Show using unit conversions that at sea level the mass of a

Show using unit conversions that at sea level the mass of a person who weight 200 lbf is 200 lbm.

Solution

Mass of an object is the amount of matter it contains and weight of an object is the force experienced on it due to gravity.Mass and weight are related by the equation.

Weight=Mass * Acceleration due to gravity

W=mg

Now, 9.81 m/s²=32.2 ft/s²

Now pound force is related to pound mass by the equation.

1 lbf=(1 lbm)*(32.2 ft/s²)

Dividing both sides by 1 lbf we get,

(1 lbf)/(1 lbf)=(1 lbm * 32.2 ft/s²) /(1 lbf)

1=(32.2 lbm*ft)/(lbf*s²)

using W=m*g

200 lbf=m*(32.2 ft/s²)/1 ( As dividing by 1 makes no difference to value.)

Now instead of 1 we can write (32.2 lbm*ft)/(lbf*s²).Puttin this value in above equation we get,

200 lbf=m*(32.2 ft/s²)/(32.2 lbm*ft)/(lbf*s²)

on cancelling the units and 32.2 by 32.2 we are left with,

m=200 lbm.

Hence, mass of a person who weighs 200 lbf is 200 lbm.