One can calculate the amount of friction needed to keep an object from moving or slipping over a surface when a force is exerted on the object. Consider the example of a safe weighing W kilograms, resting on a floor. A force of given magnitude B is exerted to move the safe. What is the least amount of friction between the block and the floor that is required to keep the block from moving? The “least amount of friction“ mentioned here is known technically as the “minimum coefficient of static friction”; it will be different for different magnitudes of B.

Calculate N, the force pressing the safe and the floor together, by multiplying the mass of the safe by the acceleration of gravity. Gravity at the Earth’s surface produces an acceleration of about 9.81 meters per second squared. The force of gravity on the safe is thus expressed as N = (W kilograms)(9.81 meters/sec/sec). For example, if the safe weighs 500 kilograms (about 1100 pounds), the force of gravity on it would equal N = (500 kilograms)(9.81 meters/sec/sec) = 4,905 kgm/sec/sec = 4,905 newtons.

Write the force, B, being exerted on the safe in units of newton, or kilogram meters per second squared.

Divide B, the force exerted to move the safe, by N, the force pressing the safe and the floor together. This is equal to the minimum coefficient of static friction. For example, assume the force exerted on the safe is 4,000 newtons (about half the force a champion weightlifter could exert to pull or push the safe). Then, B/N = (4000 newtons)/(4905 newtons) = 4000/4905 = 0.815 (rounded). The minimum coefficient of static friction is approximately 0.815. If the safe is on a rubber floor -- given that rubber can have a coefficient of static friction above 1.0 -- the safe is going nowhere.

#### Tip

The calculations are more involved if there are slopes involved, including tugging by a rope that makes an angle to the floor.