Linear Mass Density: Find 8.9866e-4 m/s to g/m

In summary, the linear mass density can be found by taking the natural log of the velocity and tension and using the formula ln(v) = 1/2 ln(T)-1/2ln(m). The y-intercept of the best fit line from five trials can be used to find the linear mass density, with units of m/s. However, it is important to be consistent with units throughout calculations to ensure the correct units for the linear mass density.
  • #1
Linear Mass Density!

Homework Statement



Find linear mass density using a graph ln(v) vs ln(T), from Velocity=squareroot Tension/linear density, take natural log ln(v) = 1/2 ln(T)-1/2ln(m). our professor told us to find it this way cause 1/2ln(m) is the y-intercept of the best fit line of five trials

Homework Equations


so y-intercept=-1/2ln(m). for y intercept I got 3.5073 from an experiment done in lab.

The Attempt at a Solution


I got 8.9866 * 10^-4 for linear mass density. but after all that my main question is what are the units? would they be m/s? if so how do I convert it to g/m?

Thanks!
 
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  • #2


it depends on units in which v and T are given. you have to extract units from formula Velocity=squareroot Tension/linear density.

Units of right and left parts of equation must be the same.
 
  • #3


the units for tension are Newtons and the units for velocity are hertz times meters, which is just m/s. So i didn't know if taking the natural log of tension and velocity changes the units or are they the same?
 
  • #4


logarithm equation and equation without logarithm are eqivalent
if [v]=m/s, it doesn't mean that [ln(v)]=m/s of course. They are two different numbers representing the same velocity and can't have the same dimension.
but if you are consistent with formulas you have in your calculations, you will get right units from the initial equation.

because

ln(v) = 1/2 ln(T)-1/2ln(m)

is the same as

ln(v)=ln(sqrt(T/m))

is the same as

v=sqrt(T/m), m=T/v*v.

So, if [T]=N, [v]=m/s, you can easily extract [m]. And it is not m/s.
 
  • #5


I would first commend you on your thorough approach to finding the linear mass density. It is important to use data and mathematical relationships to determine accurate values in scientific experiments.

To answer your question about the units, the units for linear mass density are typically expressed as mass per unit length, such as grams per meter (g/m) or kilograms per meter (kg/m). In your case, you have calculated a value of 8.9866 * 10^-4 m/s for the linear mass density. However, this unit is not consistent with the standard units for linear mass density.

To convert from m/s to g/m, you will need to use the relationship between mass and velocity. The equation for linear mass density, as given by your professor, is v = √(T/λ), where v is velocity, T is tension, and λ is linear mass density. This can also be written as λ = T/v^2. In this case, velocity is given in m/s, so you will need to convert it to m^2/s^2 in order to cancel out the units of velocity.

To convert from m/s to m^2/s^2, you can simply multiply by m, since m/s is the same as m/s^2. This gives you a value of 8.9866 * 10^-4 m^2/s^2 for the linear mass density. To convert this to g/m, you will need to multiply by a conversion factor of 1 g/1000 m^2. This gives you a final value of 8.9866 * 10^-7 g/m for the linear mass density.

In summary, the units for linear mass density are typically expressed as mass per unit length, such as g/m or kg/m. To convert from m/s to g/m, you will need to use the relationship between mass, velocity, and length, and apply appropriate conversion factors. I hope this helps clarify the units for you.
 

What is linear mass density?

Linear mass density is a measure of the mass per unit length of a one-dimensional object, such as a string or wire. It is typically denoted by the symbol λ (lambda) and has units of kilograms per meter (kg/m).

How do you find linear mass density?

To find linear mass density, you divide the mass of the object by its length. The formula is: λ = m / L, where λ is the linear mass density, m is the mass of the object, and L is the length of the object.

What is the unit for linear mass density?

The unit for linear mass density is kilograms per meter (kg/m).

How do you convert from meters per second to grams per meter?

To convert from meters per second (m/s) to grams per meter (g/m), you need to multiply by 1000. This is because 1 meter is equal to 1000 millimeters and 1 gram is equal to 1000 milligrams.

What is 8.9866e-4 m/s in g/m?

8.9866e-4 m/s is equivalent to 0.89866 g/m. This can be calculated by converting meters to millimeters (0.00089866 m) and then converting from kilograms to grams (0.00089866 kg = 0.89866 g).

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