How fast could the person have to travel?

[jenita]

a person whose mass is 48 kg wishes to gain 12 kg relativistically with respect to another reference frame. How fast could the person have to travel?


the formula is as follows...
i Think M is 48 kg
mo is 12 kg
v=? can anyone help me to do this problem

 

[hage567]

Mo will be 48 kg. M will not be 12 kg, since the question states that the person wishes to gain 12 kg (so the mass will increase by this much).

I can't see the picture yet. Does it show where you are getting stuck?

 

[jenita]

sorry i don't no why the pic is not showing up...its the formula in the pic... i hope u no the formula...if mo is 48 then what is 12kg

 

[jenita]

is 12 kg M or do we have to find M first

 

[jenita]

oh you by the way c is 3.8 * 10^8

 

[jenita]

is the answer 75000000

 

[hage567]

Is this the equation you have?

M = \frac{M_o}{\sqrt{1 - v^2/c^2}}

You want to solve for v. Don't worry about the actual value of c (you've got it wrong by the way, it's 3x10^8 m/s), just leave it as "c" in your work. At the end, you can worry about converting it.

You are given Mo. You can figure out M because you know the gain in mass is 12 kg. So, what is M, then?

 

[jenita]

but to find M don't u need V

 

[hage567]

is the answer 75000000

Please show how you got that answer.

 

[jenita]

how can i solve it if i don't have M, v, and c...dont i need to have 1

 

[hage567]

but to find M don't u need V

You are trying to solve for v. You must rearrange that equation to get v in terms of the masses. It IS the equation you are using, right?

You have the information to get both masses without solving anything!

 

[jenita]

75000000...i got this by inserting 12 for M, 48 for mo and 3.08*10^8 for c...
i divided 12 from 48 which i got.25 and the squared it and got.0625... i squared 1 and c and then multiplied by c and 1 to the .0625... i was left with 5.625e15=v^2 and i squared it and got the answer... sorry it looks confusing

 

[jenita]

and yes that is the equation we are using

 

[hage567]

Like I've already said, M is not 12 kg. 12 kg is the change in the mass. So if the mass started at 48 kg and 12 kg is added relativistically, what is the new mass (M)?

 

[jenita]

oh lol...its 60 kg

 

[jenita]

so u insert 60 for m

 

[jenita]

so for M u insert 60 and then solve

 

[hage567]

oh lol...its 60 kg

There you go! Let's see what answer you get now.

 

[jenita]

i got 375000000...i did the same way like i did to get 75000000

 

[hage567]

Well that can't be right since that is faster than the speed of light. Are you using 3 x 10^8 m/s for c?

 

[jenita]

yes i am using that

 

[hage567]

Then you've gone wrong in the algebra somewhere. Can you show me your expression for v after rearranging that equation?

 

[jenita]

60/48=1.25 1.25^2== 1.5625 and then multiply with c^2 and i got 1.40625e17=v^2

 

[jenita]

and then did the square root on both sides and got that answer

 

[hage567]

No, that's not right.

Original equation M = \frac{M_o}{\sqrt{1 - v^2/c^2}}

To get v you should start by doing this (cross multiply):

\sqrt{1 - v^2/c^2} = \frac{M_o}{M}

Does that help point you in the right direction?

Don't mix up M and Mo.

 

[jenita]

i know this is stupid question...i just came across...do break the square root u have to square it then its (v2/c2) ^2..isnt it

 

[jenita]

i got 240000000

 

[jenita]

can u check in the calculator if that is right or not

 

[jenita]

i kinda did check answer by replacing .64 for V i got 62.47 for M

 

[jenita]

omg ignore this

i kinda did check answer by replacing .64 for V i got 62.47 for M

 

[hage567]

i know this is stupid question...i just came across...do break the square root u have to square it then its (v2/c2) ^2..isnt it

If you have

\sqrt{1 - v^2/c^2}

and square it, you get 1 - v^2/c^2 NOT (1 - v^2/c^2)^2

 

[jenita]

lol...enways is my answer right...can u check it...if it is then thank yooooooouuuuuuuuuuu so much...

 

[hage567]

The 2.4 x 10^8 m/s? No, that's not what I get.

 

[jenita]

omg this is killing me...let me see what i did wrong

 

[jenita]

ok let me check i did 48/60 and i got .8 and squared it after that i squared C and multiplied with .64 and got that answer and i did what u told me to do it...

 

[hage567]

\sqrt{1 - v^2/c^2} = \frac{M_o}{M}

See the 1 under the square root on the left side? What happened to that?

 

[jenita]

you subtract that and still get the same answer

 

[jenita]

hold on a minute let me do it

 

[jenita]

i give up...i have 134164078.6 now

 

[hage567]

you subtract that and still get the same answer

You do?

Until you can show me a picture or write out your equation in latex I don't think I am going to be see what you are doing wrong.

I think you are just getting caught up in some small math error.

 

[hage567]

v = \sqrt{1-(\frac{M_o}{M})^2} c

This is what you should get after arranging your equation. Please make sure you understand how to get this.

Note: the c is not under the square root.

 

[jenita]

let me draw and sent it to you

 

[jenita]

hold on how did u get (mo/m) square

 

[hage567]

I don't have much time to do it now, it's getting late. If you send it I can try to check it in the morning.

 

[hage567]

hold on how did u get (mo/m) square

Look at post #25. To get rid of the square root, you must square both sides of that equation.

Also see what I said in post #31.

 

[jenita]

do u substitute mo/m in v2

 

[jenita]

did u get 297993288.5 the answer...if this is wrong i am so giving up

 

[hage567]

do u substitute mo/m in v2

NO. Why would you do that?? You want to solve for v. Why would you want to eliminate it from the equation? You are not supposed to be solving for c, if that's what you're up to.

did u get 297993288.5 the answer...if this is wrong i am so giving up

No that's not the right answer.

I gave you the equation for v. Put the numbers in and see what you get. But you must ask for help (perhaps from your teacher) if you can't see how to work out that answer.

Anyway, I must go. Let me know what you come up with and I will check it tomorrow.

Good night.

 

[jenita]

good night
and thanks for the help

 

[Aikenfan]

I got:

V = Square root (1-(48/60)^2 (c)
=60,000,000

Is that correct?