Math Problem Statement

We measure the maximum static friction the table exerts on a block both when we do and do not push down on the block from above. What should happen to the maximum static friction when we push down on the block?

Solution

The problem you're asking about involves understanding the relationship between static friction and the forces acting on an object.

The key point here is that the maximum static friction force, fsf_s, is proportional to the normal force, FNF_N, acting on the object. This is mathematically represented by:

fs=μsFNf_s = \mu_s F_N

where:

  • μs\mu_s is the coefficient of static friction, and
  • FNF_N is the normal force, which is the force exerted perpendicular to the surfaces in contact (in this case, the block and the table).

When you push down on the block, you increase the normal force FNF_N because you're adding an additional force to the weight of the block. Since fsf_s is proportional to FNF_N, increasing the normal force increases the maximum possible static friction.

Answer:

The correct statement is A: "The maximum static friction should be more when we push down on the block."

Would you like more details, or have any questions?

Here are some related questions to explore this concept further:

  1. What happens to the maximum static friction if the block is on an inclined plane?
  2. How does the coefficient of static friction, μs\mu_s, change between different surfaces?
  3. Can pushing the block horizontally change the normal force?
  4. How is the static friction force different from the kinetic friction force?
  5. How can you experimentally determine the coefficient of static friction between two surfaces?

Tip: Static friction only resists motion up to a certain limit. Once that limit is exceeded, kinetic friction takes over, which is usually smaller than static friction.

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Math Problem Analysis

Mathematical Concepts

Static Friction
Normal Force

Formulas

f_s = μ_s * F_N

Theorems

Static Friction and Normal Force Proportionality

Suitable Grade Level

Grades 9-12