Group3_4_ch4

__ Gravity and the Laws of Motion __
Task A: Max Llewellyn Task B: Michael Poleway Task C: Maddie Margulies Task D: Michael Poleway

- Find the value of acceleration due to gravity - Determine the relationship between acceleration and incline angle - Use a graph to extrapolate extreme cases that cannot be measured directly in the lab - Determine if there is an effect of mass on acceleration down the incline
 * Objectives: **


 * Hypothesis**: The acceleration due to gravity is -9.8m/s^2, as it is basic knowledge we have used in class throughout the year in problems dealing with free fall. The acceleration of the ball traveling down the ramp will be different though, as it changes with whatever the incline angle is. It would be between 0 and 9.8 m/s^2 because in a free fall the acceleration would -9.8, while in a horizontal launch, it would be 0. Because it's on a slant, the acceleration has to be in between those two values. As the incline angle increases, so does the acceleration and the closer it will be to -9.8 m/s^2. The mass of the ball will affect acceleration, as mass is inversely proportional to acceleration. This was stated by Newton's second law, and the heavier the ball, the less the acceleration will be. The lighter the ball though, the more the acceleration will be.


 * Method and Materials**: First, our group was given a metal ball of a certain weight. We measured the ball on an electronic balance and it came out to .225 kg. Then we went over to our ramp and measured the length of the it with a ruler, which came out to be 1.2 meters. After, we had to adjust the height of the ramp to .15 m. Once the ramp was set, we rolled the ball down the ramp and timed how long it took for it to reach the end with a stopwatch. We did about five to six trials and set the ramp to another height. We used several heights to time how long it took for the ball to reach the end of the ramp.

media type="file" key="Movie on 2011-11-18 at 11.49.mov" width="300" height="300"


 * Mass of ball**- .225 kg

1. Acceleration
 * Sample Calculations **

2. Sin(theta)

**Data**

Data table

Graph

Excel file

y= 8.0169x + 0.0274 The slope of the line in the experiment was 8.02. If the experiment resulted in perfect results, then the slope should have been 9.8. 9.8m/s/s is equal to the acceleration due to gravity. The y intercept is related to friction.
 * Slope**:

The r^2 value for this experiment was .956 due to errors, such as not timing or measuring correctly. The r^2 value should be 1 if there were perfect results. If the line r^2 was 1 then it would fit exactly on the line of best fit.
 * r^2**:

1. Acceleration due to gravity The slope of our graph is equal to the gravity in our experiment which is 8.93 m/s/s. This is close to the acceleration due to gravity which is 9.8 m/s/s. 2. What is the percent error between your experimental value for freefall acceleration and the theoretical value for freefall acceleration?
 * Analysis**

Percent error:

Percent Difference: 3. Class data at h= .15m ||
 * || Mass(kg) || Slope(experimental"g")(m/s/s) || Acceleration(m/s/s)
 * || 0.02 || 5.57 || 0.77 ||
 * || 0.07 || 8.55 || 0.84 ||
 * || 0.54 || 8.14 || 1.04 ||
 * || 0.08 || 11.45 || 0.84 ||
 * || 0.03 || 7.58 || 0.72 ||
 * || .225 || 8.02 || .917 ||
 * average || 0.15 || 8.20 || .855 ||

4. FBD of the ball on the ramp The x component of the weight force is causing the ball to roll down the ramp because the y component is balanced with the normal force. The ball rolls down the incline with a normal force and weight acting on it. Gravity is the stronger force in this experiment. The acceleration of the ball down the ramp was .917 which was a little higher than the class overage of .855.
 * //a. What force is causing the ball to roll down the ramp? Is it the whole force or just part of it? If just a part, which part?//**

