Instrument Error Height 1 example essay topic

Lab #5: Gravitational Acceleration Preparation: In preparation for the first part of this lab involving the Atwood's machine our team started by discussing the effects of the masses on the results of the machine as requested in question 1 of the lab manual. We believe that if the two masses were equal there would be no motion of either of them when released. However we believed that if the two masses were not equal, the heavier mass would fall downward pulling the lighter mass upwards. Below as requested by question 2 is a free body diagram of both situations Masses Equal Masses Unequal The tension on mass 1 is equal to the tension in mass 2 due to the same string attaching both masses and is shown mathematically above in the section where the masses are equal.

In the second part gravity is solved for. We also believe that the difference between the two masses will affect the acceleration in a linear matter as requested in question 3. In preparation for part 2 we started by answering question 4 on which graph best describes free fall based for distance vs. time. We believed graph (b) showed this and is shown below. Our rational for this was that the object in free fall is undergoing a constant acceleration meaning its velocity will increase with time.

This is shown on graph (b) by the increasing slope with time, and is the only graph to have its slope increase with time. Graph (a) has constant slope and graph (c) has its slope decrease with time. For question 5 which asked for the best velocity vs. time graph we believed that graph (a) is the best graph. Our rational for this was that because the object is under constant acceleration the velocity will increase at a constant rate. Graph (a) shows this while graph (b) shows constant velocity and graph (c) shows decreasing velocity. For question 6 which asked for the best acceleration vs. time graph we believed that graph (b) shows this the best.

Our rational for this was that the object is under constant acceleration. Only graph (b) shows a constant acceleration. Graph (a) shows decreasing acceleration while graph (c) shows increasing acceleration. Procedure: Our procedure for part 1 is the following: First we measured the masses of both sides of the Atwood's machine and record these values.

Next we held the smaller mass on the ground and measured the distance from the ground to the bottom of the larger mass, calling this value 's'. Next we released the smaller mass and timed how long it took the larger mass to fall and recorded this as 't'. We did this 4 times to allow each member of the team to do this. We then averaged the value for time and solved for gravity and the associated error. For part 2 our procedure was the following: Using a device to determine how long it takes a ball to drop from 1 sensor to another we started by measuring the distance from the bottom of the ball to the top of the sensor on the ground calling this value 's'. We then turned the machine on, reset it and allowed the ball to drop by releasing the pressure on the ball holding it to the elevated sensor.

We recorded the time given by the machine calling it 't', and repeated for 4 attempts. We did this process with 2 different heights. For part 3 our procedure was the following: Using a pendulum we started by recording the distance from the center of mass of the ball, to the top of the pendulum calling this 'L'. We then let it oscillate in a straight line for 100 periods and recorded this time. We then divided this time by 100 to get the time for 1 period 't'. We then solved for gravity and the associated error.

We did this process with 2 pendulums. Data: Part 1: (Atwood's Machine) Mass 1: 197.35+/-. 05 g Mass 2: 188.90+/-. 05 g Distance (cm) Time (sec) 237.00+/-. 05 5.81+/-. 1237.00+/-.

05 5.62+/-. 1237.00+/-. 05 5.91+/-. 1237.00+/-. 05 5.78+/-. 1 Part 2: (Free fall) First Height Distance (cm) Time (sec) 179.60+/-.

05 0.612+/-. 0005179.60+/-. 05 0.614+/-. 0005179.60+/-. 05 0.625+/-. 0005179.60+/-.

05 0.615+/-. 0005 Second Height Distance (cm) Time (sec) 49.70+/-. 05 0.319+/-. 000549.70+/-. 05 0.319+/-. 000549.70+/-.

05 0.319+/-. 000549.70+/-. 05 0.317+/-. 0005 Part 3: (Pendulum) Distance (cm) Time for 100 Swings (sec) Time for 1 swing (sec) 236.00+/-. 05 308.85+/-. 1 3.0885+/-.

001128.00+/-. 05 227.91+/-. 1 2.2791+/-. 001 Analysis: Part 1: To determine the gravity based on the Atwood's Machine we started by finding the average time for the large mass to fall. The calculations for this are below. We estimated our error for time to be.

1 seconds based on reaction time of the team members. Now after converting our values for m into kg and for's into meters we plugged the value for t,'s, m 1, and m 2 into the below equation to give us our gravity value. Finally to determine the error in this calculation we used the following calculations. With an error of. 05 grams based on the instrument for mass, and.

05 cm for distance based on the instrument This gives us a final value of g for part 1 of. Part 2: For part 2 we started by getting an average time and error for each of the two heights. The equations for this are shown below. 0005 sec based on instrument error Height 1: Height 2: Next we converted our's value to meters and solved the given equation for g and plugged in our values.

Height 1: Height 2: Finally we determined the error of these calculations using the following calculations. We estimated our error for height to be. 05 cm based on instrument error. Height 1: Height 2: Combining the error with our gravity measurements we end up with the final values listed below. Height 1: Height 2: Part 3: To determine the value of gravity by use of a pendulum we started by solving the given equation for g as shows below. We then plugged in the values for each of the 2 pendulums we used after converting to standard units and got the following values.

Pendulum 1: Pendulum 2: Next we determined the error of our calculations using the following equation and calculations. We estimated our error to be. 05 cm for height based on instrument error and. 1 sec for time of 100 swings based on reaction time. Pendulum 1: Pendulum 2: Combining our values for g with the error we ended up with the final values listed below. Pendulum 1: Pendulum 2: Critical Conclusions, Insights, and Inquiry: Overall our results for this lab fell very close to the known value of gravity at Prescott, AZ.

Our closest experimentally derived value as requested by question 7, was for the free fall experiment using the second height, which was the lesser height. This value was only off by. 004 meters per second. We believe this value was the closest because the instruments used to measure time had the least error, and gave the most consistent measurements out of any of the apparatuses used. For the pendulum as requested by question 8 an error of 1 cm would of affected the value of gravity by either increasing it or decreasing it by a small amount.

In our case an error of 1 cm in the first pendulum would of caused an error of. 04 meters per second squared in the direction of the error. An error of 1 cm in our second pendulum would of caused an error of. 08 meters per second squared in the direction of the error. Also with regards to the pendulum and question 9, the use of 100 swings of the pendulum as opposed to just 10 allowed for much less error.

Any error introduced by either reaction time, or instrument error is spread out of 100 swings allowing it to be diluted and have a much lesser affect on our calculations. As opposed to the free fall device, and the pendulums the Atwood's machine gave very poor values for gravity. As requested by question 10, below is the work to show the required force needed to put the value of g in agreement with the respected value. F is the force added on the lager mass, in a downward direction. The main results of our experiment were that the use of a pendulum and free fall to measure gravity generally give very good results, with the highest absolute error from our 4 trials involving either free fall or a pendulum being.

32 meters per second off of the accepted value of 9.7952 meters per second. Personally my initial understandings of the concepts presented in this lab have not changed. This lab has shown me that the equations accepted for free fall and pendulum motion are accurate, and it also showed me that the assumption of a mass less and friction less pulley made could alter the results by a substantial amount. This lab stimulated in me a couple of questions regarding gravity, and kinematics in general. The first of these is how does air resistance affect the results of these experiments? Also this experiment made me wonder about how the scientists in the 1600's came up with these equations from scratch?

Overall this lab has shown me the validity in classical physics concepts, and showed me that some instruments can be very precise, or that certain errors can be reduced.