Group2_6_ch4

toc Magna Leffler, Brianna Behrens, Julie Van Malden Period 6 Chapter 4
 * __Group 2__ **

=Gravity and the Laws of Motion= Part A: Julie Part B: Brianna Part C: Magna

__Objective:__
 * Find the value of accelration 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 the relationship between the mass of the rolling ball and its acceleration

__Hypothesis:__
 * The value of acceleration due to gravity is 9.8 m/s 2, the constant for all objects on earth. This has been previously proven through in-class free-fall and projectile activities, in which it was demonstrated and calculated that all objects accelerate at the aforementioned constant when gravity is the only motional influence.
 * If the angle of the ramp is increased, the acceleration will remain unchanged because it is a constant for all objects on earth that move solely under the influence of gravity.
 * The mass of the rolling ball has no effect on its acceleration because based on previous knowledge and theory, acceleration is independent of an object's mass.

__Methods and Materials:__ Acquire available materials needed to complete the lab. Insert metal pole into pole stand, and attach ramp to pole using clamp at an initial height of fifteen centimeters. Mass metal ball on electronic balance. Determine three distances for each trial that apply to three angles. Roll metal ball down ramp beginning at designated starting position for each trial distance. Use stopwatch to record time for first trial at d 1. Record time for second trial at d 2. Record time for third trial at d 3. Use ruler to measure and record second height for second angle. Record time for fourth trial at d 1. Record time for fifth trial at d 2. Record time for sixth trial at d 3. Measure and record third height for third angle. Record time for seventh trial at d 1. Record time for eighth trial at d 2. Record time for ninth trial at d 3. Display all data in Excel spreadsheet.

__Procedure:__ media type="file" key="Movie on 2011-11-15 at 13.26.mov" width="300" height="300"

__Data Table:__

__Class Data:__

__Graphs:__ __Sample Calculations:__

__Percent Error:__

__Percent Difference:__ Class Average- .853 m/s 2

__Discussion Questions:__
 * Is the velocity for each ramp angle constant? How do you know?
 * The velocity for each angle is not constant because the ball is accelerating down the ramp. We know this because the only force acting on the ball is gravity, and the value for acceleration due to gravity is 9.8 m/s2. This means that the velocity is changing by 9.8 m/s each second.
 * Is the acceleration for each ramp angle constant? How do you know?
 * Based on previous knowledge from free-fall and projectile activities, the acceleration for each ramp should be constant because the value for acceleration due to gravity is the same for all objects under the sole force of gravity. However, after reviewing the data from the trials, the acceleration for each ramp is not constant. Generally, when the ball's traveled distance was shortened, the acceleration decreased as well.
 * What is another way that we could have found the acceleration of the ball down the ramp?
 * Rather than use the current procedure, we could have found the acceleration either by using a ticker tape diagram with a spark timer or setting up a motion detector in the process. If we were to make a graph of the velocities at different points we could find the slope of the line that the velocities would have made, which is equal to the acceleration.
 * 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 due to gravity by setting up and dropping an object down two ramps. He found that the object ended at the same height as it had started each time he adjusted the distance and angle of each ramp, and this helped him to find the constant //g// and reinforced his theories. Galileo was able to do this because he knew that weight was the only force acting upon the ball. Because the ball was on an incline, it was a vector meaning that there would be an x and y component of weight, the x-component being the balls movement down the ramp.He was able to for the x-compoenent by using the equation g= (ad) / h, and tested it, finding that the result was always 9.8 m/s/s.
 * Does the mass of an object affect its rate of acceleration down the ramp? Should it affect the motion of an object in free fall in the same manner?
 * The mass of the object does not affect the rate of acceleration down the ramp because both factors are independent of each other. Acceleration is directly proportional to force and inversely proportional to the mass of the ball. Mass does not have any effect on objects solely influenced by gravity, including free fall.

