Roman Cook
Physics 207 Lab: Little g

Hypothesis:

Why are objects attracted to earth and is that attraction the same rate as other planets? How does this effect everything we do in life, especially engineering? The key to everything is gravity. As Sir Isaac Newton once said when asked how he discovered the law of gravity, “By thinking about it all the time” (A-Z Quotes). So, let’s take a closer look at gravity in this lab together.

 

Introduction:

In this lab we will use several experiments to measure and better understand the acceleration of an object due to gravity. We know Earth has its own, unique gravity and the measurement is not similar on other planets or moons. Gravity is also difficult to measure and sometimes fully grasp as a concept yet it plays a vital role in our everyday life. Knowing this makes this lab and our understanding of gravity so important as aspiring engineers.

Procedures:

Experiment 1: A rough measurement

Here, we drop a wooden block to the ground from the top of a meter stick. We use a stop watch to time the fall from the top of the meter stick to contact with the floor. Since this method is extremely error sensitive we do 3 trials and average them to optimize our results. We are able to use the height (change in y) and time (s) in the known formula y=-.5gt^2 to solve for gravity.

Experiment 2: Slo-mo free fall

In the second experiment we are to watch a video of a man dropping a ball. We are informed that the video is performed in 60 frames per second and that the scale on the wall represents centimeters. We are to watch the video and use the information given and observed to find a calculation for gravity. The ball is dropped at frame 20 and crosses the final scale at frame 51. We will use the information gathered with in these frames to make our calculations for gravity.

Experiment 3: Leveling a ramp

In this experiment we are introduced to our ramp and cart. These tools will help us better estimate gravity using a program called LoggerPro and a frictionless cart on a controlled table. Here, we will level the ramp using several turn knobs at the “feet” or base of the ramp. Once we level the ramp we can once again adjust two of the four feet on the opposite end then the cart until the cart begins to roll. When it begins to roll we can measure the height of the decline at one end and use a=gsin(theta) to calculate our acquired angle.

Experiment 4: The rolling cart at different angles

In this experiment we use spacers to create different angles in which to roll our cart and ultimately track its data using LoggerPro. Later we will analyze the data in graphs of position and time. We will calculate our angles like we did in the previous experiment. As soon as we press “start” on LoggerPro program we will release the cart and let the cart slide down the ramp, collecting our data. We repeat this at 3 different angles.

Experiment 5: Rolling cart with different masses

In this experiment we will perform our position vs time data gathering through LoggerPro like previous experiments. The difference will be that our angles are the same but the masses will be different. Once we obtain the data from both trials we will use it to further interpret and understand acceleration with mass as a variable.

Results & Calculations:

Experiment 1: A rough measurement

Key formula: change in y=-0.5gt^2

Trial 1: 0.41s
Change in Y: 1 m

1=-0.5g(0.41)^2 solve for g=-11.9m/s

Trial 2: 0.32s
Change in Y: 1 m

1=-0.5g(0.32)^2 solve for g=-19.53m/s

Trial 3: 0.38s
Change in Y: 1 m

1=-0.5g(0.38)^2 solve for g=-13.85m/s

Experiment 2: Slow-mo free fall

Key formula: change in y=-0.5gt^2

Info: 60 fps with a total of 30 frames making it 0.5s and total change in y= 130 cm 0r 1.3m

1.3=-0.5g(.5)^2

g= -10.4 m/s

Experiment 3: Leveling a ramp

Key formula: a=gsin(theta)

Info: Ramp is 1.22 m long and height of ramp level is 0.066m and when cart first moves height is changed to .069m. Change in height is 0.003m.

Theta=sin^-1((0.003/1.22) = 0.141 degrees

Experiment 4: Rolling cart at different angles

Key formula: a=gsin(theta)

Angle 1:

Info: Ramp is 1.22 m long and height of ramp level is 0.073m. With spacers it is 0.095m. Change in height is 0.022m.

Theta=sin^-1((0.022/1.22) = 1.03 degrees

Angle 2:

Info: Ramp is 1.22 m long and height of ramp level is 0.073m. With spacers it is 0.110m. Change in height is 0.037m.

Theta=sin^-1((0.037/1.22) = 1.74 degrees

Angle 3:

Info: Ramp is 1.22 m long and height of ramp level is 0.073m. With spacers it is 0.135m. Change in height is 0.062m.

Theta=sin^-1((0.062/1.22) = 2.91 degrees

Experiment 5: Rolling cart with mass

Key formula: a=gsin(theta)

Info: Ramp is 1.22 m long and height of ramp level is 0.073m. With spacers it is 0.083m. Change in height is 0.01m. Mass of weight was 526.3 grams (this doesn’t matter for this experiment)

Theta=sin^-1((0.01/1.22) = 0.47 degrees

Lab Discussion:

Discussion 1: The method of dropping a block and using a stop watch to time the fall then solving y=-.5gt^2 for gravity is extremely unprecise. It is unprecise due to a human’s inability to stop the time properly although doing more trials does and averaging does improve your number for gravity. Although it is not extremely precise it is a valuable way to see gravity at work and get a basic acceleration value for it.

Discussion 2: Is the track truly 100 % level? Let’s look at the uncertainty of theta.

Closest measurement we can obtain= 0.01 cm = 0.0001m

Uncertainty angle of the track = sin^-1(0.0001m/1.22m) = 0.0047 degrees

The reason we can get away with this tiny amount of uncertainty while leveling our track is likely because of a small amount of friction. Although the track is technically “frictionless”, we can deduce that with the wheels and metal grids there is a small amount of friction we can neglect.

Discussion 3: Estimate static friction coefficient.

F=N*u u=F/N F=w*sin(theta) N=w*cos(theta) w=m*g

Theta= 0.141 m=500g=0.5kg w=0.5kg*9.8m/s^2=4.9N

F=4.9N*sin(0.141)=0.69 N=4.9*cos(0.141)=4.85 u=F/N=0.14

Discussion 4: Do the measurements all produce similar results for g?

a = g*sin(theta) g = a / sin(theta)

Trial 1: 1.03 degrees a=0.1852 g=10.3m/s^2

Trial 2: 1.74 degrees a=0.1903 g=9.64m/s^2

Trial 3: 2.91 degrees a=0.4909 g=9.67m/s^2

The three measurements of angles produce similar results for gravity. This is because the force gravity exerts on the cart does not change. The variable is only the angle of the track. The angle changes the acceleration in the cart to change which gives us a slight variance in our calculation for gravity.

Discussion 5: Did mass affect acceleration?

Trial with mass= 0.47 degrees a=0.0954 g=11.6 m/s^2

Trial without mass= 0.47 degrees a=0.0952 g=10.9 m/s^2

The mass slightly affected the acceleration in making it increase slightly. Our prior understanding of kinematics tells us that the mass should only have an effect on the force of the cart and not the acceleration. Based off this, the results are surprising and could be attributed to error or uncertainty in measurements.

Discussion 6: The average for all group’s gravity is: (10.1-3.25-3.6-10.4+11.25+9.9-14.7+9.2-9.8)/9 = -0.144 m/s. This is not within our uncertainty and is likely a bad representation of gravity on Earth for several reasons. One is the experiment is not very accurate to start with as discussed in procedures. Also many groups did not use (-) in the formula to solve for gravity giving them positive acceleration. This we know does not accurately represent gravity. Mistakes also could have happened in the “slow-mo” experiment. In this experiment the group would have to recognize that the man doesn’t initiate the free fall until frame 20. Also groups would have to recognize that each frame did not represent a second but 60 frames per second which would drastically alter their calculation for gravity.

Abstract: Overall, this lab is tremendously important to allow us to better understand and evaluate gravity. The more precise and expensive our technology is, the more accurate we can calculate gravity and its affects. In the engineering field, information from this lab will allow us to comprehend the effects of gravity and properly compensate for the forces that gravity delivers.

Conclusion: There are many ways to calculate gravity: some more accurate than others. We tested several of these during this lab and found that using technology allows us the most accuracy. We also know that gravity effects our everyday life in many ways. This is why it is so important to study it and understand its significance. As engineers we will be expected to take gravity into account for projects throughout our career.

Works Cited

Bing.com. (2019). gravity comic – Bing. [online] Available at: https://www.bing.com/images/search?view=detailV2&ccid=0Cd8kkNj&id=23944FA906EF57F31CDED0A6F228A851FB8232DC&thid=OIP.0Cd8kkNj8dPRnD8r2Qae9gHaHo&mediaurl=http%3a%2f%2finvisiblebread.com%2fcomics%2f2012-07-05-gravity.png&exph=825&expw=800&q=gravity+comic&simid=607991841047054812&selectedIndex=0&ajaxhist=0 [Accessed 4 Mar. 2019].

A-Z Quotes. (2019). TOP 25 QUOTES BY ISAAC NEWTON (of 194) | A-Z Quotes. [online] Available at: https://www.azquotes.com/author/10784-Isaac_Newton [Accessed 4 Mar. 2019].

Bing.com. (2019). isaac newton quotes – Bing. [online] Available at: https://www.bing.com/images/search?view=detailV2&ccid=egu1SaHg&id=6DE4ECE97F6B428ABC5B0ED31BF550D8DC0ADB57&thid=OIP.egu1SaHgPb_pF9yReEF0fAHaDt&mediaurl=http%3a%2f%2fwww.quotespedia.info%2fimages%2fact%2fisaac_newton_act_1840.jpg&exph=350&expw=700&q=isaac+newton+quotes&simid=608048788050018820&selectedIndex=10&ajaxhist=0 [Accessed 4 Mar. 2019].