Question

3. A wooden block is at rest on a wooden inclined

Answer 1

As the angle the plane makes with the horizontal is increased, the magnitude of the force of static friction between the block and the plane (2) increases

Static frictional force

Since the static frictional force between the block and the plane is given by F = μN where

• μ = coefficient of static friction and
• N = normal force on plane = component of weight of block perpendicular to the plane = Wcosθ where
• W = weight of block and
• θ = angle of inclined plane

Now, F = μN

F = μWcosθ

Since μ and W are constant, we see that

F ∝ cosθ and cosθ ∝ θ

So, F ∝ θ

Since the static frictional force is directly proportional to the angle the plane makes with the horizontal, when the angle the plane makes with the horizontal is increased, the static friction between the block and the plane increases.

So, As the angle the plane makes with the horizontal is increased, the magnitude of the force of static friction between the block and the plane (2) increases

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