A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm², calculate the pressure exerted on the underlying surface in (b) atmospheres

검증된 단계별 안내

First, understand that pressure is defined as force per unit area. The formula for pressure is \( P = \frac{F}{A} \), where \( P \) is pressure, \( F \) is force, and \( A \) is area.

Next, calculate the force exerted by the person. Since weight is a force due to gravity, use the formula \( F = m \cdot g \), where \( m \) is mass (75 kg) and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).

Convert the contact area from cm² to m² for consistency in units. Since 1 cm² = 0.0001 m², the area \( A \) is \( 5.0 \text{ cm}^2 \times 0.0001 \text{ m}^2/\text{cm}^2 = 0.0005 \text{ m}^2 \).

Substitute the values of force and area into the pressure formula to find the pressure in pascals (Pa). \( P = \frac{F}{A} \).

Finally, convert the pressure from pascals to atmospheres. Use the conversion factor \( 1 \text{ atm} = 101325 \text{ Pa} \). Divide the pressure in pascals by 101325 to get the pressure in atmospheres.

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주요 개념

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Pressure

Pressure is defined as the force exerted per unit area. In this context, it is calculated by dividing the weight of the person by the contact area of the stool's foot that is in contact with the ground. The formula for pressure (P) is P = F/A, where F is the force (weight) and A is the area.

Units of Pressure

Pressure can be expressed in various units, including pascals (Pa), atmospheres (atm), and millimeters of mercury (mmHg). To convert pressure from pascals to atmospheres, one can use the conversion factor: 1 atm = 101,325 Pa. Understanding these units is essential for accurately reporting the pressure exerted.

Weight and Force

Weight is the force exerted by gravity on an object and is calculated as the product of mass and gravitational acceleration (W = mg). In this scenario, the person's weight (75 kg) contributes to the total force acting on the stool, which is crucial for determining the pressure on the surface below.

A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm2, calculate the pressure exerted on the underlying surface in (b) atmospheres