Physics Equation Questions

Factual Questions
1

Hello! Lately I have actually been thinking about physics, sparked in part by the Straight Dope. Unfortunately, I do not know very much about physics, partly due to my irrational fear of taking classes in it. What I do know comes mainly from my calculus (I’m still in beginning calculus, have yet to finish) and Advanced Chemistry class. So I was wondering if a few of the minds here could provide me with some equations…

  1. What is the equation for the mass gained the closer you travel to the speed of light? If I’m missing anything, PLEASE provide explanations. I’m only a newbie here!

  2. Which equation gives a few details on air resistence, and especially the heat produced due to friction?

  3. What is the equation that relates to the loss of energy in a reaction? I know it’s a miniscule amount, but I’m still interested.

Thank you to all whom help me here!

2

Well, #1 is
m[sub]0[/sub] = m/(sqrt(1-v[sup]2[/sup]/c[sup]2[/sup]))

3

I’m not sure, but I think Bill H. mixed up m (the mass of the object travelling at speed v) and m[sub]0[/sub] (the mass of the object at speed 0). Apart from this, the formula is correct IMHO; c is the constant speed of light.

4

Schnitte is correct of course. Should’ve read

m=m[sub]0[/sub]/sqrt(1-v[sup]2[/sup]/c[sup]2[/sup])

5

In answer to question 2, the air resistance force is F=1/2 r v^2 Cd A, where r is the density of air, v is speed, A is the frontal area of the object and Cd is the coefficient of drag. Cd basically tells you how streamlined the shape of the object is. Cd is about 1 for very non-streamlined shapes (e.g. a flat plate facing the wind is 1.28), and less than 0.05 for airfoils and other streamlined shapes.

Work is force times distance, so power is force times distance divided by time, or force times speed. Therefore power needed to overcome the air resistance, which is equal to the rate of heat generation by air resistance, is simply the F (given above) times V. You do realize, though, that the air carries most of the heat away?

Question 3 is vague. What kind of reaction?

6

For #3, I think there’s no general formula. You know the specific energy (usually given per kilomol) for a given substance, and if you know the energy for the products after the reaction, the energy loss is simply the difference:

deltaE = E[sub]after reaction[/sub] - E[sub]before reaction[/sub)

If this difference is negative, you have an energy loss, if positive you have to input energy.

The specific energy per kilomol for any substance can be looked up in tables.

That’s my guess, but others certainly can help you more.

7

Darn those brackets!!

8

Sorry if I’m being a little slow, but I too was quite interested in equation #1. However, I’m not overly familiar with mathematical abbreviations, so just one question: what does ‘sqrt’ mean?

9

sqrt is the square root.

10

Okay, thank you for all your help! I was really happy to get so many responses from so many different people! saves this thread

11

A few more questions, for those so kind to answer…

  1. What’s the equation that decides how much the force is multiplied in relation to the speed of an object?

  2. How does one determine the amount of heat generated by friction?

Thank you!

12

The force is multiplied in relation to the speed?

If the object has no engine on its own (eg if it has been thrown away), there is no force on it during its flight because the force (or thrust) is generated by the engines.

If the object does have an engine, the force caused by it can (1) equal the air resistance force, causing the object’s speed to remain constant, (2) be higher than the air resistance, causing the object to accelerate, or (3) be higher than the air resistance force, causing the object to slow down.