Physics 4A (5/10/16) Work and kinetic Energy

Physics 4A (5/10/16)

Work and kinetic Energy

Brett Mccausland

Lab Partners: Luis Diaz, Bimaya Jayaratne

Purpose

Calculate experimentally kinetic energy and work by a non constant spring force, and model the relationship between work and kinetic energy.

Procedure Experiment 1

As seen in the apparatus we placed a steel cart on a steel track and attached a force sensor to the top of it as well as a plate. we attached steel bar to the end of the table with a clamp and attached  a spring which we also attached  to the force sensor and placed a motion sensor at the opposite side of the track. We zeroed are instruments at the point where the cart sat with no tension in the spring. We connected all are instruments to logger pro . We  wanted to find work and the spring constant so we dragged the cart to the opposite side of the track and using the data on the force from the force sensor and the distance traveled from the motion sensor we created a force to position graph. The slope of this graph was are spring constant and the area under the curve was the work done on the spring.

Procedure Experiment 2

For the second procedure we used the same apparatus and we zeroed the cart at the end of the track in which the cart was attached to the spring and pulled the cart all the way to the opposite side of the track. We measure the mass of the cart and entered the data into logger pro. we released the cart, and using the motion sensor tracked its velocity along its path, and displacement. The motion sensor gave us a data point every 30th of a second. To make sure that the motion sensor was able to track the movement of the cart down the track we placed a square plate to the side of the cart that the motion sensor was directed at as in the first experiments procedure.

Calculations Exp 1

For the first procedure we pulled the cart as mentioned in the procedure exp1 section of this report and using a force sensor connected to logger pro and motion sensor we were able track force to position and graph it as seen below. Since we know that work = F*∆d the area under curve yields the total work done pulling the cart attached to the spring the length of the track. We found this area by using an integral capability on logger pro. Additionally the linear fit of the slope of this curve gave us are spring constant.

Calculations Exp 2

Are goal was to model both kinetic energy of a system and work of a system and show that they are equivalent . As mentioned in the procedure Exp 2 section of this report we dragged the cart that had the force sensor attached to it to the opposite side of the track and then gathered the data following the release of the cart. This data gave two graphs the top graph is our position to kinetic energy graph, let's talk about it a little. Logger pro calculated the kinetic energy by using the following formula KE= 1/2mV^2. Obviously logger pro didn't know are mass so we measured the mass of are kart and manually entered it into logger pro. The only other variable is velocity, logger pro used the ∆position/∆time gathered from the motion sensor to calculate the velocity. Then using this information logger pro plugged in the values it was gathering into the equation for Ke and graphed it relative to position yielding the top graph.For the Bottom graph logger pro used the data from the force sensor and ∆x from the motion sensor to yield the force to position graph. As I might have already mentioned the work at any given position is the area under the graph to that position  and this should be equal to the kinetic energy which is why we placed these two graphs on top of each other to make comparisons and test this theory experimentally. I will discuss these results in the data analysis and conclusion section.   

Conclusion and Data Analysis

The data from are two graph from exp 2 as can be seen in the data analysis boxes do not perfectly match as we would predict, for one position , the closets positional match we had the kinetic energy was .685 J and are work was 0.8473 J .There is several reasons some from random error and 1 systematic that I would like to discuss that might be the cause of these less than convincing results. The first is that while the motion sensor is very precise and creates a data point every 30th of a second the experiment entire length of time is only approximately 0.4s yielding only around 13 data points to track the position and use this to also calculate the velocity. With a more precise device we might see a slight improvement in the difference between these two graphs. One other problem is that we were trying to compare the results for work and kinetic energy at the same point on both graphs however, as can be seen, we could not exactly match the position for both graphs do to a lack in data points in the exact same position on both graphs and had to settle with a difference in position of 0.002 s not a big difference however remember this is a small measurement to begin with so it affects a larger percentage of error than previous experiments. Had I had more control over the experiment there are a couple of ways that the experiment could be made to be more accurate. The easiest two solutions is extend the track maybe by connecting two tracks thus reducing the percentage error from the instruments and also using springs with smaller constants thus lengthening the time and yielding more data points from the motion sensor. Overall despite the fact that we were not able to make a perfect match with are data from are graph for work and for kinetic energy we can still see that even under very small instances kinetic energy is directly connected to work hence the work done on the cart by the spring causes a direct change in its kinetic energy.   

Centripetal Force Physics 4A (03-10-16)

Physics 4A  (03-10-16)

Centripetal Force

Brett Mccausland

Lab Partner:

Purpose

Model the relationship between the angle made by a circular revolving mass and its angular velocity.

