A 73.5 kg person sits on a 3.20 kg chair. Each leg of the chair makes contact with the floor in a circle that is 1.74 cm in diameter. Calculate the pressure exerted on the floor by each leg of the chair, assuming the weight is evenly distributed.
find the total weight, mg. Divide it by 4, for each leg force. Next, find the area of each contact point (PI(d/2)^2). change d to meters first.
Then, pressure= forceeachleg/areaeachleg
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To calculate the pressure exerted on the floor by each leg of the chair, we can use the formula:
Pressure = Force/Area
First, we need to determine the force exerted by each leg of the chair. Since the weight is evenly distributed, we need to find the total weight supported by each leg.
The weight of the person is given as 73.5 kg. Since the chair supports the weight of the person, we need to add the weight of the chair as well.
The weight of the chair is given as 3.20 kg.
Therefore, the total weight supported by each leg of the chair is:
Total weight = weight of person + weight of chair
Total weight = 73.5 kg + 3.20 kg
Total weight = 76.7 kg
Now that we have the total weight supported by each leg, we can calculate the force exerted by each leg.
Force = Total weight * 9.8 m/s^2 (acceleration due to gravity)
Force = 76.7 kg * 9.8 m/s^2
Force ≈ 751.66 N
Next, we need to calculate the area of each leg in contact with the floor. The shape that each leg makes contact with the floor is a circle, and the diameter of the circle is given as 1.74 cm.
The formula to calculate the area of a circle is:
Area = π * (radius)^2
We need to find the radius first.
Radius = diameter / 2
Radius ≈ 1.74 cm / 2
Radius ≈ 0.87 cm
Now we can calculate the area of each leg.
Area = π * (0.87 cm)^2
Area ≈ 2.376 cm^2
Lastly, we can calculate the pressure exerted on the floor by each leg of the chair.
Pressure = Force / Area
Pressure = 751.66 N / 2.376 cm^2
Pressure ≈ 316.33 N/cm^2
Therefore, the pressure exerted on the floor by each leg of the chair is approximately 316.33 N/cm^2.