# What are my units when finding % diff. In kinetic energy?

What are my units when finding % diff. In kinetic energy???

## Homework Statement

Phrank (36.4kg) runs at 2.2 m/s and jumps onto a large stationary skateboard (2.3kg) on which Phrancine (22.7kg) is sitting. After the collision, Phrank, Phrancine, and the skateboard move at 1.3 m/s. Find the kinetic energy before and after the collision along with the percent difference.

## Homework Equations

Kinetic energy before equals= 88.1 J
Kinetic energy after= 51.88 J
Percent difference= 88.1-51.88 / (88.1 + 51.88/2 ) x 100 = 51.75 WHAT ARE MY UNITS HERE???

## The Attempt at a Solution

Need help with my units for percent difference! J is no correct!

Percent difference is a unit-less number.

haruspex
Homework Helper
Gold Member
More precisely, it is a dimensionless number.

Borek
Mentor
And not percent? I can be horribly wrong, but I was always under impression that if it goes like

$$\frac{3J}{2J}100\% = 150\%$$

ratio is dimensionless but the answer is in %.

Not that % is a physical unit. Actually now that I think about it, I have no idea what % is.

haruspex
Homework Helper
Gold Member
ratio is dimensionless but the answer is in %.

Not that % is a physical unit. Actually now that I think about it, I have no idea what % is.
You could certainly argue that dimensionless quantities nevertheless have units - whole numbers, percentages, millions.... But if I ask how many km/h a certain speed limit is the answer could be 50 - it would not, strictly speaking, be 50km/h. In the same way, if asked what percentage 3 is of 4 then the answer is 75, not 75% (which could legitimately be interpreted as 75/100 or 0.75). Does that make sense?

Borek
Mentor
Does that make sense?

More or less... not your fault, I am slow today :zzz: