# Basics: F=ma

Roundandround
Homework Statement:
Understanding between force and mass
Relevant Equations:
Word Question in Body
Background:
My understanding is force and mass are two different things.

Mass is how much matter is in a body
Force is mass multiplied by an acceleration. Here on earth, that acceleration is 32.2 Ft/s2.
Therefore, for the same mass, there can be different forces depending on the acceleration.

So, in English units, what is the mass of an 180 pound person, where 180 pounds is the force (F)?
i come up with:
mass = F/a = 180 lbs/32.2 Ft/sec2 = 5.59lbs-sec2/ft.

Not sure what I am doing wrong
Where have I gone wrong with the units?
What should be the proper unit for mass in english units?

Looking on line, some examples just convert the 180 pounds to kg, and announce 81.6kg (180/2.2) as the answer.
How can 81.6 kg be a mass when 180 pounds is a force and not a mass?

Many thanks for the help

Homework Helper
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My understanding is force and mass are two different things.
Right.
Mass is how much matter is in a body
Inertial mass is defined as the resistance to acceleration, F/a.
(This is as distinct from gravitational mass, which determines how much gravitational force bodies exert on each other.)
Force is mass multiplied by an acceleration.
Right.
Here on earth, that acceleration is 32.2 Ft/s2.
That is gravitational acceleration, at Earth's surface, and it's only an average.
Therefore, for the same mass, there can be different forces depending on the acceleration.
Yes.
So, in English units, what is the mass of an 180 pound person, where 180 pounds is the force (F)?
Ah. The confusion generated by using pound for both force and mass is regrettable. Try reading https://en.m.wikipedia.org/wiki/Pound_(force). Come back if you need any further explanation.

Staff Emeritus
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So, in English units, what is the mass of an 180 pound person, where 180 pounds is the force (F)?
i come up with:
mass = F/a = 180 lbs/32.2 Ft/sec2 = 5.59lbs-sec2/ft.

Not sure what I am doing wrong
Where have I gone wrong with the units? What should be the proper unit for mass in english units?

You haven't done anything wrong. One of the units of mass in the imperial system is the slug, with units in lbf*sec2/ft. Converting 180 pound-force to slugs using google gives me 5.59457 slugs, which is almost exactly what you came up with.

How can 81.6 kg be a mass when 180 pounds is a force and not a mass?

The kilogram is a unit of mass, and we can convert between force and mass as long as we know the gravitational acceleration of the object, which we do. A more massive object (i.e. an object with more mass, not one that is larger) will require a larger force to accelerate at the same rate as a less massive object. So if you know the acceleration is 32.2 ft/s2, you can measure the force applied to the object and then find the mass.

Note that the force applied by an object onto the ground due to its weight is identical to the force required to accelerate the object to the local gravitational acceleration (32.2 ft/s2 on average here on Earth). In other words, a mass of 81.65 kg requires a force of 180 pounds to accelerate it at a rate of 32.2 ft/s2.

Also, pound is actually the common name of several different units. There are pound-force (lbf), pound-mass (lb or lbm), and sometimes the poundal (pdl).

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