A 70 kg person sits on a 3.6 kg chair. Each leg of the chair makes contact with the floor in a circle that is 1.5 cm in diameter.
Find the pressure exerted on the floor by each leg of the chair, assuming the weight is evenly distributed.
pressure= weight/3 *1/area
Now to find the area, area= PI*(diameter/2)^2 do it in meters.
remember weight= mass*g
To find the pressure exerted on the floor by each leg of the chair, we can use the formula:
Pressure = Force / Area
First, let's find the force exerted by each leg of the chair. Since the weight is evenly distributed, each leg will support equal weight.
Weight of the person = mass × gravitational acceleration
Weight of the person = 70 kg × 9.8 m/s^2
Weight of the person = 686 N
Since there are four legs, the total weight supported by each leg is:
Weight supported by each leg = Weight of the person / Number of legs
Weight supported by each leg = 686 N / 4
Weight supported by each leg = 171.5 N
Now, let's find the area of contact between each leg and the floor. The circle made by each leg has a diameter of 1.5 cm, which gives a radius of:
Radius = Diameter / 2
Radius = 1.5 cm / 2
Radius = 0.75 cm
To find the area of the circle, we can use the formula:
Area = π × (radius)^2
Area = π × (0.75 cm)^2
Since pressure is typically measured in pascals (Pa) and 1 Pa is equal to 1 N/m^2, we need to convert the area to square meters:
Area (in square meters) = Area (in square centimeters) / 10,000
Area (in square meters) = π × (0.75 cm)^2 / 10,000
Now we can calculate the pressure:
Pressure = Weight supported by each leg / Area
Pressure = 171.5 N / (π × (0.75 cm)^2 / 10,000)
By calculating this expression, we can determine the pressure exerted on the floor by each leg of the chair.
To find the pressure exerted on the floor by each leg of the chair, we need to use the formula for pressure:
Pressure = Force/Area
First, let's calculate the force exerted by the person on the chair. The force of gravity acting on an object is given by the formula:
Force = mass * acceleration due to gravity
The mass of the person is given as 70 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the force exerted by the person on the chair is:
Force = 70 kg * 9.8 m/s^2 = 686 N
Next, we need to find the contact area of each leg with the floor. The contact area is given by the formula:
Area = π * (radius)^2
The diameter of each leg's contact circle is given as 1.5 cm, which is equivalent to 0.015 m. So the radius is half the diameter, which gives:
Radius = 0.015 m / 2 = 0.0075 m
Now we can calculate the contact area of each leg:
Area = π * (0.0075 m)^2
Area = 0.00017671 m^2
Finally, we can find the pressure exerted on the floor by each leg of the chair:
Pressure = Force/Area
Pressure = 686 N / 0.00017671 m^2
Pressure ≈ 3,882,624.34 Pa
Therefore, each leg of the chair exerts a pressure of approximately 3,882,624.34 Pascal on the floor.