SI Conversion Gravitational Elongation

[Scott S]

I have attached a pic which really explains the formula and context of the problem.

I am trying to convert the formula in (b) below into feet.

If I could reproduce the answer with English units, I could move on and apply the formula to other situations, but the multiplicity of English units is really confusing me.
The English units I have are;
g = 32.17405
x = 3277.972
Next two from my tapes manufacturer,
A = 0.003" (but I think it should be 0.034 feet)
E = 29,700 KSI
M = 0 but could be 20 lbs.
Next one again from the manufacturer,
m = 0.0102 lbs/ft.
l = 3280.84
P(sub)0 = ? but my hundred foot tape would be 23 lbs.

 

[gneill]

Hi Scott S. I've provided some annotation to your post (in red). What's the underlying issue here? Do you have a different tape from a manufacturer with different parameters from those used in the given problem and you need to know how to apply the formula with the new parameters?

I have attached a pic which really explains the formula and context of the problem.

I am trying to convert the formula in (b) below into feet.

If I could reproduce the answer with English units, I could move on and apply the formula to other situations, but the multiplicity of English units is really confusing me.
The English units I have are;
g = 32.17405 ft/s²
x = 3277.972 ft ?
Next two from my tapes manufacturer,
A = 0.003" (but I think it should be 0.034 feet) Cross sectional area should be in [length-unit]²; 0.003 in² seems a bit small.
E = 29,700 KSI Presumably kilo psi (thousands of pounds per square inch)
M = 0 but could be 20 lbs. There's no M shown in the formula
Next one again from the manufacturer,
m = 0.0102 lbs/ft. Presumably weight per unit length
l = 3280.84 Total length of the tape?
P(sub)0 = ? but my hundred foot tape would be 23 lbs.

 

[Scott S]

gneill,

That is it in a nutshell. I took a few tries at it and cannot reproduce the metric result with "english" units.

I added a jpeg of the text explanation if that helps.

 

[gneill]

The value 0.003" from your manufacturer that you're using for the cross sectional area, A, is more likely to be a tape thickness. You'll need the width as well in order to determine A.

Why don't you present a table showing, for the text's given values, the Metric and corresponding English unit values that you believe correspond to them? I might be able to spot conversion issues if I see all of your values.

 

[Scott S]

g = 9.81m = 32.17405 ft
x = 999.126m = 3277.972 ft
A = 10.2mm^2 = 0.003 inches (from manufacturer - I get 0.034 feet)
E = 2x10^5 N/mm^2 = 29,700 KSI (from manufacturer of tape)
M = 0 = 0 (theoretically any attached weight kgs in orig/lbs in conversion)
m = 0.075 kg/m = 0.0102 lbs/ft (from manufacturer)
l = 1000m = 3280.84 ft
P= 175 N tension = 39.375 lbs (?), force conversion, not sure how Newtons convert.

 

[gneill]

g = 9.81m = 32.17405 ft
x = 999.126m = 3277.972 ft
A = 10.2mm^2 = 0.003 inches (from manufacturer - I get 0.034 feet)
E = 2x10^5 N/mm^2 = 29,700 KSI (from manufacturer of tape)
M = 0 = 0 (theoretically any attached weight kgs in orig/lbs in conversion)
m = 0.075 kg/m = 0.0102 lbs/ft (from manufacturer)
l = 1000m = 3280.84 ft
P= 175 N tension = 39.375 lbs (?), force conversion, not sure how Newtons convert.

Okay. For g the units should be ft/s².

For A, the cross sectional area, the units should be square inches (in²) since the modulus of elasticity is in KSI (Kilopounds force per square inch or kPSI = 1000 x lbf/in²). The reason is that the square inches in each will cancel when you multiply them: A*E. For the text's values I find:

E = 29008 KSI
A = 0.0158 in²

For the tape's linear density the units should be pounds mass per linear foot, so the 0.075 kg/m becomes:

m = 0.05040 lb/ft

The units on the tensioning force should be pounds force, or lbf. All too commonly the same name, lb, is used for both pounds mass (lb) and pounds force (lbf), but this should be avoided as the distinction is important.

 

[Scott S]

Woohoo!

Thanks gneill, with a little tweaking of the values I managed to get the answer in INCHES and then converted to feet and looks like I'm golden.
Thanks again.