How Fast Can You Move 3.45 Meters on Tile with Different Footwear?

[Megatron20]

To meet a U.S. Postal Service requirement, employees' footwear must have a coefficient of static friction of 0.5 or more on a specified tile surface. A typical athletic shoe has a coefficient of 0.750. In an emergency, what is the minimum time interval in which a person starting from rest can move 3.45 m on a tile surface if she is wearing the following footwear?
(a) footwear meeting the Postal Service minimum


(b) a typical athletic shoe

 

[tiny-tim]

Welcome to PF!

Hi Megatron20! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Megatron20]

The problem is that i have no idea where to even start tiny tim!

 

[tiny-tim]

use one of the standard constant acceleration equations …

what do you get?​

 

[asteriatic]

To start, it is important to understand the concept of coefficient of static friction. This is a measure of the amount of force required to overcome the friction between two surfaces in order for one surface to begin moving in relation to the other. In this case, we are looking at the coefficient of static friction between a person's footwear and a tile surface.

The Postal Service requirement states that the coefficient of static friction must be at least 0.5. This means that in order for a person to move on the tile surface, their footwear must have enough friction to overcome the resistance of the tile surface. A typical athletic shoe has a coefficient of 0.750, which meets this requirement.

To answer the question about the minimum time interval for a person to move 3.45 m on a tile surface, we need to use the equation for distance traveled with constant acceleration: d = 1/2at^2, where d is the distance, a is the acceleration, and t is the time interval.

(a) For footwear meeting the Postal Service minimum of 0.5 coefficient of static friction, we can rearrange the equation to solve for t: t = √(2d/a). Plugging in the given distance of 3.45 m and the minimum acceleration of 0.5, we get a minimum time interval of approximately 1.86 seconds.

(b) For a typical athletic shoe with a coefficient of 0.750, the minimum time interval would be even shorter, approximately 1.52 seconds.

In an emergency situation, every second counts, so it is important to have footwear that meets the minimum requirement for static friction to ensure safe and efficient movement on a tile surface.