Question

A person has a mass of 65 kg. The coefficient of static friction µs, between their shoes and the floor = 0.8. Calculate the force required to slide them across the floor. 

Answer 1

The magnitude of friction force is defined as:

$$F_{fr} = \mu N$$

where $\mu = 0.8$ is the coefficient of static friction and $N$ is the magnitude of the normal force.

Since the person does not move in the vertical direction, then

$$N = mg$$

Here $m = 65kg$ is the person's mass and $g = 9.81m/s^2$ is the gravitational acceleration.

Then, obtain:

$$F_{fr} = \mu mg\\ F_{fr} = 0.8\cdot 65\cdot 9.81 = 510.12 \space N$$

In order to slide them accros the floor, one should apply the force greater or equal to $F_{fr}$.

Answer. $F \ge 510.12\space N$.