A 73 kg man in a 4.3 kg chair tilts back so that
all his weight is balanced on two legs of the
chair. Assume that each leg makes contact
with the floor over a circular area of radius
1.5 cm.
Find the pressure exerted on the floor by
each leg. The acceleration of gravity is
9.8 m/s
2
.
Answer in units of Pa
To find the pressure exerted on the floor by each leg, we need to divide the force exerted by each leg by the area of contact. The force exerted by each leg is equal to the weight of the man balanced on the legs.
Force = weight = mass * acceleration due to gravity
Force = 73 kg * 9.8 m/s^2 = 715.4 N
The area of contact is given by the formula for the area of a circle:
Area = π * radius^2
Area = π * (0.015 m)^2 = 0.00070686 m^2
Now we can calculate the pressure exerted by each leg using the formula:
Pressure = Force / Area
Pressure = 715.4 N / 0.00070686 m^2
Let's calculate the pressure:
Pressure ≈ 1,012,710.97 Pa
Therefore, the pressure exerted on the floor by each leg is approximately 1,012,710.97 Pa.
To find the pressure exerted on the floor by each leg, we need to calculate the force exerted by one leg and divide it by the area of contact.
First, let's find the force exerted by one leg. Since all of the man's weight is balanced on two legs, each leg will support half of the weight.
Weight = mass * gravity
Weight of man = 73 kg * 9.8 m/s^2 = 715.4 N
So, the force exerted by one leg will be half of this weight:
Force exerted by one leg = 715.4 N / 2 = 357.7 N
Next, we need to find the area of contact between the leg and the floor. Given that each leg makes contact over a circular area of radius 1.5 cm, we can find the area using the formula for the area of a circle:
Area = π * radius^2
Area of contact = π * (0.015 m)^2 = 0.00070685 m^2
Finally, we can calculate pressure by dividing the force by the area:
Pressure = Force / Area
Pressure = 357.7 N / 0.00070685 m^2
Pressure ≈ 5.06 x 10^5 Pa
So, the pressure exerted on the floor by each leg is approximately 5.06 x 10^5 Pa.