Question

To meet a U.S. Postal Service requirement, 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 0.800. In an emergency, what is the minimum time interval in which a person starting from rest can move 3.00 m on a tile surface if she is wearing (a) footwear meeting the Postal Service minimum? (b) a typical athletic shoe?

Answer 1

a) t = 1.905s

b) t = 0.866s

Step-by-step explanation:

From a force diagram we know that:

Ff = m*a where Ff = μ*N

`\mu*m*g = m*a_(max)`

`a_(max)=\mu * g`

For Postal Service shoes:

`a_(max)=5m/s^2`

The time interval is calculated as:

`X = Vo*t+a/2*t^2` where Vo=0; X = 3m. Solving for t:

`t_(min)=1.905s`

For Athletic shoes:

`a_(max)=8m/s^2`

Using the same formula for the time interval:

`t_(min)=0.866s`