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3 years ago

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As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted o

n the floor by the heel if it has an area of 1.64 cm2 and the woman's mass is 67.0 kg. Express the pressure in pascals. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)

1 answer:

Inessa05 [86]3 years ago

7 0

Answer:4.003 MPa

Explanation:

Given

Area of heel $A=1.64 cm^2\approx 1.64\times 10^{-4} m^2$

Mass of woman $m= 67 kg$

Pressure is defined as Force applied in over an area such that it is perpendicular to it i.e.

$Pressure=\frac{Force}{Area}$

$P=\frac{F}{A}$

$P=\frac{mg}{A}$

$P=\frac{67\times 9.8}{1.64\times 10^{-4}}$

$P=400.365\times 10^{4} Pa$

$P=4.003 MPa$

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The conservation of energy should be used to answer this question.

a)

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The roots of this quadratic equation can be solved by using discriminant.

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We should use the positive root, so

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b)

We should use energy conservation between the point where the spring is momentarily at rest, and the point where the spring is unstretched.

$K_2 + U_2 - W_f = K_3 + U_3\\U_2 - W_f = K_3$

since the kinetic energy at point 2 and the potential energy at point 3 is equal to zero.

$\frac{1}{2}kx^2 - F_fx = K_3\\K_3 = 15.987 - 2.92 = 13.067 J$

Explanation:

In questions with springs, the important thing is to figure out the points where kinetic or potential energy terms would be zero. When the spring is unstretched, the elastic potential energy is zero. And when the spring is at rest, naturally the kinetic energy is equal to zero.

In part b) the cookie slides back to its original position, so the distance traveled, x, is equal to the distance in part a). The frictional force is constant in the system, so it is quite simple to solve part b) after solving part a).

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