Question

A 68.8 kg man sits in a 5.0 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 0.94 cm. What is the pressure exerted on the floor by each leg

Answer 1

P = 651353.67 Pa

Step-by-step explanation:

The mass of the man = 68.8 kg

Mass of the chair = 5 kg

Total mass = 68.8 + 5 = 73.5 kg

Since both the chair and the man have 2 legs each, the total number of legs = 4

The force applied by each of the legs, F = ma

F = (73.5) * 9.8/4

F = 180.81 N

The pressure exerted by each of the legs, P = F/A

Radius, r = 0.94 cm = 0.0094 m

Area, A = πr²

A = π(0.0094)²

A = 0.000278 m²

P = 180.81/0.000278

P = 651353.67 Pa

Answer 2

Pressure in N/cm² = 66.46 N/cm²

Step-by-step explanation:

Total weight of the man and the chair is 68.8 + 5 = 73.8 kg

But the weight is evenly distributed to the legs of the chair with four legs.

Each tension or load on a leg of the chair is 73.8/4= 18.45 kg

The load on each chair is 18.45*10 = 184.5 N.

Pressure = load/area

Area = πr²

area = π*0.94²

Area = 2.776 cm²

pressure = load/ area

Pressure = 184.5/2.776

Pressure = 66.46 N/cm²