Answer :
To solve the problem of determining the pressure a person exerts on the ground when sitting on a chair, we can follow these steps:
1. Determine the Force Exerted by the Person:
- The weight of the person is the force they exert due to gravity. This force (weight) can be calculated using the formula:
[tex]\[
\text{Force} = \text{mass} \times \text{acceleration due to gravity}
\][/tex]
- Given that the mass of the person is 90 kg and the acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 10 \, \text{m/s}^2 \)[/tex], the force is:
[tex]\[
\text{Force} = 90 \, \text{kg} \times 10 \, \text{m/s}^2 = 900 \, \text{N}
\][/tex]
2. Calculate the Area of Contact for Each Chair Leg:
- Each leg of the chair is a square with a side length of 30 mm. To work in meters, convert the side length from millimeters to meters:
[tex]\[
\text{Side length in meters} = \frac{30}{1000} = 0.03 \, \text{m}
\][/tex]
- The area of contact for one leg, which is a square, is calculated as:
[tex]\[
\text{Area of one leg} = \text{side}^2 = (0.03 \, \text{m})^2 = 0.0009 \, \text{m}^2
\][/tex]
3. Calculate the Total Area of Contact:
- Since the chair has 4 legs, the total area of contact is:
[tex]\[
\text{Total area} = 4 \times 0.0009 \, \text{m}^2 = 0.0036 \, \text{m}^2
\][/tex]
4. Determine the Pressure Exerted:
- Pressure is defined as the force per unit area. The pressure exerted by the person on the ground can be found using the formula:
[tex]\[
\text{Pressure} = \frac{\text{Force}}{\text{Total area}} = \frac{900 \, \text{N}}{0.0036 \, \text{m}^2} = 250000 \, \text{Pa}
\][/tex]
- Convert the pressure from Pascals (Pa) to kilopascals (kPa) by dividing by 1000:
[tex]\[
\text{Pressure in kPa} = \frac{250000 \, \text{Pa}}{1000} = 250 \, \text{kPa}
\][/tex]
Therefore, the pressure exerted by the person on the ground is 250 kPa, which corresponds to option C.
1. Determine the Force Exerted by the Person:
- The weight of the person is the force they exert due to gravity. This force (weight) can be calculated using the formula:
[tex]\[
\text{Force} = \text{mass} \times \text{acceleration due to gravity}
\][/tex]
- Given that the mass of the person is 90 kg and the acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 10 \, \text{m/s}^2 \)[/tex], the force is:
[tex]\[
\text{Force} = 90 \, \text{kg} \times 10 \, \text{m/s}^2 = 900 \, \text{N}
\][/tex]
2. Calculate the Area of Contact for Each Chair Leg:
- Each leg of the chair is a square with a side length of 30 mm. To work in meters, convert the side length from millimeters to meters:
[tex]\[
\text{Side length in meters} = \frac{30}{1000} = 0.03 \, \text{m}
\][/tex]
- The area of contact for one leg, which is a square, is calculated as:
[tex]\[
\text{Area of one leg} = \text{side}^2 = (0.03 \, \text{m})^2 = 0.0009 \, \text{m}^2
\][/tex]
3. Calculate the Total Area of Contact:
- Since the chair has 4 legs, the total area of contact is:
[tex]\[
\text{Total area} = 4 \times 0.0009 \, \text{m}^2 = 0.0036 \, \text{m}^2
\][/tex]
4. Determine the Pressure Exerted:
- Pressure is defined as the force per unit area. The pressure exerted by the person on the ground can be found using the formula:
[tex]\[
\text{Pressure} = \frac{\text{Force}}{\text{Total area}} = \frac{900 \, \text{N}}{0.0036 \, \text{m}^2} = 250000 \, \text{Pa}
\][/tex]
- Convert the pressure from Pascals (Pa) to kilopascals (kPa) by dividing by 1000:
[tex]\[
\text{Pressure in kPa} = \frac{250000 \, \text{Pa}}{1000} = 250 \, \text{kPa}
\][/tex]
Therefore, the pressure exerted by the person on the ground is 250 kPa, which corresponds to option C.
