Physics 11 Experiment 3: The acceleration due to gravity
Introduction
The free fall movement is not a steady movement because there is an action over the body due to the gravity or acceleration between two bodies with different mass. The moon and the earth exert an attraction force due to their two masses (University of Tennessee Knoxville). The planets of the solar system have an orbital movement around the sun thanks to attraction force due to the mass of the sun and the planets. All the particles and bodies in the universe attract them. There is a general equation that represents that phenomenon:
F = G*m1*m2/r2
Where F is the attractive force, G is a gravitational constant (6.67 x 10-11 m3kg-1 s-2), mn are the mass bodies under consideration and r the distance between them. The gravity is an acceleration value of a small body of a planet, in this case, earth. Considering m2 the smallest body and m1 the mass of earth and r the average radius of the earth:
F/m2 = G*m1/r2
g = G*mEARTH/rEARTH2
g = 9.81 m/s2
The local value of the gravity on the earth surface may differ according to the place where it is measured. A value of gravity on the Equator line is lower than in the Poles.
The free fall movement considers only the effect of the gravity without considering the effect of viscosity (resistance of the air) and rotation of the body (angular movement). The movement in free fall is by agreement in the vertical axis, and the graphs have an equation representation in second grade, that is Y = ax2+bx+c.
The calculation of the gravity (used as a constant in textbooks) comes from the experimentation with particles in vacuum spaces avoiding the resistance of the air. The physics lab will be the scenario to recreate a phenomenon of free fall movement to calculate the gravity acceleration tracking all the movement of the particle, that is, location every interval of time.
Objectives of the experiment
■ Study the phenomenon of the free fall movement
■ Calculate with numeric method the value of gravity
■ Calculate with graphical method the value of gravity
■ Compare the results of gravity with the numeric and graphical method.
Results
The first graph is the relation between the velocity and time (Image 1). The graph is a first-grade equation according to the relation of v = vo* + a*t.
Image 1: Relation between velocity and time
The value of the gravity according to the graph is 1186cm/s2. The value is 21% higher than the reference value of gravity. The use of the straight slope forces the result of the value. The previous graph must me straight, but the values give an irregular form.
The second graph (Image 2) is the relation between the distance and time in the experiment:
Image 2: Relation between distance and time
The value of gravity is g = 2*457.07= 914.14 cm/s2. The value has a 7% of error according to the reference value of the gravity.
Conclusions
It is recommended to calculate the gravity to use the procedure of distance vs. time, avoiding the use of velocity vs. time.
The contact of the falling object over the paper may affect the results due to the position of contact. The air friction and the angular movement may affect the results of the laboratory. A high-density object as steel with polished surface and spherical form will have better results than a low-density object as rubber with a non-polished surface with an irregular form.
The reduction of the frequency, for example, to 58 Hertz may introduce error into the calculation, especially in the calculation using velocity vs. time. In the case of calculation using distance, there will be fewer points than using the 60 Hertz frequency. The value of g will be higher.
Cited Works
