### PROBLEM:

### (a) When rebuilding her car’s engine, a physics major must exert 300 N of force to insert a dry steel piston into a steel cylinder. What is the normal force between the piston and cylinder?

### (b) What force would she have to exert if the steel parts were oiled?

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**SOLUTION:**

Shown below is the table for the coefficient of static and kinetic friction copied from the book. The coefficient of kinetic friction with the system Steel on Steel (dry) is 0.3 while the coefficient of kinetic friction with the system Steel on Steel (oiled) is 0.03.

**PART A**

To solve for the unknown normal force, we shall use the formula for friction

Solving for *N*, we have

The normal force between the dry steel piston and steel cylinder is 1,000 Newton.

**PART B**

If the steel parts were oiled, the coefficient of kinetic friction will be changed to 0.03. Therefore, the required force would only be

The force would only be 30.0 Newtons.

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