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.
mg*sin A = u*mg*Cos A
Divide both sides by mg*Cos A:
sin A/Cos A = u
sin A/Cos A = Tan A
Tan A = u = 0.17
A = 9.65o
To determine the angle at which the waxed wood block begins to slide on the inclined plane of wet snow, we can rearrange the given equation:
mg sin A = umg cos A
Dividing both sides of the equation by mg and cos A:
tan A = u
Substituting the given coefficient of friction, u = 0.17:
tan A = 0.17
To find the angle A, we need to take the inverse tangent (or arctan) of 0.17:
A = arctan(0.17)
Using a calculator or math software, we can find the value of A to be approximately:
A ≈ 9.75 degrees
Therefore, the angle at which the waxed wood block begins to slide on the inclined plane of wet snow is approximately 9.75 degrees.
To determine the angle at which the waxed wood block on an inclined plane of wet snow begins to slide, we can use the given equation:
mg sin A = umg cos A
Here's how to solve this equation step by step:
Step 1: Identify the given values:
- The coefficient of friction, u, is given as 0.17.
- The mass of the wood block, m, is given (even though the value is not provided in the question).
- The values for g (acceleration due to gravity) and the mass of the block will cancel out in the equation, so we don't need specific values for those.
Step 2: Substitute the values into the equation:
0.17 * g * cos A = g * sin A
Step 3: Simplify the equation:
Divide both sides of the equation by g to eliminate it:
0.17 * cos A = sin A
Step 4: Solve for A (the angle):
To solve for A, we can use inverse trigonometric functions. In this case, we can use the arctan function (tan^(-1)) to find the angle for which the tangent is equal to the ratio of sine and cosine:
A = tan^(-1)(0.17)
Step 5: Use a calculator to find the arctan value:
Using a calculator, find the arctan of 0.17. The arctan function is typically denoted as tan^(-1) on calculators. Enter 0.17 and press the tan^(-1) button to get the angle in radians. If you want the angle in degrees, convert it using the conversion factor: 180°/π rad.
Therefore, by solving the equation and using a calculator, you can determine the angle at which the waxed wood block on an inclined plane of wet snow begins to slide.