Procedure

As seen in the photo of the apparatus we used a tripod stand to hold a meter stick attached to a steel rod with clamps. This steel rod was attached to a motor that caused the meter stick to revolve and the string and mass attached to it. Due to the net force of revolving motion (centripetal force ) the mass while revolving elevated to some angle well call theta . We measured the change in height and the length of the string in order to find this angle . We did this by placing a second stand that had a piece of paper attached to it and raised it to the point at which the mass collided with the paper. We then measured and recorded the height. Before causing the collision between the paper and the mass we recorded 10 revolutions and took the average to find are angular velocity.  

Calculations

As mentioned in the procedure we used experimental data to find a experimental value for angular velocity. The first thing we did is find the angle, we did so by using our measurement of the height of the large tripod stand and the height of the small tripod

Stand and are length. Now that we had a hypotenuse and a adjacent side we were are to find the angle by taking arccosine as seen in the image labeled find angle.   terminal velocities.After we found are general formula for are angle we next found are general formula for are angular velocity in terms of theta using summations of the forces in the x and y components as seen in the image above in the yellow highlighted box. There was also one more much simpler way for us to find are angular speed and that was with the data we had from the times we recorded on the amount of time it took for the bob to make a complete revolution. This was are angular velocity in terms of rev/sec in which we then used the formulas listed in the green box to convert to rad /sec.  

Conclusion and Data Analysis

The data in the excel spreadsheet models  circular velocity with respect to time vs the circular velocity with respect to change in the height or the change in the angle. Very consistent with what

We would hypothesis based on observation there is a linear correlation between the change in angular velocity and the change in the height at which it rotates. This is explainable based on are force summation equations we wrote out in which show that the more tension added to the string the more force is going to exerted in not just the x component but the y component as well. The force of gravity in the y component stays constant however as the bob increases speed its angle due to a net force in the y component increases, which is due to the tension force, until  the point in which it has no net force in the y component and the tension force in the y component is equal to the force of gravity. Inconsistency in the data are evident since there is not a perfect linear fit as seen in the graph of the data. Beyond the propagation of error from the precision of are tools being (+/-) 0.1cm for are lengths and 0.001 seconds in the stopwatch there are several others. The largest error that I observed was that of the apparatus use of a ruler in which was not rigid and was bending due to the force centripetal . This gives more uncertainty in are measurement for the height of the paper on the small stand since the ruler was bending it made for a slightly lower height. Also it could be observed that there was air friction, the disturbed air could be felt if you stood close to the path of the bob as it went by this non negligible force has an effect on are error in are calculations of angular speed.   

Physics 4A (9/21/16) Friction Forces

Physics 4A (9/21/16)

Friction Forces

Brett Mccausland

Lab Partner: Olivia Phuan

Purpose

Model frictional forces in five different experiments, determining the effect that both static friction and kinetic friction have in several different scenarios. Use experimental data to calculate friction coefficients.  

Procedure (1) Static Friction

As depicted below, we set a painted wood board on top of a flat table and held it in place with a clamp. At the end of the table we put a pulley, and ran a sting over it with a mass holder hanging from one side, and the other side of the string was tied to a wood block with linoleum surface. We measured the masses of the wood blocks seen in the photo.We ran 4 trials, each trial we slowly added masses to the hanging mass holder until the point at which the wood block broke static friction and began to move. The first trial we only had the single block however every trial we added one more wood block on top of the wood block on the board to increase the normal force between the board and the block.We performed this procedure in order to gather data on static friction coefficient between the board and the block. By gathering data on the mass required to set the system in motion we will be able to calculate the force required and then find the static friction coefficient.  

Procedure (2) Kinetic Friction

For this experiment we used a force sensor to read the force applied in the tension of the string tied to the block while it was being pulled at roughly a constant velocity.Like previose experiment we ran 4 trials, increasing the number of blocks evertime. We did this in order to collect data on the force required to keep the block at a constant speed.This data on the force will allow us to find the coefficient of kinetic friction

using newton's second law.

Procedure (3) Static Friction from a sloped

For the third procedure we placed the block on the wood board as well as a smart phone with the ability to read the angle of the board.We slowly raised the board until the point in which the wood block broke static friction and recorded the angle in which this occurred in order to latter calculate are static friction

coefficient

Procedure (4) Kinetic From Sliding Block Down Incline

For this procedure we taped a piece of paper to one end of the wood block and slightly raised the angle of the board from the previous experiment.We did so because for this experiment we wanted to gather experimental data on the block’s acceleration down the plane with the use of a motion sensor.The paper made it easier for the motion sensor to detect the movement of the block and the incline was increased in order to increase the magnitude of the force down the board in order to overcome the force of static friction, and put the block in a state in which its under the force of gravity and kinetic friction.

