Physics lab report 3 - newton\'s second law of motion - variable forces PDF

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newton's second law of motion - variable forces...

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Lab #3: Newton’s Second Law of Motion Misheel Dolguun, Anna Hofbauer

Experiment 1 - Variable Forces Introduction The objective of this experiment is to use a force sensor and a motion detector to simultaneously measure the force on a small cart and its acceleration. These devices will allow for the relationship between the net force on the cart, its mass, and its acceleration to be determined, which is Newton’s Second Law of Motion. Newton’s Second Law of Motion describes the relationship between forces acting on an object, the mass of the object, and the acceleration of the; the net force is equal to the object’s inertia and its acceleration. As a vector equation, it is: . In the equation mass is used instead of inertia because for objects moving in a straight line, the object’s inertia is equal to its mass. The amount of acceleration a force provides is scaled by the object’s inertia; the greater the inertia, the smaller the acceleration, and the smaller the inertia, the greater the acceleration. In the first part of the experiment a motion detector was attached to a small cart that was pulled across a track by a string, and in the second part of the experiment a hanging mass was attached to a cart over the edge of a table. Procedure For the first experiment a motion detector was attached to a cart, total mass 357.5 g, that was dragged by string wire manually across a track, with a force sensor measuring the changes in amount of force applied to the cart. The cart was oriented with a force sensor pointing towards the track and the wheels of the cart were placed into the grooves of the track. The cart was pulled along the axis of the track by attaching a hook and string wire to the cart and manually pulling on the string for each trial. The process was repeated, pulling and pushing instead of just pulling the cart. For the second experiment, a 50 g hanging mass was attached to the cart by string and dropped over the edge of the table.The mass was dropped and the tension in the string was recorded by the force sensor while the acceleration of the system was recorded by the motion sensor. The dropping of the mass, was the mechanism for accelerating the cart in this experiment. Data Analysis Repetitions of the pulling, and the pushing and pulling of the cart, with additional masses were not completed due to time constraints. Time was lost due to multiple replications of the first part of this experiment, pushing the cart with a string.

Theoretically applied force (N)

Estimated acceleration (m/s^2)

1.0 N

1

1.5 N

0.5

2.0 N

0

Force vs Time Green - Pulling Cart Blue - Pushing and Pulling Cart

Pulling the cart: The shape of the force graph curves down as force is applied to pull the cart by string across the track . The general shape of the downward curve is u-shaped, but there are some trenches to the curve, indicating that the applied manual force was not even. Pulling and pushing: The shape of the graph has symmetrical alternating peaks and trenches in the positive and negative direction. This indicates that the manually applied force was decently even. Acceleration vs. Time Orange - Pulling Cart Purple - Pushing and Pulling Cart

Pulling: The shape of the acceleration graph is one with one large peak, and more smaller trenches and peaks. This indicates changing acceleration. Pulling and pushing: there are similarly sized peaks and trenches alternating vertically across the horizontal time axis. This indicates constant acceleration. When the force is maximum, the acceleration is near maximum. This indicates that the relationship between force and acceleration is direct. The constant of proportionality that scales the relationship is inertia, or the object’s mass. Using F=ma, the theoretical mass of the cart would be: pulling: 0.72 N = m (0.51 m/s^2), m =0.51 g, pulling and pushing: 0.5 N = m (0.4 m/s^2), m = 1.25. The actual measured mass of the cart was 357.5 g. The percent error can be determined by:pulling: % error = [(357.6 - 0.51)/ 357.5] x 100% = 99.9% error, pulling and pushing:[(357.6 - 1.25)/ 357.5] x 100% = 99.7%. This is an extremely high amount of error in the calculated mass of the cart for both cases, indicating error in the handling of the procedure. However, pulling and pushing gives slightly less error. Force vs Acceleration

The slope is 0.00347, the value is small because the upper right section resembles a straight line so the difference in values is very small. The units of the slope of N/ms^-2.

Experiment 2 - Constant Force with Tension Data Analysis Tension of String as Hanging Mass Falls

The mass was falling from 6.000s to 6.400s during which the mean value of the force was -0.196

N and the mean value of the acceleration was 0.41 m/s2. The mean force represents the average tension in the string during that time period. The highlighted region only illustrates the initial fall before the mass lightly bounced several times. Free Body Diagrams of the Cart and Hanging Mass m1 = cart m2 = hanging mass

Theoretical value for the tension in the string (calculated) T = (m1m2 / m1+m2) g T = 0.430 N

Measured value for the tension in the string (from graph)

Theoretical value for the acceleration of the system (calculated) a = (m2 / m1+m2) g a = 1.202 m/s2

Measured value for the acceleration of the system (from graph)

T = 0.593

a = 0.97 m/s2

Percent Error:

Percent Error:

|0.593 N - 0.430 N| x 100% = 37.9% error | 0.430 N |

|0.97 m/s2 - 1.202 m/s2| x 100% = 19.3% error | 1.202 m/s2 |

If the cart had a constant speed before the mass is released the results would change. This is because in order to calculate tension of the cart you need the acceleration in the x direction, as seen in the equation below.

T = m1ax This acceleration will be affected by the cart having an initial velocity other than zero.

Conclusion

Both experiments in this lab utilized Newton’s Second Law of Motion to analyze force, tension, and acceleration of a moving cart. From the first experiment, the calculated masses were 0.51 g from the trial pulling the cart, and 1.25 g from pushing and pulling the cart. Both these masses produced extremely high percentages of error of 99.8% and 98.7%, this high percentage of error was most likely due to lack of constant control over the acceleration of the cart. The slight difference between the two sets, indicates that pushing and pulling had a more constant acceleration, this was due to pushing and pulling being easier to control there was a constant motion in both directions of the horizontal axis. A motion in both directions is easier to balance, than trying to control a motion in a singular direction, in other words the system of pushing and pulling is more stable because the net force of the horizontal axis is balanced. For the results of the second experiment, the calculated tension in the string was 0.430 N and the measured value was 0.593 N. This 37.9% error is most likely due to air resistance in the lab as well as friction on the cart’s track. Likewise for the 19.3% error in acceleration. Air resistance and friction both affect the acceleration of the system by slowing it and therefore the tension of the string will be altered. Overall, using the data and free body diagrams it's possible to create a formula to calculate the acceleration of the cart as a function of the amount of the falling mass (shown above)....