Physics 051 Lab 3 - Linear Dynamics PDF

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Physics 051 Lab Report 3...

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Physics 051 Linear Dynamics – Newton’s 2nd Law

Riley Forbes

September 20th, 2018

Lab TA – Sanish Paramadam Lab Mates – Matt Bierach, Ethan Lauricella, and Patrick Ladd

Results and Discussion Graph 1 – This graph shows the force, in newton’s (N), on the y-axis over time, in seconds (s), on the x-axis. Some specific points to mention include when the cart was let go of, at a little after 1 second, and when the cart was caught, right around 2 seconds. The region when the cart was in motion and moving across the ramp was from 1 to 2 seconds. Looking at the region from about 0 to 1 seconds, just before the cart was let go, the average force is 0.7933N which is not as you would expect as the acceleration of the cart was zero.

Force (N)

Force (N) over Time (s) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 -0.1

0.5

1

1.5

2

2.5

3

3.5

Time (s)

Graph 2 – The acceleration, in meter per seconds squared (m/s2), is located on the y-axis over time, in seconds (s), on the x-axis. The same regions mentioned in the description of graph 1 can be applied to the acceleration; from about 1 second on the cart was released, which can be seen as the acceleration increases and the cart was caught right around 2 seconds (after 2.2 seconds or so the acceleration returns to zero).

Acceleration (m/s²) over Time (s) Acceleration (m/s²)

4 2 0

0

0.5

1

1.5

2

2.5

3

3.5

-2 -4 -6 -8 -10 -12

Time (s)

Table 1 – This table describes the masses of the bare cart, the cart with the 2 slugs, and the cart with 4 slugs. Additionally, the average standard deviation for the force and acceleration are listed as recorded by the Lab Quest machine for each of the 4 different hanging mass values chosen by my group mates and I. Bare Cart Mass Cart + 2 Slugs (kg) (kg) 0.281 0.531 Hanging Mass Value (kg): Acceleratio Forc Acceleratio Forc n e n e Avera 0.49 0.53 ge: 1.633 0 0.938 0 Acceleratio Forc Acceleratio Forc n e n e Std. 0.01 0.00 Dev. 0.017 1 0.019 8 Hanging Mass Value (kg): Acceleratio Forc Acceleratio Forc n e n e Avera 0.57 0.62 ge: 1.865 0 1.092 0 Acceleratio Forc Acceleratio Forc n e n e Std. 0.01 0.01 Dev. 0.029 5 0.015 1 Hanging Mass Value (kg): Acceleratio Forc Acceleratio Forc n e n e Avera 2.081 0.60 1.228 0.68

Cart + 4 Slugs (kg) 0.781 0.060 Acceleratio Forc n e 0.56 0.647 0 Acceleratio Forc n e 0.00 0.015 8 0.070 Acceleratio Forc n e 0.65 0.769 0 Acceleratio Forc n e 0.00 0.012 8 0.080 Acceleratio Forc n e 0.855 0.71

ge: Acceleratio n Std. Dev.

0.023

0 Forc e 0.02 5

Acceleratio n 0.015

Hanging Mass Value (kg): Acceleratio Forc Acceleratio n e n Avera 0.71 ge: 2.453 0 1.501 Acceleratio Forc Acceleratio n e n Std. 0.02 Dev. 0.056 9 0.018

0 Forc e 0.01 4 Forc e 0.82 0 Forc e 0.01 9

Acceleratio n 0.018 0.100 Acceleratio n 1.067 Acceleratio n 0.023

0 Forc e 0.01 2 Forc e 0.87 0 Forc e 0.01 3

Table 2 – The hanging mass value that I used for the three cart runs was 80 g which is equivalent to 0.080 kg. To calculate the mass value of the bare cart and/or the cart with slugs, I rearranged the equation 3.1: Fnet = maner to solve for the mass and plugged in the average force over the acceleration given in table 1. For each of the calculated mass values there is an associated percent error which was determined by taking the force/acceleration, subtracting it by the actual mass of the cart, and then dividing that by the actual mass. To get the value into a percent, we multiplied by 100. When looking at the percent error, you can see that the error steadily increased as the mass increased. I do not believe that the error was “random” as my group mates also had a similar pattern of error, but rather the small amount of friction or the unevenness in our track played a larger role as the mass of our cart increased. Hanging Mass Value: Mass (cart + Force/accelerati slugs): on: Cart: 0.288 Cart + 2 slugs: 0.554 Cart + 4 slugs:

0.830

80 g Percent error: 100*((F/a)M)/M 2.606 4.284 6.326

Table 3 – This table shows the masses in kilograms, of the bare cart and/or the cart with slugs times a hanging mass (red = 0.06 kg, orange = 0.07 kg, purple = 0.08 kg, and blue = 0.1 kg) divided by the same cart and hanging mass, and compares it to the tension of the string between the cart and the hanging mass. The tension was determined by multiplying the mass times

gravity. All of these calculations were derived from equation 3.3: T = Mcart*mhanging*g/( Mcart+mhanging). Mass (kg) 0.049

Tension 0.485

0.054 0.056 0.056 0.062 0.064

0.528 0.546 0.549 0.606 0.630

0.062 0.070 0.073 0.074 0.084

0.610 0.681 0.711 0.723 0.825

0.089

0.869

Graph 3 – From the calculations in Table 3 a graph was prepared with tension in newtons (N) located on the y-axis over time in seconds (s) on the x-axis. From the plotted points, a line of best fit was determined and the equation was derived and is shown (y=9.8x – 3E-15). As one can see, and we would expect, the slope of the line is equivalent to gravity at 9.8 m/s2. There is however, a very small y-intercept at 3x10-15 which is not expected, but may account for a very small amount of the error that was seen in our mass calculations as this y-intercept is showing a slightly decreased tension prior to

Tension (N)

Tension (N) Versus Combined Mass (kg) 1.00 0.90 f(x) = 9.8 x − 0 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.05 0.05 0.06 0.06 0.07 0.07 0.08 0.08 0.09 0.09 0.10 Mass (kg)...