LAB Report Newton\'s Second Law PDF

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LAB REPORT

PHY 113: “Newton’s Second Law” Name: Aylen Perez Vazquez Group Number: Class number: 71466 Time: 4:00pm Wednesday TA's name: Chao Ji

Objective: The objective of this lab is to validate both First and Second Newton’s Laws of

Motion. Experimental Data: Experiment 1 - - Newton's First Law Table 1 Slope of linear fit of the V v/s t graph

-0.0463 ± 0.0017

What physics quantity does V v/s t graph re-presents? acceleration

Experiment 2 - Newton's Second Law mass of the cart = 504.5 g mass of the hook = 5.1 g Total mass of the system (cart+hook+weights) = 559.6 g = 0.56 kg Table 2 Mass on the cart

Mass on the hanger

Acceleration

40.0 g

10.0 g

0.234 m/ s ❑2

30.0 g

20.0 g

0.412 m/ s ❑2

20.0 g

30.0 g

0.576 m/ s ❑2

10.0 g

40.0 g

0.753 m/ s ❑2

0

50.0 g

0.908 m/ s ❑2

Experiment 3 - Prediction

Mass of the system

Applied Force

Predicted acceleration

Experimental Acceleration

1.03 m ¿ s ❑2

569.6 g = 0.57 kg 0.59 N

1.01 ± 0.014 m 2 ¿s❑

Data analysis: Experiment 1 - - Newton's First Law – no calculations required. Experiment 2 - Newton's Second Law

❖

Slope = 1/m 1.72 = 1/m m=

1 = 0.58kg 1.72

[ ]

Δ slope = slope

❖

Δ m= m

(

Δ slope slope

)

Δm m

= 0.58 kg x

(

−1

0.022m ❑ −1 1.72m❑

)

= 0.0074 kg

Percent Discrepancy: ❖

− m measured ( m experimental ) m measured

=

kg−0.56 kg ( 0.58 0.56 ) x 100 = 3.6% kg

Experiment 3 F= M ❑system x a ≈ 0.59 N 1 a= xF M ❑system 1 a= x 0.59 N 0.57 kg a= 1.03 m/ s ❑2 Percent Discrepancy

F= m x g = 0.06 kg x 9.81 m/ s ❑2 = 0.5886 N

(

m experimental − m measured ❖ m measured 2.0%

)

2

2

1.01 m /s ❑ −1.03 m /s ❑ = 2 1.03 m/ s❑

x 100 ≈

Results: Experiment 1: velocity of the cart = ____constant velocity____ Measured mass , kg

Percent discrepancy, %

Newton’s Second Law

Experimental mass and its uncertainty, kg

Experiment 2

0.58 ± 0.0074 kg 0.56 kg

Prediction

Predicted acceleration, m/s2

Experimental acceleration, m/s2

Percent discrepancy, %

Experiment 3

1.03 m/ s ❑2

1.01 ± 0.014 m 2 ¿s❑

2.0%

3.6%

Discussion and Conclusion: The objective of this experiment is to verify the validity of Newton’s Laws of Motion. Newton’s Laws are the essential part of Dynamics- the area of physics that studies the cause of motion experienced by an object. Newton’s second law was the conceptual basis of the investigation and was used to determine both mass and acceleration. Newton’s First Law states that an object will be at rest or will maintain constant velocity motion until a force is applied on it, which was tested in Experiment # 1. Newton’s second law states mathematically  that ∑ = , meaning the magnitude of acceleration an object experiences is directly proportional to the magnitude of the net force acting on the object, and that they follow the same direction. These two quantities, net force and acceleration, are related through the mass of the object in question. This relationship is pertinent to the procedure of the experiment, in which mass and velocity were the measured quantities. In the first part of the lab, a motion sensor was used to record the velocity of a cart pulled along a

horizontal track by a variable tension force caused by a weight at the end of a string, all while the total mass of the system remained constant. The second part followed the same process, with the exception that the system mass was not kept constant. The third part of the lab involved using a new value of applied force that was not used before and predicting the acceleration of the cart and then determining the experimental values to see if both values are in agreement with each other. After doing all three experiments, results for the experimental mass of the system and gravitational acceleration were obtained. The mass of the system derived from the slope was found to be 0.58 kg with an uncertainty of 0.0074 kg, off by a percent error of 3.6% from the expected value of 0.56 kg, which was measured using a scale. The expected value of acceleration in Experiment 3 was of 1.03 m/ s 2 and the experimental value was of 1.01 ± 0.014 m 2 ¿ s ❑ only showing around 2% of discrepancy which supports the mathematical model of Newton's Second Law of Motion. A source of errors could have been friction between the cart and the track, which was unaccounted for in the first part of the experiment when the cart only moved in the same direction as the tension force, and therefore, friction always acted opposite the tension. Another source of error was the fact that the masses added to the hanger weighed more than was considered (due to manufacturing discrepancies), meaning the gravitational force values used in calculations were smaller than reality. Another source of error could have been that the track may not have been completely leveled, or the string may not have been perfectly horizontal. Any slight deviation in these angles would inevitably alter the force components acting on the cart and alter its motion in ways that weren’t accounted for. Overall I think that the objective of the experiment was achieved. The results of our data and calculations verify Newton’s first and second laws of motion because the determined values are reasonably close to the theoretical values taking into consideration sources of error and imperfections in the experimental setup....