Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm working with this:

A 50 kg mass is shot from a cannon straight up with an initial velocity of 10m/s off a bridge that is 100 meters above the ground. If air resistance is given by 5v determine the velocity of the mass when it hits the ground.

I haven't much experience with forces, but I understand that their dimension is $\frac{mass\times length}{time^2}$.

So if I have some force acting on a mass, then these should be the dimensions. The force acting on the mass in the question from gravity is 50(9.8)N, which has the correct dimensions. The next step in the solution tells me that $mv'=mg-5v$.

I don't understand this. $v$ has dimensions $\frac{m}{s}$. Am I supposed to assume that 5 has dimensions $\frac{mass}{sec}$? If so, what kind of a unit is this?

share|cite|improve this question

migrated from Nov 18 '12 at 22:01

This question came from our site for people studying math at any level and professionals in related fields.

you should assume that 5 has dimensions of $\frac{Ns}{m}$. – Tpofofn Nov 18 '12 at 4:04
Anyway, yes, the $5$ has dimensions of force per unit velocity = $\mathrm{N\:s\:m^{-1} = kg\:s^{-1}}$. This is no more unusual than if I were to say a thermometer's mercury level rises 2 millimeters whenever the temperature goes up by a degree Celsius, giving units of $\mathrm{m\:K^{-1}}$. – Rahul Nov 18 '12 at 19:42

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.