefficient of friction, u, we can use the equation mg sin A = umg cos A.
Given that the angle at which the glass plate begins to slide is 43º, we can substitute this value into the equation.
mg sin 43º = umg cos 43º
Since the mass, m, and the acceleration due to gravity, g, are common on both sides of the equation, they cancel out.
sin 43º = u cos 43º
Next, we can divide both sides of the equation by cos 43º to isolate the coefficient of friction, u.
u = sin 43º / cos 43º
Using a scientific calculator or trigonometric identity, we can simplify this expression.
u = tan 43º
Using a calculator, we find that tan 43º is approximately 0.926
Therefore, the coefficient of friction, u, is approximately 0.926.
None of the given options (A) 0.43, (B) 0.22, (C) 0.90, or (D) 0.93 matches the calculated value.