Computing Apparent Mass From Rest Mass and Speed
Date: 05/27/2002 at 14:11:09 From: Dustin Subject: The actual equation to find the mass of a moving object I've been trying the following equation that I found that is supposed to find the mass of a moving object.... Apparent Mass = Rest Mass * 1/sqrt(1 - v2/c2) v = speed c = light speed Could you tell me if this is the correct equation? If it is, could you show me an example where Rest Mass = 10 v = 20 I am going to assume v is in mph, so 20 mph, and rest mass is 10 grams. I would really appreciate an example that shows the value you plug in for lightspeed and the steps to solve this equation. Thank you very much!
Date: 05/27/2002 at 19:58:29 From: Doctor Rick Subject: Re: The actual equation to find the mass of a moving object Hi, Dustin. That's the correct formula (although we usually write "v^2" for v squared so it doesn't look like v times 2). You're using a strange mixed set of units: metric mass and English system for distance. That won't be a problem, though, as long as you express c, the speed of light, in the same units as v, because these units will cancel out, leaving a dimensionless number inside the square root. The speed of light is approximately 3*10^8 km/s (that's 300,000,000 km per second). Convert this to miles/hour and use it for c. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 05/27/2002 at 20:57:31 From: Dustin Subject: (Continued) Ok, thank you for finally clearing what the value for light speed is for me. But I see one problem with this equation. The moving mass comes out to be exactly the same no matter what numbers you plug in for the rest mass and for the speed. How fast does an object have to be going for it to change mass? Either I am doing something extremely wrong, or this equation gives you basically the same number answer (19.9999 = Apparent mass when Rest Mass = 20 and speed = 20 when I plug in numbers, along with the value you've given me for lightspeed). Its always coming out the same. Why? Thank you.
Date: 05/28/2002 at 08:28:31 From: Doctor Rick Subject: Re: (Continued) Hi, Dustin. It doesn't come out *exactly* the same, but the difference is so many decimal places to the right that your calculator or whatever doesn't show it. At speeds like 20 mph, Newton's laws describe the world very well, and they don't include any mass increase with velocity. As a rule of thumb, "relativistic" effects such as mass increase don't start to become noticeable until the velocity is about 1/10 the speed of light -- that is, 3*10^7 (30,000,000) km/sec, or 6.7*10^10 (67,000,000,000) mph. That's a lot more than 20 mph! - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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