A 67.8 kg man sits in a 6.3 kg chair so that
his weight is evenly distributed on the legs
of the chair. Assume that each leg makes
contact with the floor over a circular area
with a radius of 2.4 cm.
What is the pressure exerted on the floor
by each leg? The acceleration of gravity is
9.81 m/s2 .
Answer in units of Pa
p =F/A =(m+M)g/4πr² = (6.3+67.8)9.8/4π(0.024)²= …
To find the pressure exerted on the floor by each leg, we can use the formula:
Pressure = Force / Area
First, let's calculate the force exerted by the man on the chair:
Force = mass * acceleration due to gravity
Force = (67.8 kg + 6.3 kg) * 9.81 m/s^2
The total mass is the sum of the man's mass (67.8 kg) and the chair's mass (6.3 kg).
Force = 74.1 kg * 9.81 m/s^2
Now, we need to calculate the area of contact between each leg and the floor:
Area = π * radius^2
Area = 3.14 * (0.024 m)^2
Finally, we can calculate the pressure on the floor by each leg:
Pressure = Force / Area
Pressure = (74.1 kg * 9.81 m/s^2) / (3.14 * (0.024 m)^2)
Pressure = 72742.9 N / (3.14 * 0.000576 m^2)
Pressure = 39873657.58 N/m^2
The pressure exerted on the floor by each leg is approximately 39873657.58 Pascal (Pa).
To calculate the pressure exerted on the floor by each leg, we need to first calculate the total force exerted on the floor by the man and the chair.
The total force can be determined by multiplying the mass of the man and chair by the acceleration due to gravity:
Total force = (mass of man + mass of chair) * acceleration due to gravity
mass of man = 67.8 kg
mass of chair = 6.3 kg
acceleration due to gravity = 9.81 m/s^2
Therefore, the total force exerted on the floor is:
Total force = (67.8 kg + 6.3 kg) * 9.81 m/s^2
Next, we need to find the total area over which this force is distributed. Since each leg makes contact with the floor over a circular area with a radius of 2.4 cm, we can find the total area by multiplying the area of one leg by the number of legs.
Area of one leg = π * (radius of each leg)^2
radius of each leg = 2.4 cm = 0.024 m
Therefore, the area of one leg is:
Area of one leg = π * (0.024 m)^2
Since there are four legs in total, the total contact area is:
Total contact area = 4 * (π * (0.024 m)^2)
Finally, we can calculate the pressure exerted on the floor by dividing the total force by the total contact area:
Pressure = Total force / Total contact area
Plug in the values and calculate to find the pressure in units of Pascals (Pa).