__Analysis:__
 * Free Body Diagram of the ball on ramp

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 * The x-component of the force was causing the ball to roll down the ramp.
 * Acceleration is the y-component of the force acting upon the ball.
 * The equation for this situation should be a= gsin(theta)
 * In this case g, also the slope, would theoretically 9.8 m/s/s.
 * On our acceleration vs. sin(theta) graph, the equation of the line is y=6.59x+.4309. The slope, 6.59, represents the acceleration due to gravity which would be 6.69 m/s 2 . Clearly, our predicted acceleration due to gravity is far from the actual value of 9.8 m/s 2 . The error in our calculations of acceleration due to gravity may have been a result of inaccurate or not precise measuring and inaccurate timing, as well as the presence of friction on the surface of the ramp. The y-intercept of .4309 represents the friction force when both the acceleration and theta are 0.

__Conclusion:__ Based on the collected data and calculations from this experiment, our hypothesis is incorrect. When we set the y-intercept of our acceleration vs. sin(theta) graph to zero, we found out that our accleration due to gravity was 6.75 m/s 2, instead of the expected acceleration due to gravity of 9.8 m/s 2. Our prediction was rather inaccurate in comparison to the calculated acceleration due to gravity, resulting in a relatively high percent error of 32.8%. This value can be attributed to any number of procedural errors, including inaccuracy while measuring the height of the ramp and inaccuracy during the trials with the hand stopwatch. We were also incorrect in our assumption that the acceleration would remain constant at any angle and that gravity would make this possible. Upon experimentation, we discovered that as the angle or incline increased, the acceleration increased. When we compared our results to those of groups, we found that our third hypothesis proved to be, for the most part, accurate. The accelerations of the balls with different masses seemed to have the same, if not relatively similar, accelerations when all were tested at the same height and angle. In order to attain a better collection of data, and ultimately better calculations and results, we could alter this lab to eliminate the errors. Instead of using a ruler to measure the height, we could use a pole on which there were already measurements, and therefore the ramp would need proper alignment; this would completely remove the need for a ruler. In addition to one pole for measuring, a second pole could be used to hold up the other side of the ramp, which kept tilting as we adjusted the height. Also, we could add more trials for each angle which might help us to see a possible pattern in acceleration. Furthermore, we could double check the distance at which we start the ball before rolling it down the ramp to increase the accuracy of the time and calculations. If we used a gate and touch pad system, we could rid the procedure of the timing error all together. The timer would start when the gate opens, and stop when the ball hits the touch pad at a designated point.

=Newton's Second Law Lab= Part A- Magna Part B- Julie Part C- Brianna Part D- All

__Objective:__ What is the relationship between system mass, acceleration and net force?

__Hypothesis and Rationale:__
 * The purpose of this lab is to find the relationship between the system mass, the acceleration, and the net force. We can predict that the relationship between mass and acceleration and net force and acceleration by looking at Newton's Second law, which can be expressed by the equation ∑F = m • a. From prior knowledge of Newton's Second Law, as well as the fact that acceleration occurs in the presence of an unbalanced force, it can be inferred that mass and acceleration will be inversely proportional, while net force and acceleration will be directly proportional. We know this because Newton's law states that objects remain in constant motion (at rest or at a constant velocity) unless acted upon by a force that is unbalanced. As seen by substituting values, the acceleration always increases or decreases alongside the net force, while the system mass will always do the opposite of the acceleration.

__Methods and Materials:__ media type="file" key="physics.mov" width="330" height="330" Acquire all required and necessary materials. Set up a track that is level and parallel to the ground. Set a cart attached to a pulley system with a hanging mass of 5g on the end on the track. In order to make sure the the experimental data is correct, the pulley string must be parallel to the track. Clamp a photo gate and wheel at the end of the track to collect the acceleration data, which is needed to complete this experiment. The masses of the hanging mass and the cart are vital to this lab, which can be found by using a scale or recording the engraved values before beginning the procedures. This experiment tested the acceleration of the system when the total weight was distributed in various ways. For example, ten grams are placed on the hanging mass while 15 grams are placed on the cart. In each trial the total mass must be maintained. The photo gate collected the final data for each run of the experiment, which was later used to make the graphs.

