Motion Along An Incline Lab Report PDF

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Genae Dixon 06/26/2020

Motion Along An Incline Lab Report  Introduction and Abstract: During the 17th century, Galileo did an experiment where he rolled a ball down an incline, and the results were the idea of acceleration. The rate at which an object picks up speed may or may not be impacted by different factors. This report explores and analyzes the motion of a cart along an incline with various environmental factors. Newton’ second law of motion F=m*a,  or Force equals mass times acceleration and Galileo’s incline experiment results a=g*sinθ, will help us analyze our data. The  objective of these experiments is to determine how mass and the angle of an incline impact the acceleration of an object along an incline. Our goal is to replicate Galileo’s original experiment to find data to support a mathematical relationship between mass, angle of incline and the acceleration of an object.  Procedures: For part A of the experiment, we will release the cart at different positions along the incline and measure its time of travel. We will release the cart from rest at various starting positions to the end of the track (100.0cm) and record the time it takes for the cart to get from its initial to its final position. Start the timer and release the cart at the same time for the best results. We will have 3 trials for each starting position. For part B of the experiment, we will do the same process as part A except the starting position will be the same for each run. Will place 5 different masses on the cart and record the time it takes for the cart to reach its final position. We will still begin at rest and take 3 trials of each mass. For part C of the experiment, we will keep displacement contrast as we did in part B, but we will vary the angle of the incline. We will run the experiment with 5 different angles varying from 5 to 15 degrees, and have 3 trials per angle.  Data Tables, Calculations, and Analysis: Data Table for Part A – Displacement vs. Time

Angle of Inclination

θ= 0.7 deg







Initial Final position position xi (m) xf (m)

Displacement Δx = xf − xi (m)

Trial 1 time Trial 2 time Trial 3 t1(sec) t2(sec) time t3(sec)

Average time tave (sec)

1

.80

1.0

.20

2.67

2.63

2.73

2.68

2

.60

1.0

.40

3.48

3.45

3.52

3.48

3

.40

1.0

.60

4.18

3.97

4.1

4.08

4

.20

1.0

.80

4.5

4.52

4.51

4.51

5

0.00

1.0

1.0

4.67

4.69

4.65

4.67

Genae Dixon 06/26/2020

 

Δx/Δt (m/s)

Δx/Δt 2 (m/s2)

Average velocity Vave (m/s)

Final velocity Vf (m/s)

Average acceleration aave(m/s2)

Net acceleration anet(m/s2)

1

.075

.029

.075

-.150

.029

.029

2

.115

.033

.115

-.230

.033

.033

3

.147

.036

.147

-.294

.036

.036

4

.177

.039

.177

-.354

.039

.039

5

.214

.046

.214

-.428

.046

.046



.146

.037

Average









.054

.006

Std. dev.









Data Table for Part B – Mass and Acceleration Due To Gravity Angle of Inclination θ= 0.7 deg

Displacement Δx = .8m  

Load mass Trial 1 M (kg) t1(sec)

Trial 2 t2(sec)

Trial 3 t3(sec)

Average time Net accel. anet(m/s2) tave (sec)

Is acceleration in range?

1

00

4.41

4.56

4.5

4.49

.040

No

2

.10

4.26

4.27

4.3

4.28

.044

Yes

3

.20

4.21

4.27

4.35

4.28

.044

Yes

4

.30

4.24

4.2

4.2

4.21

.045

Yes

5

.40

4.36

4.3

4.38

4.35

.042

Yes











Average

.043













St. dev.

.002



Data Table for Part C – Acceleration vs. Incline

Displacement Δx= .80 m  

Angle θ (deg) 

Sine of angle Trial 1 t1 θ (deg)  (sec)

Trial 2 t2(sec) Trial 3 t3(sec)

Average time tave(sec)

St. Dev. σ t (sec)

Genae Dixon 06/26/2020

1

2.9

.051

1.9

2.15

1.8

1.95

.180

2

4.5

.078

1.67

1.63

1.65

1.65

.020

3

5.1

.089

1.51

1.52

1.45

1.49

.038

4

6.3

.110

1.3

1.35

1.24

1.30

.055

5

7

.123

1.15

1.27

1.18

1.20

.062



Net Accel. anet(m/s2)

Error in net accel. δ a net (m/s2)

Ideal accel. g sinθ  ag(m/s2)

% Error anet vs. ag

1

.210

-.169

.500

58%

2

.294

-.085

.765

62%

3

.360

-.019

.873

59%

4

.473

.094

1.08

56%

5

.556

.177

1.21

54%

 

  CONCLUSION: In these experiments, we explored how different factors impact the acceleration of an object. In experiment A, we performed a simple run where we record displacement over time of a cart. The sample standard deviation of the experiment showed that acceleration is constant even when displacement changes. In the pre-lab I predicted that “the heavier an object is, the faster it will move down an incline; there will be a higher level of force pushing it downwards, causing the acceleration to increase with mass”. For experiment B, we varied the mass of the cart and compared the accelerations associated with the different masses. The trend in our data supports the idea that acceleration increases with mass. In experiment C, we varied the angle of the incline to determine if angle impacts acceleration as well. According to the data gathered in our experiment, when the angle of incline increases, the acceleration increases as well. The incline causes a steeper downward fall for the cart, increasing the parallel component of the incline....