Free Fall Motion Lab - lab PDF

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Kevin Allen Partner: Joshua Preciado, Chad, Panos, Alex Free Fall Motion 1410L-812 Ananya Mukherjee 2 October 2018 Objective: The motion of a body falling freely under gravitational attraction will be exclaimed, and from the measured rate at which the velocity changes with time the acceleration due to gravity (g) will be determined.

Introduction: If a net force acts upon a body, then that force causes the body to accelerate. If the force Is constant magnitude, then the acceleration of the body will also be constant.. If the distance of the fall is very much less than the earth’s radius, then the gravitational force is the acceleration due to gravity (g). We ignore the force due to air resistance, which also acts on a falling body because for smooth, dense bodies falling only a short distance, air resistance is very small. The acceleration can be defined as the rate of change of velocity over time: 1.) a = v – v0 * t ”a” represents the acceleration of the object while “v” represents the final velocity and “v0”represents the initial velocity. The average velocity of a body is defined as the total displacement (s) travelled by the body divided by the time taken to travel that distance: 2.) v = s * t

Apparatus: A 40Hz timer with a marker pen is used to mark a dot on a strip of paper 40 times every second. The strip of paper is attached to a 200g mass and dropped so that the marked paper traces the displacement of the mass during freefall Procedure: 1) First, we set up the paper strip and mass and turn on the timer and drop the mass. 2) After the fall the dots are marked and measured with vernier calipers and written into the data table 3) The total displacement is added up in the total s column, and the instantaneous velocity at each dot. 4) The value of g is calculated by the slope at two random points on the s vs t graph which you can use in the equation a = (v2-v1) / (t2-t1)

Results: n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

t = n * dt (s) 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35

Sn (cm) 0 0.39 0.76 1.72 3.27 5.37 8.19 11.63 15.65 20.23 25.38 31.23 37.72 44.84 52.49

dSn (cm)

t (at midpoint) (s)

v = dSn / dt (cm/s)

0.39 0.37 0.96 1.55 2.1 2.82 3.44 4.02 4.58 5.15 5.85 6.49 7.12 7.65

0.0125 0.0375 0.0625 0.0875 0.1125 0.1375 0.1625 0.1875 0.2125 0.2375 0.2625 0.2875 0.3125 0.3375

15.6 14.8 38.4 62 84 112.8 137.6 160.8 183.2 206 234 259.6 284.8 306

S vs t 60 50

S (cm)

40 30 20 10 0

0

0.05

0.1

0.15

0.2

t (s)

0.25

0.3

0.35

0.4

V vs t 350 300

f(x) = 948.08 x − 27.79

V (cm/s)

250 200 150 100 50 0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

t (s)

Analysis: If you take the instantaneous velocity at every point on the s vs t graph and plot it versus t, you get the V vs t graph above. The slope of the V vs t graph will give the experimental value of g. In the equation of the trendline, the slope is 948.08 cm/s2 which is equal to 9.4808 m/s2 Discussion: The results from the graphical method is very consistent with the actual value of g. The slope that was measured from the log graph came out to be g = 9.4808 m/s2, where the actual value of g is about 9.81 m/s2. This is a 3.3% error in the value of g which is very acceptable for the level of precision in the measurement of dS since we could only measure to the closest tenth of a millimeter. In order to achieve even more accurate results in future experiments, higher precision measurements would be required and also we would need to eliminate all friction with air resistance and the friction of the paper against the timer. Conclusion: The results from the lab successfully determined an experimental value of g which was very close to the actual accepted value of g....