Procedure (5) Predicting the acceleration of a two mass system

For the final procedure we first made are calculations for what are experimental kinetic friction between the wood board and the wood block was from are previous data.Then based on the mass hanging, the mass of block and the kinetic friction coefficient we found, we made a prediction on what the acceleration would be when the system was put in motion. The system as seen in the image was the block on top of a wood board, with a string attached to it, that went over a pulley, and had a mass attached to the other end suspended off the edge of the table.With the use of the motion sensor like previous experiment we found are experimental acceleration and made a comparison to are calculated theoretical acceleration.

Calculations (1) Static Friction

In order to find the coefficient of static friction for the block given the data we collected I first drew a force diagram for the sum of the forces in the x direction and the sum of the forces in the y direction. Since we were taking static friction the sum of the forces in the x and the y direction are equal to 0. I solved for static friction and then made a excel spread sheet with my data using the formula I found for static friction . The I found the average of all for trails .

Calculations (2) Kinetic Friction Force Sensor

Like the previous experiment I first made a force diagram, since for this experiment I had a force reading and the block was pulled at a constant acceleration the net force was equal to zero. Therefore I divided the force reading by the natural force to solve for the coefficient of kinetic friction. After I found the formula for Kinetic friction coefficient I entered in all the data into excel to calculate the kinetic friction coefficient for all the trails as well as get a average.  

Calculations (3) and (4) Static and Kinetic Friction From Sloped Surface

The next two experiment were done on an incline, experiment 3 was static friction on an incline and the data we had was the mass of the block and the angle and we wanted to solve for the coefficient for static friction. I did so by first drawing a force diagram, due to the fact that the block was not moving in either direction the sum of the forces in the x and the y direction were equal to zero.  Solving for natural force and the for due to gravity and I arrived at the sum of forces seen in the image of the calculations .I then moved the force of gravity over and divided by the normal force to isolate static friction coefficient and from there we plugged in are experimental values and found a experimental coefficient for static friction of (0.426). For experiment (4) I used the force diagram I had drawn in the previous experiment. For this calculation we wanted to solve for the value of are kinetic friction given the angle of the board and the acceleration of the block. Since the block was in motion there was a net force equal to the mass of the block and its acceleration that we found from are experiment. Therefore for this calculation I solved for the kinetic friction by first solving for the natural force and the force due to gravity and set them equal to the net for on the block.Then solved for kinetic friction coefficient that I found to be 0.135. See image for full calculations.

Calculations (5) Predicting the acceleration Of a Two Mass System

We began the calculations for the theoretical acceleration that we expected using the average kinetic friction that we found from experiment (2). As seen in the image of the calculations I began by drawing a force diagram and solved for acceleration. Using the average kinetic friction coefficient and the mass of the two objects I found a theoretical  acceleration of 1.4 m/s^2. The experimental acceleration was 1.2 m/s^2 a

difference of 0.2 m/s^2 and a error of 14.28%

Conclusion and Data Analysis

For the first experiment the accuracy of the static friction was only as accurate as the amount of weight that was being added at a time.For instance if every time the block didn't break free you added 20 g then if it broke free on the next mass added than the accuracy would be (+/-) 20 grams which would not be very accurate.For us do to lack of time and supplies the mass was increased at 5 gram increments therefore the accuracy of the static friction is +/- 5 grams.Also there was a good deal of possible random error in the data since at different places on the board there was slightly different texture to the board that the block was sitting on. For Kinetic friction experiment 2 the angle at which the block was being pulled was very important since in the calculations we were taking the force read as the magnitude of the force in the x direction so any slight angle to the pull would cause error. Also with experiment 2 the pull velocity was very error prone since there needed to be no acceleration since we were setting the sum of the forces equal to zero any acceleration could effect this data and it was difficult to be consistent using only human accuracy.The third experiment for static friction on an incline the greatest variable was the texture of the surface, it had proven to be the greatest inconsistency of the experiment. The kinetic friction on an inclined board was of all the experiments the least error prone since there was very little external influences once the block was put in motion. The block did experience unaccounted for air friction especially since we added a large flat surface to the back of the block for the motion sensor reading. Overall though since the block never reached a very high velocity it is still negligible for are purposes. The prediction experiment for acceleration as mentioned had a experimental error of 14%. After evaluating the data the most consistent friction coefficient was static friction. The first value for static friction that I found was on the mass pulling the block which was (0.478) and the second value for static friction that I found was  (0.425). In comparison the first value found for kinetic friction was (0.23) and the second value for kinetic friction was (0.135). It does however make sense that we were not able to calculate kinetic friction as accurately as we were for static friction since static friction is a much larger force it takes less precision and will have less percentage of the measurements be in the range of propagated error.

