Lab Quiz 8

You measure the mass of a string to be 4.35grams with an error of 0.1 grams, and the length of the string to be 151cm with an error of 2 cm. The string runs over a pulley and has 101.1grams suspended from it as shown in the figure above. You neglect the error of the suspended mass. What is the absolute error of the traveling wave velocity on the string (Ch10 sheet 20) ? (Hint: calculate the relative error of the linear mass density u=m/L using equation (7) of "Error and Uncertainty" ("EU"). Then write the wave velocity v in the form v=constant x u^.5 (since you neglect the error of the suspended mass and hence the error of the string tension), and use equation ( in "EU" to calculate the relative error of v. Finally change the relative error of v into the absolute error of v)

Number 3.

Does anyone know how to solve it?

I did sqrt((.0001/.00435)^2+(.02/1.51)^2)=.0265311 which is the error of u.

Now I did the tension (.1011x9.81=.991791), which I think is the constant.

Then I do .991791 x .5(.0265311) which is .01315, and the answer should be .2461

Anyone know what I did wrong or what to do right?

Calculation for u is correct, but then you dont need to calculate the constant because it drops out. Instead you take u and multiply it by 1/2 and then multiply that by the velocity to get the absolute error of the velocity. that will give you .2461

You measure the mass of a string to be 4.47 grams, and the length of the string to be 132 cm. The string runs over a pulley and has 87.3 grams suspended from it as shown in the figure above. What is the velocity of a traveling wave on the string (Ch10 sheet 20)? Indicate with a positive (negative) sign whether the string length to be measured extends from points A to B (A to C).

How to solve:


You vary the frequency, which excites standing waves on a string and record it every time a standing wave pattern is observed. You plot the frequencies fn versus the number n of half waves observed and measure the slope of the linear graph you obtain to be 8.35 Hz. You relate the slope to the traveling wave velocity v (Ch10 sheet 19) and calculate v from the slope and the string length of 109.1 cm. What is the value of v? Indicate with a positive (negative) sign whether the string length to be measured extends from points A to B (A to C).

How to solve:

1)

V= SQRT(T/u)

u= m/L, m is the MASS OF THE STRING , in KG, and L is the LENGTH OF THE STRING, in m

T= M*g, where M is the MASS OF THE ATTACHED WEIGHT, g is 9.81 m/s

Now it should be easy to solve for V (I got 15.985 m/s)

2)

V= f1* 2L

Which basically means multiply the slope of the graph, f1 by DOUBLE the given length of the string

(I got 18.585m)

how do u find the velocity in Q3?

DELTA V = SQRT((delta m/ m)^2 + (delta L/ L)^2) * 1/2 * V

V= SQRT (T/u) Just like you did in question 1 (look at my previous post for question 1 if you are not sure)

wut r the signs?

1) Neg

2) Pos

3) Pos

can u help explain 3 with numbers please srry about new subject post hehe

I cant figure out 3 either can someone explain it please?

Yes, I don't understand what L would be-- they don't specify a length.

You measure the mass of a string to be 3.76 grams with an error of 0.1 grams, and the length of the string to be 164 cm with an error of 2 cm. The string runs over a pulley and has 90.5 grams suspended from it as shown in the figure above. You neglect the error of the suspended mass. What is the absolute error of the traveling wave velocity on the string

First, convert everything into SI units
Find T = M * g like posted in the first question where M is mass of suspended weight in kg and g is 9.81
In this question, T = .0905 * 9.81 = .8878
U = m/L where m is mass of string and l is length
U = .00376/1.64 = .002292

Then find v = sqrt (T/u) = sqrt (.8878/.002292) = 19.67

Then find DeltaV = sqrt ((deltam/m)^2 + (deltaL/L)^2) * 1/2 * V
Delta v = sqrt ((.0001/.00376)^2 + (.02/1.64)^2) * 1/2 * 19.67
I First calculated the value under the squareroot = .0292584 and then do .0292584 * 1/2 * 19.67
And the answer I got was .28787

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