I need help with my physics lab questions: Different parts of my lab Questions:

Question

I need help with my physics lab questions: Different parts of my lab
Questions: 1. From your estimate of the uncertainty in the resultant angles in part one of the vectors lab, would the ex of better than one hal equilibrium? finer degree marks along the rim of the table improve the accuracy of riment? Consider that reading angles to the nearest degree gives a precision f degree. Do changes of one half degree noticeably affect the ed value. In parts 1 2. The weights used in the lab are accurate to 1% of their stamp a) and 1 b) you estimated an uncertainty in the applied weight (the resultant vectors 1% ) and the magnitude). Make a rough comparison of the expected uncertainty uncertainties you estimated 3. Assume that the weights used were accurate to 1%. To improve the accuracy of the experiment which would you do first: get more precisely marked weights, get a finer degree scale, or install pulleys having less friction. Explain your choice. 4. Suppose in part 1 a) the pulleys remain fixed but the total weight on each string is doubled. If the system was in balance before the weights were added, would equilibrium still exist after the weights are added? If 100 g is added to each string in part 1 a) will the system still be in equilibrium? Explain your answers. values from par t 5. Do the values ofer and /in part 4 of the vectors lab agree with the 5? What does this tell you about the magnitude of the uncertainties in the experiment? Is your answer different for the graphical and analytical methods?

Explanation / Answer

1. for two forces

A = |A|, at angle theta

A = |A|[cos(theta)i + sin(theta)j] [ where i and j are unit vectors in x and y direction]

so, dA = [cos(theta)i + sin(theta)j]*d|A| + |A|*[-sin(theta)i + cos(theta)j]d(theta)

|dA| = sqroot((d|A|cos(theta) - |A|sin(theta)*d(theta)))^2 + (d|A|sin(theta) + |A|cos(theta)*d(theta))^2)

|A| is the weight value, d|A| is the uncertianity in weights, |dA| is the uncertianity in measurement of A

assuming d|A| = 0

d(theta) = 0.5 degree = pi/360 radians

|dA| = |A|sqroot((|sin(theta)*d(theta)))^2 + (cos(theta)*d(theta))^2)

|dA| = |A|*d(theta)

|dA| = pi*|A|/360

so for adding two vectors, A and B

|dR| = pi(|A| + |B|)/360

this is a small but measurable amount and makes a difference in the resultant angle

2. d|A| = 0.01 ( given)

d|theta| = pi/360

so, |dA| = sqroot((d|A|cos(theta) - |A|sin(theta)*d(theta)))^2 + (d|A|sin(theta) + |A|cos(theta)*d(theta))^2)

|dA| = sqroot((0.01cos(theta) - |A|sin(theta)*pi/360))^2 + (0.01sin(theta) + |A|cos(theta)*pi/360)^2)

|dA| = sqroot(0.01^2 + |A|^2*pi^2/360^2 +2*|A|cos(theta)pi*0.01sin(theta)/360 - 2*0.01cos(theta)|A|sin(theta)*pi/360)

|dA| = sqroot(0.01^2 + |A|^2*pi^2/360^2) = sqroot(0.0001 + 0.00007615*|A|^2*)

this error > 1% but close to 1% for small values of |A| ( weights)

3. |dA| = sqroot(0.01^2 + |A|^2*pi^2/360^2) = sqroot(0.0001 + 0.00007615*|A|^2*)

so this error is very small, so better pulleys and better marked scales are more importnat

4. when the weights are doubled, the system will still be in equilibrium as both the weights have been increased proportianally, which will maintain the equilibrium

whereas, when 100g is asdded to both the weights, due to orifginall\lly different weights, this marks to a disproportionatew change in weights, and hence change in equilibrium

5. not all the values from part 4 agree agree with the 5, but they are close

this tells us that most of the uncertianities in this experiment are well within the theoretical limit as the actual answers found theoretically are inside the uncertianitites of part 4 measured experimentally, but one reading does ot agree within the error limits, but is close to the real reading by the eror margin of two times the expected error. this can be due to human error or some other random error in the experiment as well

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