If you were performing this experiment in an in-class laboratory, you would be given one or more small iron balls. These would be utilized with a variant of the Free-Fall apparatus shown in the graphic below. (INSERT PICTURE HERE) You would first raise the upper black clamp to the desired height above the middle clamp. Then you would place the ball firmly in the upper clamp. Next, you would turn on the timer and adjust its initial reading to zero. After you release the ball, it falls towards the middle clamp. When it encounters this clamp, the timer stops and you can read the time of fall. Results are usually within 10% of the standard value of g. Here, in this online version, I will supply values of height (h) and time (t). First, calculate the average time (tav) for each height and use it as described next. You will use the third equation above to calculate the value of gravitational acceleration (g) in each case. Then, you will determine the average value of g (gav) and compare this with the standard value, (gst = 980 cm/s2) in calculating the Percent Difference (PE). You will calculate Percent Error for your determination of g at each height using: (gav-gst) (gav-980) PE = 100 ____________ = 100 __________ (gst) 980 Free Fall Table Height h Time 1 Time 2 Time 3 Average time (tav) g= 2h/tav2 PE (cm) (sec) (sec) (sec) (sec) (cm/s2) ______ _____ _____ _____________ _________ ______ 40 0.27 0.26 0.27 50 0.33 0.31 0.34 60 0.36 0.35 0.37 80 0.40 0.41 0.41 100 0.43 0.45 0.44 _______________________________________________________________ gav = Question: The Earth’s radius is about 6400 km. The International Space Station (ISS) orbits about 400 km above Earth’s surface. So the center-to-center distance between Earth’s center and the space station is about 6800 km. Estimate Earth’s gravitational acceleration at the space station orbital height, giss. Use the ratio approach: giss / g = giss /980 = (6400 /6800)2 = giss = cm/s2.
If you were performing this experiment in an in-class laboratory, you would be given one or more small iron balls. These would be utilized with a variant of the Free-Fall apparatus shown in the graphic below.
(INSERT PICTURE HERE)
You would first raise the upper black clamp to the desired height above the middle clamp. Then you would place the ball firmly in the upper clamp. Next, you would turn on the timer and adjust its initial reading to zero. After you release the ball, it falls towards the middle clamp. When it encounters this clamp, the timer stops and you can read the time of fall.
Results are usually within 10% of the standard value of g. Here, in this online version, I will supply values of height (h) and time (t). First, calculate the average time (tav) for each height and use it as described next. You will use the third equation above to calculate the value of gravitational acceleration (g) in each case. Then, you will determine the average value of g (gav) and compare this with the standard value, (gst = 980 cm/s2) in calculating the Percent Difference (PE).
You will calculate Percent Error for your determination of g at each height using:
(gav-gst) (gav-980)
PE = 100 ____________ = 100 __________
(gst) 980
Free Fall Table
Height h Time 1 Time 2 Time 3 Average time (tav) g= 2h/tav2 PE
(cm) (sec) (sec) (sec) (sec) (cm/s2)
______ _____ _____ _____________ _________ ______
40 0.27 0.26 0.27
50 0.33 0.31 0.34
60 0.36 0.35 0.37
80 0.40 0.41 0.41
100 0.43 0.45 0.44
_______________________________________________________________
gav =
Question: The Earth’s radius is about 6400 km. The International Space Station (ISS) orbits about 400 km above Earth’s surface. So the center-to-center distance between Earth’s center and the space station is about 6800 km. Estimate Earth’s gravitational acceleration at the space station orbital height, giss. Use the ratio approach:
giss / g = giss /980 = (6400 /6800)2 =
giss = cm/s2.
The gravitational acceleration at the space station due to the gravitational force from Earth is calculated by using the formula , where is the gravitational constant , is the mass of Earth and is the radius of the orbit of space station .
The mean value of three measurements is the sum of the individual values divided by 3.
The acceleration due to gravity of a falling object can be calculated by using the formula , where h is the height of the mass and is the average time taken.
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