**Consider a 70-kg woman who has a total foot imprint area of 400 cm^{2}. She wishes to walk on the snow, but the snow cannot withstand pressures greater than 0.5 kPa. Determine the minimum size of the snowshoes needed (imprint area per shoe) to enable her to walk on the snow without sinking.**

# Solution:

### Let us assume that her weight is uniformly distributed on the imprint area of the shoes and that the weight of the shoes is negligible. When she walks, her entire weight is placed on one foot at a time.

### The mass of the woman is given to be 70 kg. For a pressure of 0.5 kPa on the snow, the imprint area of one shoe must be A=\frac{W}{P}=\frac{mg}{P}

### =\left(\frac{(70kg)(9.81{m}/{s^{2}})}{0.5kPa}\right)\left(\frac{1N}{1kg\cdot m/s^{2}}\right)\left(\frac{1kPa}{1000N/m^{2}}\right)

### =1.37m^{2}

THOSE ARE HUGE

Yup, they have to be huge snowshoes.

why dont we divide the mass of woman between the two feet so each shoe has 35 kg mass?

That is because when she walks, her entire weight is placed on one foot at a time. Hope that helps!

when should I divide the weight over the pressure ? in which cases ?

When you want to find the area.

why we didnâ€™t use 400 cm2

??

It wasn’t required.

it sohuld be half of that result. Because there are two shoes . we have to consider as per shoe according to question. We can put first off all 2A=….

When you walk, you use one foot at a time, except when standing. So one shoe needs to hold the full weight of her body.