Question

A 200-pound man has a total foot imprint area of 72 in \(^{2} .\) Determine the pressure this man exerts on the ground if \((a)\) he stands on both feet and \((b)\) he stands on one foot.

Short answer

Question: A man weighs 200 pounds and has a total foot imprint area of 72 square inches. Calculate the pressure exerted by the man when he stands on (a) both feet, and (b) one foot. Answer: (a) The pressure exerted when the man stands on both feet is approximately 2.78 psi. (b) The pressure exerted when the man stands on one foot is approximately 5.56 psi.

Step-by-step solution

Convert given weight into force

Since pressure is measured in force per unit area, we need to convert the man's weight into force. Recall that weight is equivalent to the force of gravity acting on an object. So, we will use the following formula to convert the man's weight into force: Force = Weight In this case, the man's weight is 200 pounds, so the force is also 200 pounds.

Determine total foot imprint area

The total foot imprint area for the man is given as 72 square inches.

Calculate the pressure exerted when the man stands on both feet

Next, we will calculate the pressure exerted by the man when he stands on both feet. Since the man's weight is evenly distributed across both feet, we can use the total foot imprint area to calculate the pressure as follows: Pressure = Force / Area In this case, the force is 200 pounds, and the area is 72 square inches. Therefore: Pressure = (200 pounds) / (72 in^2) Pressure ≈ 2.78 psi (pounds per square inch)

Calculate the pressure exerted when the man stands on one foot

Now, we will calculate the pressure exerted by the man when he stands on one foot. Since all the weight is now on one foot, the area in contact with the ground is half that of when he stood on both feet. Therefore, the area for this part of the problem is 36 square inches (72 / 2). Using the same formula as before, we can calculate the pressure exerted on the ground as follows: Pressure = Force / Area The force is still 200 pounds, but now the area is 36 square inches. Therefore: Pressure = (200 pounds) / (36 in^2) Pressure ≈ 5.56 psi (pounds per square inch) In conclusion, the pressure exerted by the man on the ground when he is standing on both feet is approximately 2.78 psi, and when standing on one foot, the pressure exerted is approximately 5.56 psi.