Determine the angle to the nearest degree at which a desk can be tilted before a paperback book on the desk begins to slide. Use the equation mg sin A = umg cos A and assume u = 1.11. (Enter only the number.)
I got 115 degrees.
huh? 115° ?
So, it was tilted up past the vertical, and then over onto its back?
When you get an answer, check to see whether it makes sense.
I still don't understand the lesson, but 48 degrees?
It was 48
yep. tan A = 1.1
Mg*sinA = Force parallel with plane.
Mg*CosA = Normal force or Force perpendicular to plane.
u*Mg*CosA = Force of static friction.
Mg*sinA - u*Mg*CosA = M*a. a = 0.
Divide both sides by Mg:
sinA - u*CosA = 0,
u*CosA = sinA,
sinA/CosA = u,
TanA = u = 1.11,
A = 48o.
To determine the angle at which the desk can be tilted before the book begins to slide, we can use the equation mg sin A = umg cos A, where m is the mass of the book, g is the acceleration due to gravity, A is the angle of tilt, and u is the coefficient of static friction.
In this equation, mg sin A represents the force pulling the book downwards (its weight) and umg cos A represents the maximum frictional force between the book and the desk. When the book is about to slide, these forces will be equal.
Given that u = 1.11, we can substitute this value into the equation:
mg sin A = umg cos A
Now, we need to solve for A by canceling out the common factors:
sin A = u cos A
Next, we can use the trigonometric identity sin A / cos A = tan A to rewrite the equation as:
tan A = u
Now we can find the angle A by taking the inverse tangent (tan^⁻1) of both sides:
A = tan^⁻1(u)
Substituting the value of u = 1.11 into the equation, we get:
A = tan^⁻1(1.11)
Using a scientific calculator, we can find the inverse tangent of 1.11, which is approximately 46.79 degrees. Rounding this to the nearest degree, the angle at which the desk can be tilted before the book begins to slide is approximately 47 degrees.
Therefore, the correct answer is 47.