A block is sliding down a frictionless incline of angle 30 degrees. If the incli
Practice Questions
Q1
A block is sliding down a frictionless incline of angle 30 degrees. If the incline has a coefficient of static friction of 0.5, what is the maximum angle at which the block can remain at rest?
30 degrees
45 degrees
60 degrees
90 degrees
Questions & Step-by-Step Solutions
A block is sliding down a frictionless incline of angle 30 degrees. If the incline has a coefficient of static friction of 0.5, what is the maximum angle at which the block can remain at rest?
Correct Answer: 26.57 degrees
Step 1: Understand that the block is on an incline and we need to find the maximum angle where it can stay at rest.
Step 2: Know that the coefficient of static friction (μs) is given as 0.5.
Step 3: Use the formula for the maximum angle of static friction, which is tan(θ) = μs.
Step 4: Substitute the value of μs into the formula: tan(θ) = 0.5.
Step 5: To find θ, take the arctangent (inverse tangent) of 0.5: θ = tan⁻¹(0.5).
Step 6: Calculate tan⁻¹(0.5) using a calculator or a table, which gives approximately 26.57 degrees.
Step 7: Conclude that the block can remain at rest at angles less than 26.57 degrees.
Static Friction – Understanding the role of static friction in preventing motion on an incline.
Inclined Plane Dynamics – Analyzing forces acting on an object on an inclined plane.
Trigonometric Relationships – Using trigonometric functions to relate angles and coefficients of friction.