__Data and Graphs:__





__Sample Calculations:__ //net force-//

//average acceleration-//

__Percent Error:__ Theoretical- 1.87 Actual- 1.8475

Theoretical- .03626 Actual- .0363

__Analysis:__
 * Explain your graphs:

The slope of the trendline for this graph is 0.5018, and this value corresponds to the reciprocal of the mass. 0.5018 -1 is equivalent to 1.99, while in comparison, the actual observed value was 1.87. The percent error is 1.2%, insinuating that our value was close to the observed, however not exact. Ideally, the slope should be equal to this quantity because it is the reciprocal of the mass; therefore, the numbers should be identical with completely accurate results in consideration of the actual mass. The y-intercept is the friction value divided by the mass. The theoretical absence of friction results in a y-intercept of zero on this graph.
 * If linear: What is the slope of the trendline? To what actual observed value does the slope correspond? How does it compare to this actual observed value (find the percent error between the two)? Show why the slope should be equal to this quantity. What is the meaning of the y-intercept value?

The power of the x in the equation of this line is -2.476, whereas the correct value should be -1. This is because the equation y = Ax -B is equivalent to a = ∑F • m -1. If the power of the x is any numerical value other than -1, the variable will no longer be the reciprocal of the mass. The coefficient in front of the x is 0.3365, and this value is equivalent to the weight of the hanging mass, which can be found by multiplying mass by the gravity constant. The percent error between the theoretical and experimental coefficients of x is 0.44%
 * If non-linear: What is the power on the x? What should it be? What is the coefficient in front of the x? To what actual observed value does the coefficient correspond? Find the percent error between the two. Show why this value should be equal to this quantity.

With the addition of friction to this lab, the cart's acceleration would decrease. A larger force would ultimately be needed in order to maintain the same acceleration value. The slope of either graph was larger than the actual compared values, and friction can be considered the cause of error in calculations, ultimately affecting the results. Although the force of friction is relatively small during this lab procedure, its presence still interferes with the calculations.
 * What would friction do to your acceleration? Would you need a bigger or smaller force to create the same acceleration? Was your slope too big or too small? Can friction be a source of error in this experiment? Redo the calculation of acceleration WITH friction to show its effect.

__Conclusion:__ The experimentation proved that our hypothesis was correct. As depicted on the acceleration vs. net force graph, the straight line shows that the two factors are directly proportional to each other. The acceleration vs. mass graph shows an inverse relationship by observing the downward curve, also proving our prediction correct. The percent error for the acceleration vs. net force was 1.2%, while that of the percent error for the acceleration vs. mass graph was 0.44%. The relatively small percent errors reflect the accuracy of this experiment and the minimal errors made. Although these are not primary and authentic data collections, it can be assumed that this percent error was a result of a lack of parallelism between the pulley system and an unlevel track. If the string and the track are not parallel, the data collected would be compromised by the angle at which the string was, in reference to the pulley system. In addition, an unlevel track adds the force of gravity on an incline or decline; therefore, the cart's acceleration would not only be due to the force of weight on the hanging mass, but also the acceleration on the inclined angle. The large R 2 values for both graphs support the consistency and accuracy of the results. Given the opportunity to redo the lab experiment in an effort to eliminate the error, a level would be used to ensure that the track was even, to reduce the presence of an incline or decline. Also throughout the experiment, the pulley system would be regulated so that the string remained parallel to the track. A real life application of the pulley system would an elevator, in which a counteracting mass or force is used to move the elevator up and down. This is important to know because the maximum weight per elevator must be determined by calculating the forces acting upon this system.

