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Free Fall

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Lab Report- Calculate and Prove the Acceleration Due to Gravity
David Chen
Introduction:
We know that the acceleration due to gravity on the earth is 9.8ms -2. This acceleration is very important since we can use it to calculate gravity force, mass, and so on. In this lab, we use a free fall object to calculate its acceleration due to gravity to check if it is 9.8ms-2. We use the acceleration formula a=V2-V1t2-t1 to calculate the acceleration.
Hypothesis:
The acceleration due to gravity on the earth is 9.8ms -2. So in this lab, the acceleration in the result should also be 9.8ms-2 since the object experiences the free fall on the earth.
Diagram:
Free fall object diagram
Free fall object diagram
Motion detector
Motion detector

1 meter
1 meter
Point 2(V2 T2)
Point 2(V2 T2)
Point 1(V1 T1)
Point 1(V1 T1)
Free fall object
Free fall object

Method: In this lab, we used a motion detector to measure the velocities and times of the falling object. The range of the motion detector is one meter, so we have to drop the object from one meter above the ground. So to make the result more accurate, first we placed the motion detector on the top of the metal ring which is approximately one meter above the ground. After that we held the object under the motion detector. Then we started the motion detector and dropped the object at the same time. At last we observed the data in the computer provided by the motion detector. We chose two points which the falling object experienced from the data. The points were far from each other. Then we copied the velocity and time of each point separately and wrote them down in table. At last we use the formula a=V2-V1t2-t1 to calculate the acceleration due to gravity. We repeated these steps three times.
Results:
| Run 1 | Run 2 | Run 3 | | Point 1 | Point 2 | Point 1 | Point 2 | Point 1 | Point 2 | Velocity m/s | 0.666 | 2.206 | 1.221 | 1.993 | 0.866 | 1.585 | ±0.001 m/s | Time/s | 0.60 | 0.85 | 0.60 | 0.80 | 0.40 | 0.65 | ±0.05/s | acceleration/ms-2 | 6 ±1 | 4 ±1 | 2.9 ±0.6 | The average acceleration: 4.3±2ms-2 |

Run 1: Velocity : 2.206-0.666=1.540m/s Uncertainty: 0.0011.540×100=0.06%
Time: 0.85-0.60=0.25s Uncertainty: 0.050.25×100=20%
Acceleration: 1.540.25=6.16ms-2 Total uncertainty: 20% + 0.06% = 20.06% 6.16× 20.06%=1.24m/s-2= 1m/s-2 The result: 6±1 m/s-2
Then I did the same steps and got the accelerations and uncertainties for run 2 and run 3.
Average acceleration: 6+4+2.93=4.3ms-2 uncertainty: 6-2.92=1.55ms-2=2ms-2 result: 4.3±2ms-2
Conclusion and evaluation:
At last, the result I got is 4.3±2ms-2. It is very different from the acceleration due to gravity on earth, which is 9.8ms-2. I think there are two main reasons make the results not accurate. First is the air resistance, it hinders the free fall of the object. Second is the range of the motion detector. Although the detector is accurate, its maximum range is only 1 meter. The detector may be above the ground for more than 1 meter. So it cannot detect the motion of the object after it falls more than 1 meter. That makes the result inaccurate. To improve the experiment, we should use a motion detector which has larger maximum range so that it can completely detect the motion of the falling object and makes the result more accurate.

Lab report- measure and calculate the horizontal displacement of a ball in parabolic motion
David Chen
Introduction:
Parabolic motion is very common in physics world since we always use it to measure the distance, velocity, or time of an object in parabolic motion. In this lab, we will measure the horizontal displacement of a ball in parabolic motion by using a motion detector to detect its motion. We will also calculate the horizontal displacement by using the distance formula- d=vt and the formula for parabolic motion- d= ut+ 12at2. We will check if the result of our calculations is the same as the result of our measurement.
Hypothesis:
Motion detector
Motion detector Since we measure and calculate the same thing- the horizontal displacement of the ball, the results of the measurement and the results of the calculations should be the same.
Diagram:
Parabolic motion diagram
Parabolic motion diagram
Vx
Vx

Vy
Vy
The height of the table Y=0.78m
The height of the table Y=0.78m

Horizontal displacement X

Horizontal displacement X

00000000

Method: First we measured the height of the table. Then we placed the ball on a rail to make sure it could go in a straight line to make the results accurate. Then we placed the motion detector near the ball to measure the initial horizontal velocity (Vx) and time of the ball. Then we pushed the ball and started the motion detector at the same time. After the ball reached the ground, we immediately marked the point which it reached on first. Then we measure the distance between the ball and the table, which is the horizontal displacement. At last we used the formulas d=vt and d= ut+ 12at2 to calculate the horizontal displacement and compared it with the result we got from the measurement. Then we recorded the two results and did the same steps for two more times.
Results:

| Run1 | Run 2 | Run3 | Velocity X (ms-1) | 0.3087 | 0.4201 | 0.4621 | The height of the table(m) | 0.78 | Horizontal displacement (measured) (m) | 0.09 | 0.23 | 0.35 | Horizontal displacement (calculated) (m) | 0.12 | 0.17 | 0.18 |

Run 1: d= ut+ 12at2, a= 9.8m/s2, d=-0.78, u=0, -0.78= 0×t+12×9.8×t2, t= 0.40s
Horizontal displacement: X= 0.40×0.3087=0.12m.
Then we repeat the steps for run 2 and run 3. The results are recorded in the table.
Conclusion and evaluation: Compare the results of measurements with the results of calculation, we can see some results are close (0.09 and 0.12), but some results are very different (0.35and 0.18). I think there are reasons make the results inaccurate. First is the air resistance. It hindered the movement of the ball. Second is the range of the motion detector is only 1 meter. So it could not detect the motion of the ball when it moves out of its range. Third is when the ball reaches the ground, we did not find the exact point it reached first, so the measurements are inaccurate. To improve the experiment, we should use a motion detector that has lager range to improve the accuracy of the results. We should be careful and fast when we check the point the ball reaches on the ground.

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