//**1. Is the velocity for each ramp angle constant? How do you know?**// No, the velocity for each ramp angle changes because through our calculations for acceleration we can see that it changes depending on the angle. Also, we found the acceleration of the ball, so if it was accelerating the ball was not constant. //**2. Is the acceleration for each ramp angle constant? How do you know?**// Yes, the acceleration is constant at each ramp angle because we tested it multiple times. However, when we changed the angle for the other trials, the higher the angle the higher the acceleration. //**3. What is another way that we could have found acceleration of the ball down the ramp?**// Another way we could have found the acceleration of the ball down the ramp is using the sensors that we used in the beginning of the school year. We could have plugged the sensors into our computers and looked at the graphs to find the acceleration. //**4. How was it possible for Galileo to determine g, the rate of acceleration due to gravity for a freely falling object by rolling balls down an inclined plane?**// Galileo determined the rate of acceleration by doing many trials. He rolled a ball down and up the ramps and then measured where the ball stopped because this should have been the initial height. He measured the height and theta of different experiments using balls with different masses. Galileo observed that all objects that are affected by gravity should fall at the same rate every time. No, the mass does not affect the rate of acceleration shown in the class data. There are no coerlations between the mass and the acceleration. We also learned that in our last unit of Newton's laws that mass does not affect the time our acceleration of free falling objects.
 * Discussion Questions**
 * //5. Does the mass of an object affect its rate of acceleration down the ramp? Should it affect the motion of an object in freefall in the same manner?//**

There were many parts to our hypothesis and most were all correct. Like we hypothesized, acceleration due to gravity is 9.8m/s^2, which has been proved through our previous labs. This is basic knowledge that we've been using since the first few days of physics. When an object is put onto an incline though, the acceleration is going to change like we thought. We said that the acceleration would be in between 0 and 9.8 m/s^ 2, and that it would increase with a larger incline angle. When looking at our data, it is obvious that as the incline increases, so does the acceleration. Although we were correct in several aspects, we believed that the mass would have an effect on the acceleration. According to Newton's second law, mass is inversely proportional to acceleration, so we believed that the heavier the ball, the slower it moved. This was an incorrect assumption though, as everyone's acceleration was very similar. The differences in acceleration were due to friction, as mass didn't play a role in determining it.
 * Conclusion:**

We had a percent error of 8.88% and a percent difference of 6.31%. Whenever you have a percent error or difference below 10%, you've done a good job with your data. It would be more preferable that the percent error be lower than it is though, because 8.88% is still pretty high. Our percent difference was very good though, as it shows that our results were similar to those of other groups. There could have been many errors while doing this experiment that contributed to a higher percent error. First, there was friction when the ball rolled down the incline, which caused it to reach the bottom slower than it would in an environment without friction. If there was no friction and the only force acting upon acceleration was gravity, then the acceleration would be 9.8 m/s^2. Furthermore, when timing the ball going down the incline, the timer's reaction time could have been off. This would have caused wrong times and messed up our acceleration. For example, when Maddie rolled the ball down the incline and yelled "go", I may have started the stopwatch too early or too late. In addition, it is possible that whoever was rolling the ball down the hill put force into it. An unbalanced force like a hand pushing the ball would cause different results and create a higher acceleration. All these factors could have contributed to a higher percent error, but if we did this experiment again, we could avoid these errors. Eliminating friction is almost impossible because you would have to put it into a vacuum, so that's out of our reach. To eliminate errors in timing, we would have to do several trials to make sure we were precise. We could also have one person time and let the ball go at the same time to get better reaction times. Finally, we would need to make sure we weren't using any force when letting the ball go down the ramp. In reality, these human errors are also very hard to get rid of. To fully avoid these errors, we would have to base the experiment around a machine, where it would accurately time and drop the ball down the ramp. This experiment relates well to a skier skiing down a mountain. If the incline angle is larger, then the skier's acceleration is going to be larger too. It is important to know that as the incline angle increases, so does the acceleration. With this, you'll know when to slow down when your approaching a larger incline. This concept also relates with bicycles or cars traveling down big hills. By knowing this, you'll be more cautious and wary when approaching steeper inclines.

