This paper involves a physics simulation to determine gravity. The simulation is run at six distances 1m, 2m, 3m, 4m, 5m, and 6m, to see the time it takes for an object dropped to fall that distance. The simulation is run on the Earth, the Moon, and Mars. The results are plugged into the formula 2s/t*t to determine the gravitational constant for each of the three bodies. Those results are compared with the accepted gravitational constants.
Physics Simulation
Displacement, Velocity, and Acceleration
In the session long projects for this class, you will be asked to conduct experiments in a "virtual" laboratory.
We will use the falling-ball simulation (Background: University of Oregon, n.d.) to calculate the acceleration of gravity on the Earth, Moon, and Mars.
The most general equation for displacement is a = s0 + V0t + (1/2)at2
where's = displacement after time t s0 = initial displacement (location at t = 0)
V0 = initial velocity (velocity at t = 0)
t = elapsed time in seconds
a = acceleration in m/s2
If the object starts at point s0 = 0 with initial velocity V0 = 0, then the equation becomes
s = (1/2)at2
Solving for a in terms of s and t, we get a = 2s/t2
For a freely falling object in a vacuum, a is the acceleration of gravity, g. If we record the time required for an object to fall a distance s in a time t, we can solve for g. Using the simulation, record the time required for the ball to fall 1, 2, 3, 4, 5, and 6 meters. Organize your results in a table, as follows (the first row has been completed for you). Round numbers to the nearest two decimals.
Earth
S (distance, m)
t (time, s)
2s
t2
(2s/t2)=g
1
.44
2
.19
10.33
2
.63
4
.40
10.00
3
.77
6
.59
10.17
4
.89
8
.79
10.13
5
1.00
10
1.00
10.00
6
1.10
12
1.21
9.92
Moon
S (distance, m)
t (time, s)
2s
t2
(2s/t2)=g
1
1.10
2
1.21
1.65
2
1.56
4
2.43
1.65
3
1.92
6
3.69
1.63
4
2.21
8
4.88
1.64
5
2.48
10
6.15
1.63
6
2.71
12
7.34
1.63
Mars
S (distance, m)
t (time, s)
2s
t2
(2s/t2)=g
1
.73
2
.53
3.77
2
1.03
4
1.06
3.77
3
1.27
6
1.61
3.73
4
1.44
8
2.07
3.86
5
1.64
10
2.69
3.72
6
1.80
12
3.24
3.70
Answer the following questions.
Why are all the number in the last column approximately the same?
All of the numbers in the last column are approximately the same because they are supposed to approximate a gravitational constant.
Which of the six trials would probably yield the most accurate estimate for g? Why?
I would assume that the trial on the moon would yield the most accurate estimate for g because the moon is probably the closest to a vacuum, so that there would not be the same effect of friction on the falling object.
Compare your answer with the accepted value for g. How would you account for the discrepancy, if any?
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