What is the value of Ts in seconds?

[DLHill]

Homework Statement

Ts (subscript s) = 2∏*√(4.5*10^-2 kg / 2.0*10^3 kg/s^2)
kg = Kilograms
s = seconds
Ts = ?

Homework Equations

I do not have any relevant questions.

The Attempt at a Solution

Ts = 2∏*√(4.5*10^-2 kg)/√(2.0*10^3 kg/s^2) Simplified
Ts = 6.28*[(0.212 kg)/√(44.72 kg/s^2)] Simplified
I am not sure what to do past this step. I don't think i could cancel out the kg because I would have only s^2 on the bottom. I have never seen a unit like kg/s^2, so I am confused. Does that unit even make sense? Any help is appreciated.

 

[CWatters]

You are on the right lines. Consider this bit..

4.5*10^-2 kg / 2.0*10^3 kg/s^2

You have kg top and bottom so they cancel giving

4.5*10^-2 / 2.0*10^3 /s^2

Then multiply top and bottom by s^2 giving

s^2 (4.5*10^-2 / 2.0*10^3)

Now put that back into your equation giving...

T_s = 2∏*√( s^2 (4.5*10^-2 / 2.0*10^3))

What does √(s^2) equal?

See the dimensions work out just fine.

 

[DLHill]

Oh I think I understand now, so would Ts = 2(pi)*sqrt(0.005)s^2 = 2(pi)*0.0707s = 0.443s?

 

[CWatters]

I think you have done sqrt twice by mistake.

 

[DLHill]

Oh, I just saw that. Thanks. So 2(pi)*(0.005)s^2?

 

[CWatters]

No now you forgot to sqrt the s^2 part

T_s= 2(pi)*(0.005)s