Energy Needed To Go A Given Speed

  • Thread starter Thread starter Sothh
  • Start date Start date
  • Tags Tags
    Energy Speed
AI Thread Summary
To determine the energy required to accelerate a mass to a given speed, the kinetic energy formula changes based on the speed relative to the speed of light. For low speeds, the equation is KE = ½mv², while for speeds approaching light speed, it becomes mc²/√(1 - v²/c²). The additional energy needed to reach speed v is calculated as mc²(1/√(1 - v²/c²) - 1). For example, accelerating a 20-kilogram mass to 0.1c requires approximately 9e+12 kilojoules. Understanding these equations is crucial for calculations involving relativistic speeds.
Sothh
Messages
11
Reaction score
0
Hey, I don't have much of a physics background.

I have been searching for an equation that shows how much energy is needed to make a given mass go a given speed.

For example, let's say I want to send 1 gram at half light speed. How much energy is required?

Thanks!
 
Physics news on Phys.org
Sounds like you want to calculate the kinetic energy of the mass.

For low speeds (compared to the speed of light) the kinetic energy is KE = ½mv². But for fast speeds, it's a bit more complicated:
76cc95f8c7e7d0edde43428308072182.png


(I can't seem to get Latex to work.)
 
Welcome to PF!

Hi Sothh! Welcome to PF! :smile:

For a speed of v metres per second, the energy of a mass of m kilograms is mc2/√(1 - v2/c2) joules.

If v = 0 (the mass is at rest), that energy is obviously just mc2, which is therefore called the rest-mass.

So the extra energy needed to get it to speed v (the kinetic energy) is mc2(1/√(1 - v2/c2) - 1) joules. :wink:

If v/c is very small, then that extra (kinetic) energy is approximately mc2(v2/2c2), ie mv2/2.
 
Thanks!

Just to confirm I am using this correctly, it should take 20 kilograms around 9e+12 kilojoules to go .1c, correct?
 
Sothh said:
Just to confirm I am using this correctly, it should take 20 kilograms around 9e+12 kilojoules to go .1c, correct?
Sounds about right.
 
Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Here are two fragments from Banach's monograph in Mechanics I have never seen the term <<velocity of transport>> in English texts. Actually I have never seen this term being named somehow in English. This term has a name in Russian books. I looked through the original Banach's text in Polish and there is a Polish name for this term. It is a little bit surprising that the Polish name differs from the Russian one and also differs from this English translation. My question is: Is there...
View full post »

Thread 'Inclined treadmills and Galilean Invariance'

This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
View full post »

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Similar threads

I Why does the main muscle use the most energy in body movements?
Replies
24
Views
2K
Does it take longer to accelerate from high speed to higher
Replies
19
Views
2K
Why is the most probable energy different from the speed?
Replies
32
Views
3K
Does speed affect energy consumption over a certain distance?
Replies
6
Views
3K
Energy transformed in a collision
Replies
5
Views
2K
B Understanding Momentum: The Relationship Between Mass, Velocity, and Force
Replies
29
Views
3K
I Drag equation - relative flow velocity
Replies
11
Views
3K
B Why is speed constant when centripetal acceleration is constant?
Replies
24
Views
3K
Energy required to accelerate itself
Replies
11
Views
4K
Conservation of energy given the Earth's rotation?
Replies
22
Views
1K

Hot Threads

Recent Insights

Back
Top