Static Friction Formula

Friction is a force that prevents some sliding objects from moving. We can find friction in our surroundings at any time. It acts in a direction opposite to that of the object’s movement. We can stop quickly if we run down the sidewalk and slow down and then eventually stop because of the frictional force between our footwear and the ground. Friction can occur with either a moving or stationary body. As a result, it can be both dynamic and static.

What is Static Friction?

Friction occurs when people attempt to move a non-moving object on the ground without actually causing any displacements among the surfaces.

Ever observed how much more difficult it is to get a shopping trolley travelling than to keep moving? When attempting to push a bed or sofa across one corner, the very first push is the most difficult. People may believe that it is purely psychological, but there is a physical reason for it. This happens because of static friction. 

In other words, static friction can be defined as the force that keeps an object at rest.

Static Friction Formula

F_s = μ_s × F_n

where,

• μ_s is static friction coefficient
• F_n is normal force acting upon the object.

Examples on Static Friction

Example 1: Determine the static friction acting on a couch of 7 kg, given the force applied, is 45 N and the coefficient of friction is 0.6. (Take g = 9.8 m/s²)

Solution:

Given: 

Weight of Couch = 7 kg

g = 9.8 m/s²

F_n = 7 × 9.8 N

    = 68.6 N

μ_s = 0.6

Since, F_s = μ_s × F_n

= 0.6 x 68.6 N

= 41.16 N

Thus, the friction force applied is 41.16 N

Example 2: Determine the static friction acting on a table of 10 kg, given the force applied, is 200 N and the coefficient of friction is 0.7. (Take g = 9.8 m/s2)

Solution:

Given: 

Weight of Table = 10 kg

g = 9.8 m/s²

F_n = 10 × 9.8 N

    = 98 N

μ_s = 0.7

Since, F_s = μ_s × F_n

= 0.7 x 98 N

= 68.6 N

Thus, the friction force applied is 68.6 N

Example 3: Find the coefficient of static friction if an object is being pushed from a state of rest by applying a force of 500 N and the static friction acting on it is 250 N.

Solution:

Given: 

F_s = 250 N and F_n = 500

Since, F_s = μ_s × F_n

250 = μ_s x 500

μ_s = 250/500

μ_s = 0.5

Example 4: Determine the static friction acting on an object of mass 50 Kg, given the force applied, is 1000 N and the coefficient of friction is 0.4.

Solution:

Given: 

Weight of Object = 50 kg

g = 9.8 m/s²

F_n = 50 × 9.8 N

    = 490 N

μ_s = 0.4

Since, F_s = μ_s × F_n

= 0.4 x 490 N

= 196 N

Thus, the friction force applied is 196 N