Air Resistance Physics 4A (8/17/16)

Physics 4A (8/17/16)

Air Resistance

Brett Mccausland

Lab Partner: Olivia Luphan

Purpose

Model the relationship between air resistance , force, and velocity, and analyze the velocity when the net force is 0 .

Procedure

We measured the mass of 250 coffe filters and then calculated the approximate mass of a single coffee filter. We then dropped coffe filters from a indoor balcony with a black sheet draped behind the path of the falling filter. On the black sheet we taped a meter stick in order to give a perspective of distance traveled. We made 6 separate recordings, the first recording with single coffee filter and with every recording we added 1 coffee filter.  

Calculations

We did some video analysis with logger pro by using the meter stick we had taped on the canvas to give logger pro the ability to have a perspective of distance then by marking the displacement of the coffee filter we gathered and plotted a displacement to time graph, using this  we found data on the falling filters velocities with use of the slope of the data points. We recorded the data from logger pro towards the end of the filters fall in order to capture its terminal velocity .

Next we modeled are force as a exponential function using a power fit, F= (k )( V)^n with V being terminal velocities. The graph to left illustrates this, the graph is force to velocity. Using excel and the data we found on terminal velocities,and  air resistance force we inserted in are data into excel and extend the calculations down over 60 rows or until we find the point in which the velocity stays constant, since we only had a limited distance for the filter to fall this allows us to find out had the filter had more distance to fall what would its final velocity be at the point in which the forces balance.  were able to find terminal velocities of the filters .

Conclusion and Data Analysis

The data in the excell spreadsheet models the falling object vey consistant with what is theorically known to be true.As can be seen on the excell sheet the change in velocity is continually decreaing and begins to level out as predicted. The graph seen in the excel sheet is based on a single coffee filter and as can be seen thru excel we have a calculated 2.5 m/s terminal velocity. Choosing to use the data from the first filter in hindsight was probably not a good decision since it gives us a higher propagation of error since the accuracy in the mass of the filter is an approximation based on 250 coffe filters. Also Of all the drops we made this drop was the most prone to be affected by external forces such as a breeze. Additionally even with the black canvas background, in many shots of are filming, it’s very difficult to make out the coffee filter, leading to error in marking are displacement in logger pro.

Physics 4A (9/14/16 ) Projectile Motion

Physics 4A (9/14/16 )

Projectile Motion

Brett Mccausland

Lab Partner: Myself

Purpose

To use my “understanding of projectile motion to predict the impact point of a ball on an inclined board”.Use kinematics equations of motion in 2 dimensions to describe the motion of a projectile accurately in a way that allows us to make predictions.

Procedure

As depicted below, we set a steel stand on top of the table with a clamp holding one end of a steel tray. The other end of the tray sat on another steel tray that was supported by two wood blocks. The second tray was extended to the end of the table. I taped a piece of paper to the ground were a steel cylinder released from the top would approximately land. The piece of paper had a piece of carbon paper on top of it to mark the paper on impact. Then I measured the distance from the end of the steel track to the point of impact on the paper.

For the second procedure depicted in the image I repeated the previous procedure except for the two papers were taped to the board that was positioned at an angle on ramp. Note the image was taken before the board was positioned to be directly to the end of the steel track.  

Calculations

I measured the height from the end of the tray to the ground, and the horizontal displacement from the end of the tray to the marking measured with a meter stick .Using equation (1) labeled in the photo of the calculations, I found the time that it took for the cylinder to hit the ground.Then plugging time into equation (2) I found the initial velocity of the cylinder, that is the velocity of the cylinder as it left the track. Next I wanted to predict where the cylinder would land on the wood board at an incline. Using the angle measured with a smart phone.  Using equation (3) I solved for time and substituted the value into equation (4) to find distance. The theoretical calculation for distance was approximately 19.99 m. The experimental measurement was exactly 19.99 m, wow!

