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(I) Lets start with very simple data table 1.0 2.0 3.0 4.0 5.0 6.0 -1 ± 1.8 4±2.0 9+ 1.0 14 + 0.8 19 s 0.8 24 + 1.2 2% 1.8 34 ± 2.0 7.0 8.0 9.0 1. Plot a graph of y vs. X on a piece of graph paper 2. Is it a straight line? Draw the best-fit line. 3. Compute the slope and y-intercept for this line. Write the equation for y in terms of x using the straight line equation y mx+ b, where m is slope of the best-fit line and b is y-intercept 4. How is the b value calculated from the graph, and how is it calculated from the equation Gust saying that it is the b in the equation y -mx + b is not sufficient). Demonstrate this latter calculation.
(II) Not we have a slightly more complicated set of data, for position vs time: Time t (sec) 0.5 1.3 2.1 2.8 3.4 Position y (m) 0.6 4.2 20 29 42 76 5.5 6.3 1. Plot the values of position vs time. What is the shape of the graph? 2. What shape you expect to obtain when you plot y vs. t2? Make this plot. 3. Using these two plots, derive a mathematical relationship expressing the time dependence of y; it will help for you to write down the slope with correct units for the graph of y vs t. Explain this position-time relationship clearly in your lab report, noting the physical significance of any terms which appear in your expression. 4. Compute slope of the original plot y vs t at time t-2.0 sec. To help you do this, consider what is the physical significance of this slope (write your answer down). Give the proper units of the slope.
(III) Now let us consider the relationship between time period for an oscillation and length for a simple pendulum Length L. (m) Time period T(se 0.15 0.3 0.45 0.61 0.75 0.91 1.03 1.2 1.35 0.8 1.1 1.3 1.6 1.7 1.9 2.0 2.2 2.3 The time period (lime for one oscillation) of a simple pendulum depends on the length of pendulum. This above data set includes time periods T for different length of pendulum. 1. Plot this data on a piece of graph paper 2. Linearize the graph as necessary 3. Show the final form of functional dependence of time period T on length L
IV) Let us known consider the relationship between pressure and volume for a gas trapped in a non-rigid container Pressure P(psi Volume V(ml) 59 52 39 34 28 23 18 2.0 2.4 3.3 3.8 5.0 6.2 8.4 For any given mass of a gas and at constant temperature, the volume of gas varies with pressure exerted on it. This data set shows the real life values for pressure and volume for fixed amount of air 1. Plot V vs. P 2. Linearize the plot if needed (e.g. if it is not already a straight line). 3. Based on the shape of plot, express the form of the functional relationship between pressure and volume 4. This expression represents one of the gas laws. Do you know which one is that?
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Answer #1

Question 1.

614949494 11223 IS 1 2 3 4 5 6 7 8 9

Part (a). Plot is below

40 Y 30 20 10 0 -10 6 X Axis Title Linear Regression R2:1, aR2:1. PO, SE:0 ▼ Fit Method y 5x-11 Linear

Part(b) Above plot is straight line since data i fitted with equation y = mx +c , where m is slope of straight line and c is y-intercept of straight line.

Part (c). From graph slop m= 5, and intercept c=-11.

Part (d). m= b= 5 is slope of straight line. By hand it can be calculated using formula

2-91 T2-1

where (x1,y1) and (x2,y2) are any two points in graph.

I will be glad to see your comment if you have any query and thumb up if you are satisfied. Thanks...

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