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A block is sliding down a frictionless incline of angle 30 degrees. If the incli

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Question: 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?

Options:

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 90 degrees

Correct Answer: 45 degrees

Solution: 

The maximum angle for static friction is given by tan(θ) = μs. Here, θ = tan⁻¹(0.5) which is approximately 26.57 degrees, so the block can remain at rest at angles less than this.

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?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 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.
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