Physics (Phys 215): Experiment - Newton\'S Laws - 2018 September PDF

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my lab report for this lab - I earned an A in the lab. includes my theory, procedure, results, and conclusions, including sources of error ...

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Experiment: Newton’s Laws 9/11/2018 PHYS 215, T 3pm

Purpose The purpose of this experiment is to demonstrate and use Newton’s Second Law to measure the acceleration of an object. In order to do this, a frictionless air track was used. Theory Galileo struggled with obtaining proper measurements for free fall experiments due to the fact that his available equipment was lacking. He instead conducted experiments with inclined planes of different slopes in order to study the acceleration due to gravity. He noticed that the acceleration of the ball traveling down the inclined plane each time was constant. Newton also studied motion, as he developed his own three laws of motion. Newton’s Laws of Motion are: 1) a body in motion tends to stay in motion, whereas, a body at rest tends to stay at rest, 2) the net force on an object is equivalent to its mass multiplied by its acceleration, and 3) for every action, there is an equal and opposite reaction. Newton’s second law also means that he rate of change in the momentum of an object is directly proportional to the amount of force exerted on the object. It can also be written as Fnet=ma, where Fnet is the net force or sum of all forces, a is the acceleration, and m is the mass of the object. Free body diagrams can be drawn to help represent force vectors on an object. Below is a free body diagram representing the forces enacted on an object 1) sliding down an inclined plane (one-body system), and 2) being pulled by a string on a frictionless pulley (two-body system). 1)

2)

In the case with the object on an inclined plane (1), the object will move down the wedge (with an angle of theta) with some acceleration. Because the object is only moving in the x direction, the following equation can be used to solve for its acceleration.

Additionally, sin theta can be found from the same equation. Sin theta is equal to the height of the incline divided by the distance the object travels down the incline.

In the case with the objects on the pulley (2), the magnitude of the acceleration of each object will be the same, as the objects are connected by a string, but the directions will be different. Using Newton’s Second Law, the acceleration can be calculated with the following equation.

Also, there are forces in both the x and y direction in this case, so the tension needs to be calculated with the following equation.

The percent error can be found in order to compare the measured values of acceleration to the generally accepted value. This helps determine the accuracy of our measurements in the lab.

Procedure First, we made sure that the air track was level so that the cart would remain in the center of the track when the blower was turned on. We then measured the distance, d, in centimeters between the two legs of the air track using a meter stick. Next, we used a caliper (below) to measure the thickness (or height, h) of the wooden blocks, which were used to create the inclined air track. I was responsible for this part. We then followed the directions of the lab protocol in order to set up the computer system. We selected a two-graph display and set the first to measure velocity vs. time, and the other to measure position vs. time. We began the trials by releasing the cart from the starting end of the track (near the sensor), and the motion sensor measured the cart’s motion. The computer’s Record button was clicked as soon as the cart was released, and the Stop button was clicked as the card reached the end of the track. I was also responsible for passing the cart back to the front of the air track after each trial. This was repeated twice for each height, at five different heights (1 to 5 blocks), for a total of ten trials. The computer provided values for acceleration and standard deviation. A linear part of the graph was selected in order to find a better slope value (see attached).

The second aspect of the experiment included a pulley system. We attached a string to the end of the cart and a weight at the other end (below). The string was passed over a

frictionless pulley, allowing the weight to hang freely. Again, the computer system recorded acceleration and standard deviation, and the different masses used were 10g, 20g, and 30g. I was responsible for attaching the weights to the string each time. We did three trials for each weight, and the Stop button was pressed once the mass reached the floor. We then solved for average acceleration and percent error for each of the three weights.

Lastly, we measured the mass of the cart in kilograms using a triple beam balance (below).

Data (attached) Analysis (attached)

Conclusion In this lab, we tested Newton’s Laws of Motion. After calculating the heights of the blocks, the sin theta of each incline, and gathering the acceleration values, I created a graph of acceleration as a function of sin theta. The slope of this graph gave our value of acceleration due to gravity

to be 9.44 m/s^2. This slope was compared to the GAV for g, and the resulting percent error was 3.67%, which is a fairly low percent error. Sources of error include slow or varying reaction times for hitting the Record and Stop buttons, obstructions in the path of the motion sensor, scratches creating friction on the air track, and incorrect measurements of the blocks when using the caliper. The standard deviation values for acceleration given by the computer program were small (see attached), indicating precision in our measurements. The computer program produced graphs for displacement vs. time and also for velocity vs. time. They appeared as expected, with the displacement vs. time graph following a parabolic curve, and the velocity vs. time graph was mostly linear (representing constant acceleration). See attached graphs. Our computer was not interacting with the printer properly, so my group had to take pictures of the graphs instead of printing them. For the second part of the lab, we calculated the following percent errors for the 10g, 20g, and 30g trials: 8.37%, 8.18%, and 7.55%, respectively. Sources of error include slow or varying reaction times when interacting with the computer and improper massing of the cart on the triple beam balance. We also calculated the force of tension for each mass due to the calculated acceleration (see attached)....