  

Conclusion and Data Analysis

The values theoretical and experimental matched way more accurately than I expected.There are several reason why the measurements I took were so accurate, and likely more accurate than my classmates. First of all I didn't get over carried away with the incline of the ramp, this made for a smoother transition from one ramp to the other and less speed means less air resistance which we were neglecting to calculate for. Also I made my ramp very secure with tape so it didn't move positions. The launches were so consistent that they on all of the test runs, the cylinder hit the first mark on the paper only slightly offset from center.Also the measurement were done with several meter sticks to ensure that the measurements on the ground were done from the true starting position of the trajectory as seen in apparatus image two.With use of accurate instruments and with the use of the kinematics equations we can very accurately predict the behavior of a trajectory.  

lab 3 Propagation of Error

Physics 4A (9/07/16 )

Propagation of Error

Brett Mccausland

Lab Partner: Olivia Luphan

Purpose

Calculate propagation of error in a experimental calculation (density), and draw conclusions to the accuracy of are calculated propagation of error by seeing if the true density falls within the range of error for each calculation.  

Procedure

We used a clinometer,2 cylinders, and a scale as seen in the image below.

With the use of the clinometer we measured the height and diameter of the cylinder.With  the use of the scale we measure the mass of each cylinder.

Calculations

The clinometer had an precision of (+/-)0.01 cm and the scale had a precision of (+/-)0.1 g. Are goal was to find the density of the cylinders so we used the formula and to find the propagation of error of are experimental calculation given the precision of are instruments.In order to do this me needed to take the partial derivative of are original equation for row for each of are uncertain values . Since the volume of a cylinder is we plugged that  v in for are formula for density and we took the partial derivative for d , h and m. Once we had are partial derivatives we then needed to plug in are values and multiply the partial derivatives by their corresponding measured uncertainty, square them , add them all together, and take their square root.

Conclusion and Data Analysis

As you can see calculated a density of are aluminum cylinder of 2.84 g/cm cubed with a propagation of error of (+/-) 0.02. The actual density of aluminum is 2.70 g/cm cubed which means that the value does not fall within are predicted range of error.   We calculated a density for the brass cylinder of  8.17 g/cm cubed with a propagation of error of (+/-) 0.14.The reason being for the brass cylinder having a less precise calculation is that it was much smaller in volume, this shrink in size of the measurement means that the inaccuracy of the instrument is a larger percentage of the entire measurement being made. The actual density of brass is 8.55 g/cm cubed which means it also is not within the range of error that should be occurring. Since the first cylinder is off by +0.14 and the second cylinder is off by -0.28 the error appears to be random. The brass cylinder produced a error of 4.4% and the aluminum cylinder produced a error of 5.1%.There are many unknown as far as what could have gone wrong in the data however the calculations stand correct. The one area I see to be the most probable for producing the error was in the scale, since we never confirmed for ourselves that it was working at the precision it was supposed to be, and it had the lowest precision to begin with. Also when it comes to measuring the diameters and heights each of the group members took turns taking measurements and reading the instrument and it is possible that the instrument moved during a handoff and an incorrect value was recorded or that it was not being read correctly since the markings on the instrument are near microscopic.Had one person done all the measurements I think it would have either eliminated the error or made the error systematic instead of random.  

Physics 4A Free Fall and Experimental Uncertainty

Physics 4A (8/31/16 )

Free Fall and Experimental Uncertainty

Brett Mccausland

Lab Partner: Olivia Luphan

Purpose

Find the constant acceleration of gravity through use of experimental data. Compare data and discover whether the experiment contains errors of the systematic nature or random error.

Procedure

We placed the cylinder onto an electromagnet at the top of the apparatus shown in the image and turned a  spark generator on just before releasing the cylinder.The cylinder contained a metal ring around its rubber base and this ring left burn marks on a piece of wax paper that was extended out from a spool at the bottom all the way to the top of the path of the falling cylinder.

Calculations

These marks on the wax paper provided us with a displacement and the sparker gave us a know time. Using this data we found velocity at each corresponding displacement by first finding a mid interval time. We  used the mid interval times to find a mid interval velocity which we then graphed on a velocity to time graph.The points on the graph made a linear graph as expected and with the use of a trim line we found the slope which gave us are acceleration.

Conclusion and Data Analysis

After comparing data from all the groups who were conducting the exact same experiment we found that we had a standard deviation of about 24 cm/s^2 .This however was with the use of an outlier point the was under the average deviation of the mean by approx 50 cm/s^2. We made the determination that this data was invalid and removed it from the calculations. After doing so this brought us to a standard deviation of about 16 cm/s^2.The remaining deviation in the data was not leaning toward any particular value, leading us to believe the experimental errors were random since the measurements were scattered.Of course we all know the theoretical value of gravity is estimated to be approximately 9.8 m/s^2 and the results were more scattered around 9.5 m/s^2. The theoretical value is what you would expect in a vacuum with no air resistance and are object encounters air resistance. The shape, mass, and low velocity of the object makes for near negligible air resistance however it still contributes to why we have a lesser calculation for  g.