# Definition of Kinetic Energy?

Okay, I'm confused and need someone smarter than me to explain something to me about Kinetic Energy.

In studying some Ballistics concepts...I have ran across the definition of Kinetic Energy thus:

"one half the mass of the body times the square of its speed" or 1/2Mass x Velocity^2

And in ballistics, the KE numbers are measured in FtLbs...and this is what throws me.

I understand that mass can be measured in LBS, but Velocity is not just measured in Feet...but in Feet Per Second! So what the heck happened to the Seconds in the KE result?

Example: 1/2mass of a 10lb cannonball is 5lb, so 1/2M=5lb.
Velocity^2 of it moving at 10fps would be 100fps.
Using the formula for KE we end with a product result of 500FtLb.

HOW did we drop the "seconds" from velocity in the formula result...and why are we not measuring kinetic energy in FtLb/second? (I know this is actually a measurement for "power", so why am I confusing "Kinetic Energy" with "Power"?) How are they different? What happened to the "time factor" in the Energy equasion...if velocity is a part of the formula?

Thanks for ANY clarification.

Pengwuino
Gold Member
A pound is not a unit of mass, contrary to popular belief. A pound is a force. The unit of mass is the Slug.

Dale
Mentor
2020 Award
The confusion stems from the units. The pound is both a unit of mass and a unit of force (the weight of a 1 pound mass). Sometimes you will see a pound mass written as "lbm" and a pound force written as "lbf". Otherwise you have to determine from the context which is being used. In this case it is refering to a pound force.

russ_watters
Mentor
.....so the units ft-lb don't come from that equation directly: you have to apply f=ma to convert the units to units of work.

A pound is not a unit of mass, contrary to popular belief. A pound is a force. The unit of mass is the Slug.
Okay, I agree that the pound (weight) is the measurement that gravity exerts on mass, but sadly in common ballistics we end up measuring the mass of a bullet (here on earth) in "grains" which is a measurement of weight...from the avoirdupois system, which uses 7,000-grain pound.

So, to simplify we still measure bullets in a fraction of a pound, and calculate KE energy in units of "feet" (distance) and "pounds" (weight).

Consider that my question is being asked here on the surface of the earth and not on the moon where the "force" of the pound would change. So, we use the "weight" to calculate the "1/2M" part of the KE formula as standard. Correct?

Example: 1/2mass of a 10lb cannonball is 5lb, so 1/2M=5lb.

and the Velocity (of my example above) was 10fps, so Velocity^2 would = 100fps

In the KE formula those two are multipled together (5lb x 100fps) and a result of 500FtLb is created.

I don't see anywhere that F=MA is applied in that formula...and the "seconds" (time) part of the velocity just seems to be "conveniently" dropped/ignored...to create a result of KE (in FtLb).

Something's wrong with that picture. The "seconds" are just "dropped" from the result.

Perhaps I'm not understanding the difference between "Kinetic Energy" and "Power".

I'm not sure where I'm going wrong here...but somehow the TIME factor of velocity is just "dropped" from the KE equasion's final units. That bothers me.

Last edited:
To clarify further...a KE "Foot-Pound" is measured here on the earth's surface as the Energy required to raise a 1LB weight a vertical distance of 1FT. This makes no mention of Velocity units...yet velocity is one of the variables in the KE formula.

Simply,

1.) So if kinetic energy of the projectile is measured in FtLb,

and 2.) one of the KE formula's multipliers is "Velocity"...

then 3.) where is the complete Velocity Unit (to include time) in the result?

Why do we throw away the TIME factor of velocity in the KE result? Shouldn't the KE result be in FtLb/second rather than just FtLb? (as a full measure of the "capacity to do work")

Last edited:
Do a dimensional analysis
[L] = length
[T] = time
[M] = mass
kinetic energy = ½mv²
velocity is [L][T]‾¹
so kinetic energy is [M][L]²[T]‾²
A foot pound is a measure of work: force times distance.
The pound is a measure of force here.
Force is defined from F=ma
acceleration is [L][T]‾²
so force is [M][L][T]‾²
foot pound is [L][M][L][T]‾²
foot pound is [M][L]²[T]‾²

So, where is the "unit of time" in the FtLb result?
Shouldn't it be FtLb/second?

Do we measure Velocity or acceleration in the Ballistic formula?
(1/2M x Velocity^2). (how do you "square" the time factor of velocity?)

Energy is something difficult for me to understand. I know the formulas and I see its evidence and effect/affect, but I don't quite fully grasp it For instance, why is KE (and there are different forms of energy) described as = 1/2m (v squared) and momentum described as = mv. Both address the the mass and velocity of an object but in very different ways. Why is only half the value of mass, and the squared value of velocity used in the calculation of KE? We say it's energy (the combination of mass and velocity) that causes bullet and tissue deformation, but why isn't it momentum?

Dale
Mentor
2020 Award
Energy is something difficult for me to understand. I know the formulas and I see its evidence and effect/affect, but I don't quite fully grasp it
Energy is the capacity to do work and work is a force times a distance. So kinetic energy is simply the capacity that a moving object has to crash into something and thereby exert a force on it over some distance.