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Chapter 4: Problem 7

Use the concept of pressure to explain why snowshoes are better than regular shoes for walking in deep snow.

Short Answer

Expert verified
Answer: Snowshoes have a larger surface area in contact with the snow compared to regular shoes. This larger surface area allows for the person's weight to be distributed more evenly, leading to lower pressure exerted on the snow. The reduced pressure prevents the person from sinking into the snow, making it easier to walk in deep snow.

Step by step solution

01

Define Pressure

Pressure can be defined as the amount of force applied per unit of surface area. Mathematically, this can be written as: $$P = \frac{F}{A}$$ Where P represents pressure, F represents force applied, and A represents the surface area in contact.
02

Force applied by the person

In this case, the force applied is the person's weight, which can be represented as: $$F = mg$$ Where m is the mass of the person and g is the acceleration due to gravity (approximately 9.81 m/s^2).
03

Surface area of regular shoes and snowshoes

To understand the benefits of snowshoes, compare the surface area of regular shoes with that of snowshoes. Snowshoes have a larger surface area which helps distribute the weight over a greater area. Let's represent the surface area of the regular shoes as $$A_{shoes}$$ and the surface area of the snowshoes as $$A_{snowshoes}$$. We can assume that $$A_{snowshoes} > A_{shoes}$$.
04

Calculate the pressure exerted by regular shoes and snowshoes

Now we can calculate the pressure exerted on the snow by regular shoes and snowshoes using the pressure formula: $$P_{shoes} = \frac{F}{A_{shoes}}$$ $$P_{snowshoes} = \frac{F}{A_{snowshoes}}$$
05

Comparing the pressures

Since the force applied (the person's weight) is constant for both cases, we can compare the pressures to understand why snowshoes are better for walking in deep snow. As mentioned earlier, the surface area in contact with the snow is greater for snowshoes, so the pressure exerted by snowshoes would be less than that of the regular shoes. $$P_{snowshoes} < P_{shoes}$$ This lower pressure spreads the person's weight over a larger area, which reduces the chances of sinking into the snow, making it easier to walk in deep snow.

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