Consider a 70-kg woman who has a total foot imprint 4


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}

 

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