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Lecture

# Verification of Galileo’s Experiments on Gravitational Effects.docx

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School
Department
Astronomy
Course
CAS AS 101
Professor
Paul Withers
Semester
Fall

Description
Jarrett 1 Kate Jarrett AS 101 Lab Report: Gravity Lab Due: 10/24/13 Lab: B5 Verification of Galileo’s & Newton’s Experiments’on the Effects of Gravity and Momentum Introduction: This lab served to prove Galileo’s and Newton’s past experiments about gravity, acceleration and momentum accurate. Galileo’s past experiments showed that all bodies accelerate in the same way and that the acceleration of gravity is constant for all objects at the surface of the Earth. In order to recreate Galileo’s experiments and test them for ourselves we performed 2 experiments. These two experiments will answer our questions on how gravity affects acceleration and how a bodies’mass affects acceleration as well. Our third experiment will focus more on Newton’s theories. Newton’s first law states that an object’s velocity will not change unless a force acts upon it. Which is a natural consequence of the conservation of momentum. We performed a third experiment to answer our questions on the conservation of momentum. Procedure/Analysis: Our first experiment was a recreation of Galileo’s experiment. For this experiment tested the acceleration of gravity. We recorded and learned how the mass of the ball relates to its velocity during acceleration. Equipment forAcceleration of Gravity – Galileo’s experiment: 1. Balance/Scale 2. 4 different marbles (different masses & sizes) 3. Wood (serve as inclined plane) 4. Stopwatch 5. Protractor (to measure angle) 6. Something to put the wood on to be on an incline. [Type text] [Type text] [Type text] 2 Procedure forAcceleration of Gravity – Galileo’s experiment: First, we weighed and recorded the mass of each marble using the balance. Next, we raised and measured the planks incline. We did this between each trial. Then, we measure its angle with a protractor. Next, we made some predictions on how each marble, of different sizes, mass and material will affect its acceleration down the inclined plane. Then we rolled the marbles down the inclined plane, timing it from start to stop with our stopwatch. Then we measured and recorded their average velocity. We measured their average velocity by finding how much time it takes the marbles to reach the bottom of the inclined plane. The formula is V= ∆s / ∆t. We repeated this procedure for each marble for each incline. The inclines we chose were, 14 degrees, 22 degrees and 32 degrees. It is important to know that the force of gravity caused the marbles to roll, G= 9.8 meters/s . Equipment forAcceleration of Gravity – Cart Track Experiment: 1. Ruler 2. Meter Stick 3. Air Track 4. Cart for track 5. Computer with Logger Pro Software 6. Stopwatch Procedure forAcceleration of Gravity – Cart Track experiment: This procedure is almost identical to the first one. However instead of using the marbles and wooden plane, we used the Air Track and cart. The reason we replicated the first experiment with an Air Track and a cart is because the carts have very little rotating mass. This is important because less mass means less energy to be sapped from the acceleration down the track. The first thing we did in this experiment was measure the angle. This is different than Galileo’s experiment; we can’t just use a protractor. Instead we measured the height of the track, at the front where it is a smaller height and Jarrett 3 then we measured the back of the track where it is a larger height. Next, we measured the distance from point A, where the cart starts, to point B, where it ends. The formula we used was Tan θ = ∆y/∆x. After we calculated the angle we began recording the carts position versus time. We did this with Logger Pro. We set up the sensors to Dig/Sonic and then zeroed it between each trial. To record the data we clicked the collect button. After our data was recorded we looked at the graph after each trial and took note of the slope. This slope gave us the necessary information to learn the average velocity while the cart was moving. Remember, it is important to know that the force of gravity still affected the cart, G= 9.8 meters/s . Equipment for Momentum – Track Experiment: 1. Ruler 2. Meter Stick 3. Air Track 4. 2 Carts for track (with Velcro) 5. Computer with Logger Pro Software 6. Stopwatch 7. Balance/Scale Procedure for Momentum – Track Experiment: First, to test and verify Newton’s first law we simply pushed a cart down the track with no incline. We did this to witness that its velocity will not change, since no force is acting upon it. We collected the data the same way as in the previous experiment, making sure to zero between trials. Next, we moved on to 2 carts and observed how momentum is conserved when they collide. Both carts have Velcro on one side, in order to measure in elastic collision (will stick when carts run into each other) and elastic collision (will not stick). We took qualitative predictions in the pre lab to test the qualitative observations we made during this experiment. We recorded as we placed one car at rest and propelled the other car at it. We did this for both inelastic and elastic collision and recorded when they did and did not stick. Afterwards we turned to quantitative observations. First, we measured the [Type text] [Type text] [Type text] 4 mass of each cart with a balance / scale. We then placed cart 1 (with mass M and 1lunger depressed) against the barrier and cart 2 (mass M ) 20cm away from cart 1. We made sure to note the position where the edge of cart 2 will be hit by cart 1 (referred to as d). Then, we began collecting data with Logger Pro. We tapped the end of the plunger and it propelled down the track to collide and stick to cart 2 at position d (collision occurred). Next, we viewed the data table on the computer screen and recorded the highest velocity (v 12 after the collision – before friction has time to act. We performed this experiment multiple times so we could later take an average. Lastly, we have to set up cart 1 by itself again. We did this to measure the velocity before it would have hit cart 2. Again, we collected with Logger Pro. We again, looked at the data on the computer and noted the velocity, v where 1 position d occurred. We performed this multiple timed for an average. The formula we used to later calculate our results are: M1 1= (M +1M ) v2& 12= M v12M + 1 1 /Th1s wil2 be further explained later during the results. Results/Discussion forAcceleration of Gravity – Galileo’s experiment: Marble #1 Marble #2 Marble #3 Marble #4 Wood Mass (grams) 63.5g 521g 40.8g 9g 4 Incline Velocity (sec.) o 1.80s 1.55s 1.66s 2.40s 14 Incline Speed (sec.) o 1.31s 1.43s 1.41s 1.63s 22 Incline Speed (sec.) 1.21s 1.23s 1.26s 1.36s 32 Incline Speed (sec.) 0.90s 0.91s 0.92s 1.09s The results we concluded in this experiment and the observations we made show that the relationship between acceleration and marble size. The table reflects varying acceleration in respect to the marbles. However, we learned that the higher the incline, the less the marble’s size affected its acceleration. On the smaller inclines the marbles’size has a larger impact in its acceleration rate. With Jarrett 5 the larger incline, we proved Galileo’s theory and experiment correct, in that all bodies accelerate in the same way. It is important to know that the force of gravity caused the marbles to roll, G= 9.8 2 meters/s . This experiment was subject to multiple errors. The first being friction, A rolling ball is not subject to much friction. Another issue is energy, it takes energy to make
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