A person whose mass is 150 lbm weighs 144.4 lbf. Determine: (a) The person’s mass in kg (b) The person’s weight in N
The correct answer and explanation is:
Correct Answers:
(a) The person’s mass in kilograms is 68.04 kg
(b) The person’s weight in newtons is 642.56 N
Explanation:
Mass and weight are related but distinct physical quantities. Mass is a measure of the amount of matter in an object, while weight is the force exerted by gravity on that mass. In the Imperial system, mass is measured in pound-mass (lbm) and weight is measured in pound-force (lbf). The standard relationship connecting the two is given by Newton’s Second Law, which states that weight equals mass times gravitational acceleration.
First, to convert mass from pound-mass to kilograms, the conversion factor is 1 lbm equals 0.45359237 kg. So, for a mass of 150 lbm: 150 lbm×0.45359237kglbm=68.04 kg150 \text{ lbm} \times 0.45359237 \frac{\text{kg}}{\text{lbm}} = 68.04 \text{ kg}
This shows the mass in the SI unit of kilograms.
Next, weight in the SI system is expressed in newtons. One pound-force is equivalent to 4.4482216 newtons. This conversion comes from the definition that 1 lbf is the force required to accelerate 1 lbm by 32.174 ft/s², which corresponds to 9.80665 m/s² in SI units. So, to convert 144.4 lbf to newtons: 144.4 lbf×4.4482216Nlbf=642.56 N144.4 \text{ lbf} \times 4.4482216 \frac{N}{lbf} = 642.56 \text{ N}
This value represents the gravitational force acting on the person’s mass at standard Earth gravity.
Understanding the difference between mass and weight is fundamental in physics and engineering. Mass remains constant regardless of location, but weight changes if gravitational acceleration changes, such as on the Moon or other planets. Engineers must know when to use each unit system and how to convert between them to ensure accurate calculations and safe designs, especially when working with mechanical systems, structural loads, or aerospace applications where units may vary between Imperial and SI standards. Conversions like this are also useful in scientific research, international projects, and everyday contexts like medical measurements or athletic performance assessments.