A man and a woman are walking across soft ground. The woman wears stilettos; each heel has a cross-sectional area of 0.95cm^2 (0.000095m^2) The man wears a flat shoe with a heel area of 110cm^2 (or 0.011m^2)
1. If the woman weighs 520 Newtons, how much pressure does she exerts on the ground beneath her?
p=f/a=520N/.000095m^2=5473684.211 N/m^2 Is this correct?
2. What would the man's weight need to be for him to exert an equal pressure? Don't know how to figure this one out?
check on part 1
2.
W/A = p
W = .011 * 5473684
= 60210 N
Huge because the pressure from the stiletto was huge.
1. Your calculation for the pressure exerted by the woman is correct. The formula for pressure is force divided by area, so in this case, it would be 520 Newtons divided by 0.000095m^2, resulting in a pressure of 5473684.211 N/m^2.
2. To determine the weight the man needs to exert to achieve the same pressure, we can use the equation p = f/a, where p is the pressure, f is the force, and a is the area. Since we want the pressure to be the same as the woman's pressure, we can set p equal to 5473684.211 N/m^2.
Let's call the man's weight W. The area of his shoe's heel is 0.011m^2. Therefore, we have the equation:
5473684.211 N/m^2 = W / 0.011m^2
To isolate W, we can multiply both sides of the equation by 0.011m^2:
5473684.211 N/m^2 * 0.011m^2 = W
Simplifying, we find:
W = 60105.132 N
So, the man's weight would need to be approximately 60105.132 Newtons for him to exert the same pressure as the woman.