Learning Library

# Factors Affecting Friction

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### Problem

What factors affect friction?

### Materials

• Large book (e.g. text book, coffee table book)
• Protractor
• Ice cube
• Rubber eraser
• Coin

### Procedure

1. Lay the book flat on a table.
2. Place one of your objects (ice cube, eraser, or coin) on the book.
3. Slowly lift one end of the book (or the book’s cover) until the object starts sliding. Use the protractor to note the angle the book makes with the table when this happens.
4. Repeat the above steps for each of your objects. Do the objects start sliding at different angles? Which object starts sliding at the shallowest angle? The steepest?
5. Tear the eraser into several smaller pieces of different sizes. Place all the pieces on the book and tilt it again. Do they all start sliding at the same angle? How does this angle compare to the angle you recorded for the whole eraser?
6. Break up the ice cube into smaller pieces (easy to do if you put the cube in a zip lock bag and whack it a few times with a hammer). Repeat step 5 with the ice cube pieces.

### Results

The ice cube slides first, followed by the coin, and then the eraser. Breaking the eraser and ice cube up into smaller pieces doesn’t make a big difference in regard to the angle at which everything starts sliding. All the pieces should start sliding at roughly the same angle.

### Why?

The frictional force does not depend on mass or surface area. All that really matters is the types of materials that are in contact. Physicists describe the strength of friction with a single number called the coefficient of friction. The coefficient is a number usually between zero and one; the higher the number, the stronger the friction. The coefficient is also unique to every pair of objects: rubber on ice has a different coefficient of friction than rubber on wood, for example.

To make things a little more complicated, there are actually two coefficients for every pair of materials, one for when the objects are moving and one for when they’re standing still. When everything is stationary, the objects feel static friction. When they are moving, kinetic friction takes over. Kinetic friction is almost always lower than static friction. That’s why it takes more force to get something moving but less to keep it moving.

In this experiment, you had to keep tipping the book until the force of gravity became stronger than the friction force. Both forces depend on the angle of the book. As long as the friction force is larger, the objects won’t move.

For extra credit, you can use the angles you recorded to calculate the coefficient of friction for the ice, coin, and eraser. Looking at the figure, there are two forces that determine whether or not the objects move: friction and gravity. The force from friction is Ff = μmgcosθ, where

• μis the coefficient of friction,
• m is the mass,
• g is gravitational acceleration, and
• θis the angle of the book.

The force from gravity is Fg = mgsinθ. The objects start sliding when gravity is greater than friction, or mgsinθ > μmgcosθ.

Because m and g are on both sides of the inequality, they cancel out. Mass and gravity don’t matter! All that matters is the angle. Rearranging that inequality, you find out that things start sliding when tanθ > μ. To calculate the coefficient of friction for each of your objects, take the tangent of the angle at which each started sliding (that’s the TAN button on your calculator). Write down your results here:

 Object Angle (degrees) Coefficient Ice Coin Eraser

How do the coefficients compare? Do you notice a relationship between the value of the coefficient and when it started sliding?

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