__ The Second Law of Carts Newtonian Physics __
Task A: Michael Poleway Task B: Max Llewellyn Task C: Max Llewellyn Task D: Michael Poleway

What is the relationship between system mass, acceleration and net force?
 * Objectives: **


 * Hypothesis**: Our group hypothesized that with constant force mass would be inversely proportional to acceleration, and with constant mass net force would be directly proportional to acceleration. We estimated the relation between mass and acceleration (Assuming constant force) to be such that if mass was halved acceleration would double. We estimated the relation between force and acceleration (Assuming constant mass) so that if force doubled so would acceleration.


 * Method and Materials**: Our group used a cart (on wheels of (hopefully) negligible friction) containing mass puled via a string (over a pulley, with an encoder, of (hopefully) negligible friction) connected to a hanging mass. When determining the relationship between force and acceleration with constant mass we hung varying weights (therefor varying forces acting on a cart) to be pulling on a cart of varying mass while measuring velocity and calculating acceleration. To determine the relationship between mass and acceleration with constant force we hung a constant amount of weight to provide a constant force while varying the mass of the cart while measuring velocity and calculating acceleration.


 * Data**


 * Acceleration vs. Net force ksdjfksjdfksj dkfjsk Acceleration vs. Mass**

The first set of data shows the correlation between acceleration and net force. This is directly proportional because as the net force increased, so did the acceleration. We increased the net force by adding more hanging mass and taking it away from cart mass.

The second set of data shows the correlation between acceleration and mass of the cart. As the mass of the cart increased, the acceleration decreased, or vise versa. In our experiment, as the cart mass decreased, the acceleration increased. This makes the two inversely proportional.


 * Graphs**






 * Conclusion**

In conclusion, our hypothesis stated that with constant force, mass would be inversely proportional to acceleration, and with constant mass, net force would be directly proportional to acceleration. If you look at our data table this is evident because when there was constant force, as mass went down, the acceleration went up. This show an inversely proportional identity. In contrast, when there was constant mass, as net force rose, so did acceleration. This created a directly proportional identity. This can also be seen in our graphs, as in our acceleration vs mass graphs as our mass grows, our acceleration decreases just like previously stated. In addition, in the acceleration vs net force graph there is a straight incline going up, so its obvious that as the force increases so does the acceleration. All in all, our hypothesis was correct and our data and graphs show this.

We got a percent error of 4.56 percent, which is a very acceptable percent. Anytime a percent is below 10, its considered good. We still could've got a percent more close to 0 though and there were obviously some factors that hurt our results. For example, the wheels of the cart went under friction with the ramp, causing the car to slow down. Unfortunately, there's nothing we could have done to eliminate friction, as its all around us. The only way we could've fixed it is if we put this experiment into a vacuum, which is impossible. Although it does contribute to our percent error, we have to deal with friction. In addition, its possible that when all the weight was in the cart I may have pushed the cart by accident when letting it go. My force could have created a different acceleration. To fix this, I'd have to make sure I didn't exert any force. Furthermore, its possible that the distance you start from could make a difference, as if you start farther, it may take longer for the cart to travel full speed. If you start shorter, it may take quicker to get to full speed. This could have contributed to our error, as our accelerations could have been a little messed up. To fix this, we could start the cart from the same distance each time to make sure it travels the same amount of time. All in all, we did very well with this experiment because a 4.56 percent error is very good, yet we could've done better like always.

Our plans to fix these errors are in the aforementioned paragraph, and this lab can be used in several real world applications. The pulley can be seen in gyms all around the world, helping you gain muscle. The more mass lifted, the more weight is forcing on the weight plates, and this means there is more force to lift those plates. You need to exert that amount of force, and as you add more mass, you need more force. This is what gets you stronger. Pulleys are also used in construction sites, and this helps give us good insight on how these work.

coaster excel W/ accel