Question

A 66.8 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 1.16 cm. What is the pressure exerted on the floor by each leg?

Answer 1

Mass of the man,Mm=66.8 kg

Mass of the chair,Mc=5 kg

Total Mass,m=Mm+Mc=71.8 kg

Mass on each leg is total mass on Chair

m=71.8 kg

Weight,W=71.8*9.81=704.358 N

Radius of the leg r=1.16 cm=1.16*10^-2 m

pressure,p=W/A

                =W/pi*r^2

                =704.358/pi*(1.16*10^-2 m)^2

                =166.62*10^4  N.m^2

Comments

Pressure exerted on the floor by each leg is 0.38 M Pa.

Answer 2

Pressure is defined as force per unit area.

P = F/A.

Mass of a man is 66.8 kg

Force = m*a = mass * gravitational acceleration = m*g where g = 9.8 mt/sec² .

Force exerted by a man on the floor = 66.8 * 9.8 = 654.64 N

Mass of a chair is 5 kg

Force exerted by a man on the floor = 5 * 9.8 = 49 N

Total force exerted on the floor by both the man and the chair = 654.64 + 49 = 703.64 N.

This wll be distributed equally for all the four legs.

Therefore force exerted on the floor at each leg = 703.64/4 = 175.91 N.

Area of a cicle = πr² where r = 1.16 cm = 1.16 * 10^-2 mt = 0.0116 mt.

                      = 3.412 (0.0116)²

                           =0.00045911 = 4.5911 × 10^-4 m²

Pressure exerted on the floor by each leg is force exerted on the floor at each leg / Area formed by the legs.

∴ P = 175.91 N / 4.5911 × 10^-4 m²

      = 38.3154 × 10⁴ N / m² or Pascal

      = 0.383154 × 10⁶ N / m² or Pascal

      = 0.38 Mega pascal.

Pressure exerted on the floor by each leg is 0.38 M Pa.