Static friction is calculated using a range, not a single value, up to a maximum value. Here's how to understand and calculate it:
Understanding Static Friction
Static friction is the force that prevents an object from starting to move when a force is applied. It's a reactive force, meaning it adjusts itself to match the applied force, up to a limit. Once the applied force exceeds this limit, the object begins to move, and the friction becomes kinetic.
The Formula and Calculation
The formula for the maximum static friction force is:
*Fs,max = μs FN**
Where:
- Fs,max is the maximum possible static friction force. This is the point just before the object starts to move.
- μs is the coefficient of static friction. This is a dimensionless number that depends on the two surfaces in contact. It's determined experimentally. A higher coefficient means more friction.
- FN is the normal force. This is the force pressing the two surfaces together, usually the object's weight if the surface is horizontal (FN = mg, where m is mass and g is the acceleration due to gravity).
Important Considerations:
-
Static Friction is not constant: The actual static friction force (Fs) can be any value between zero and Fs,max. It adjusts to match the applied force, preventing movement. For example, if you push a box with 5N of force and the box doesn't move, the static friction force is 5N in the opposite direction.
-
The Coefficient of Static Friction (μs): This value is experimentally determined and is a property of the two surfaces in contact. It typically ranges from 0 to 1, but can sometimes be greater than 1. You usually need to look this value up in a table or be given it in a problem.
-
Normal Force (FN): On a flat, horizontal surface, the normal force is usually equal to the weight of the object (mg). However, if the surface is inclined, or if there's another vertical force acting on the object, you need to calculate the normal force carefully. Draw a free body diagram!
Example Calculation
Let's say you have a 10 kg box resting on a wooden floor. The coefficient of static friction (μs) between the box and the floor is 0.4.
- Calculate the normal force: FN = mg = (10 kg) * (9.8 m/s2) = 98 N
- Calculate the maximum static friction: Fs,max = μs FN = (0.4) (98 N) = 39.2 N
This means that the static friction force can be anywhere between 0 N and 39.2 N, depending on the applied force. If you push the box with a force of 20 N, the static friction will be 20 N. If you push with 40 N, the static friction cannot be 40 N; it will only reach a maximum of 39.2 N, and the box will start to move.
In Summary
To calculate static friction, you're typically finding the maximum possible static friction force using the formula Fs,max = μs FN. Remember that the actual* static friction force will be equal and opposite to the applied force, up to this maximum value.
