Final answer:
The magnitude of the horizontal force exerted by a customer sitting down on a stool at a restaurant depends on the coefficient of static friction and the weight of the customer. This force is needed to overcome static friction and allow the customer to slide into position.
Step-by-step explanation:
When a customer is in the process of sitting down on a stool at a restaurant that is anchored to the floor, a horizontal force is exerted. This force is needed to overcome the static friction between the stool and the floor and allow the customer to slide into position. The magnitude of this force depends on the coefficient of static friction between the stool and the floor, as well as the weight of the customer.
The magnitude of the force can be calculated using the formula:
F = μN,
where F is the force, μ is the coefficient of static friction, and N is the normal force (equal to the weight of the customer). Therefore, the magnitude of the force can be expressed as:
F = μmg,
where m is the mass of the customer and g is the acceleration due to gravity.
For example, if the customer has a mass of 70 kg and the coefficient of static friction between the stool and the floor is 0.5, the magnitude of the force would be:
F = (0.5)(70 kg)(9.8 m/s2) = 343 N.