Question

A large man sits on a four-legged chair with his feet off the floor. The combined mass of the man and chair is 95.0 kg. If the chair legs are circular and have a radius of 0.500 cm at the bottom, what pressure does eachleg exert on the floor

Answer 1

Answer on Question 61580, Physics, Other

Question:

A large man sits on a four-legged chair with his feet off the floor. The combined mass of the man and chair is 95.0 kg. If the chair legs are circular and have a radius of 0.5 cm at the bottom, what pressure does each leg exert on the floor?

Solution:

By the definition of the pressure we have:

$$P = \frac {F}{A},$$

here, $P$ is the pressure that each leg exert on the floor, $F$ is the force acting on the floor, $A$ is the total area of the four legs.

The force acting on the floor is the weight of the man and chair:

$$F = W = m g,$$

here, $m$ is the combined mass of the man and chair, $g$ is the acceleration due to gravity.

We can find the total area of the four legs from the formula:

$$A = N \pi r ^ {2},$$

here, $N$ is the number of the chair legs, $r$ is the radius of the chair leg.

Finally, substituting $F$ and $A$ into the formula, we get:

$$P = \frac {F}{A} = \frac {m g}{N \pi r ^ {2}} = \frac {9 5 k g \cdot 9 . 8 \frac {m}{s ^ {2}}}{4 \cdot \pi \cdot (0 . 0 0 5 m) ^ {2}} = 2. 9 6 \cdot 1 0 ^ {6} P a.$$

Answer:

The pressure that each leg exert on the floor is $P = 2.96 \cdot 10^{6} Pa$.

https://www.AssignmentExpert.com