=Coefficient of Friction Lab= Part A- Brianna Part B- Magna Part C- Julie Part D- All

__Objectives:__
 * To measure the coefficient of static friction between surfaces
 * To measure the coefficient of kinetic friction between surfaces
 * To determine the relationship between the friction force and the normal force

__Hypothesis:__ The coefficient of static friction between the cart and the track will be approximately 1, and the coefficient of kinematic friction between the surfaces will be relatively close to zero. This hypothesis can be rationalized by the support of class notes. Static friction, which occurs when there is a lack of motion, is stronger than kinetic friction, when an object is sliding, because the force is preventing the object moving. Theoretically, the value of the coefficient of the latter is less than that of the former. In addition, when the normal force, which in this lab is equivalent to the weight, is increased by adding more mass to the cart, the friction between the two surfaces will also increase; these factors are directly related.

__Methods and Materials:__ media type="file" key="labbbb.mov" width="330" height="330" Acquire all necessary and available materials. Mass the friction cart using a scale and record mass. Set cart on a level track and place two masses, 501g and 498g, inside. Cut string to approximately fifteen centimeters and tie to one end of the cart; make sure the string is horizontally parallel to the surface for accurate results. Attach the force meter to the opposite end of the friction cart. Insert USB link into computer and set up Data Studio. Press zero before each trial and pull cart along track at a constant speed. Complete multiple trials for each combination of masses.

__Data and Graphs:__ THANK YOU FOR COMPLETING THIS LAB, AS ASSIGNED. HOWEVER, YOUR RESULTS KIND OF STINK, TO BE BLUNT. LOOK AT THE R 2.

__Sample Calculations:__

__Class Data:__

__Analysis:__

Max Tension vs. Normal Force

Friction vs. Normal Force Max Tension vs. Normal Friction vs. Normal
 * Compare your result with the class results

__Discussion Questions:__
 * 1) Why does the slope of the line equal the coefficient of friction? Show this derivation.
 * The slope of the line equals the coefficient of friction because in this experiment, the equation y = mx is equivalent to ƒ = µ • N. µ is calculated by dividing friction by normal.
 * 1) Look up the coefficient of friction between your material and the aluminum track. Discuss if your measured results fall within the range of theoretical values. Be sure to cite your source!
 * In this lab the friction was created from the bottom of the plastic friction cart and the table top, so the coefficient of friction was between the plastic and the plastic and the tabletop. As researched, the theoretical value for the coefficient of static friction should be around .25 to .35, which is not consistent with our observed one of .1278. The coefficient of kinetic friction is supposed to range from about .1 to .3. We can see here that our measured kinetic friction coefficient was pretty accurate because .1491 falls in between these two numbers.
 * []
 * 1) What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?
 * The addition of mass to the friction cart affected the force of friction as well as the coefficient. They are directly related, meaning that as mass increases, the friction does as well. Different weights in the cart alter the force of friction proportionally.
 * 1) How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?
 * The coefficient of static friction is greater than that of kinetic friction. When the object is not in motion, the force of friction is stronger than when the object is sliding.

__Conclusion:__ Our hypothesis was incorrect, the coefficient of static friction between the cart and the track was not one 1 and the coefficient of kinematic friction between the surfaces was not relatively close to zero. The coefficient for static friction was .1491, while the coefficient of kinetic friction was .1278. We also predicted that when the normal force, which in this lab is equivalent to the weight, is increased by adding more mass to the cart, the friction between the two surfaces will also increase because these factors are directly related. This part of the hypothesis was correct, because we found that normal force and the coefficient friction are directly proportional which can be shown through the equation f = µ N. Our percent errors were relatively small, being 3.7% and 8.8%. These percent error may have resulted from a pulling source(the string) that was at a slight angle or dragging the friction cart at a speed that was not perfectly consistent. To eliminate this problem in the future, we would use some type of device or application on data studios that would show that the rate at which the cart was being pulled was consistent, or even use a machine that would do the pulling at a programmed rate. If we had to apply this to an everyday situation to an everyday life situation, we would could apply it to sledding or skiing. We could see how the kind of snow affects the coefficient of friction between the ski and the surface which it is moving on.