Acceleration Due to Gravity in Physics

The acceleration because of gravity, g, was determined by dropping a steel bearing and measuring the free-fall time with a pendulum of identified interval. The measured value is 9.706 m/s2 with a standard deviation of 0.0317, which doesn’t fall within the vary of known terrestrial values. Centrifugal forces and altitude variations can’t account for the discrepancy. The calculation could be very sensitive to the measured drop time, making it the probably source of error.

Theory

The acceleration because of gravity is the acceleration experienced by an object in free-fall at the surface of the Earth, assuming air friction can be uncared for.

It has the approximate worth of 9.eighty m/s2, though it varies with altitude and site. The gravitational acceleration could be obtained from principle by making use of Newton’s Law of Universal Gravitation to search out the force between the Earth and an object at its floor. Newton’s Law of Universal Gravitation for the drive between two bodies is

 

where m1 and m2 are the plenty of the bodies, r12 is the space between the centers of mass of the our bodies, and G is the Universal Gravitational Constant which has a present accepted value of 6.

673 × 10-11 Nm2/kg2. The force between the Earth and a mass, m, could be the place ME and RE are the mass and radius of the Earth, respectively. For a selected location, G, ME, and RE are constant and could additionally be grouped underneath a single constant, g.

For obvious causes, g is usually called the local gravitational fixed.

It might be numerically equal to the acceleration as a outcome of gravity on a spherical, non-rotating planet. The actual acceleration because of gravity might be different than the above due to “centrifugal” and Coriolis effects. The values that comply with were taken from the CRC Handbook of Chemistry and Physics, 75th ed. and illustrate the variability of the value. As anticipated, the value is lower on the equator because of centrifugal pressure.

In this experiment, g was measured using kinematics. A metal bearing was dropped from a identified height and the time was measured. The kinematic equation that provides position as a operate of time is We will apply this equation to a “drop” (v0 = 0) of top, h, as proven under. Making these substitutions, we obtain

 

Rearranging

Experimental

The solenoid electromagnet was a simple coil of #18 wire with an iron core. The energy source for both solenoids was a standard LabVolt regulated power supply. The steel bearing had a diameter of 1.6 cm and a mass of 28.four g. The bodily pendulum consisted of an aluminum rod which is weighted on the bottom. A stopwatch was used to document the period of the pendulum. The distance was measured with a normal meter stick.

The interval of the pendulum was measured by measuring the time for five oscillations and dividing. The experiment was arranged as shown in Figure 2a. The pendulum was pulled away from equilibrium and held in place by an electromagnet. The bearing was held in place by one other solenoid wired to the identical power supply. A piece of spark tape was hooked up to the inside surface of the pendulum. When the facility supply was shut off, the bearing and pendulum had been released concurrently. The bearing contacts the pendulum as proven in Figure 2b, leaving a mark on the tape. The distance was then measured. After a number of calibration runs, ten experimental runs were carried out. The results have been obtained using the same time and ten measured distances.

Results and Discussion

The acceleration as a end result of gravity was measured to be 9.706 m/s2 with a regular deviation of zero.0317. The values quoted within the concept section show that this measurement is properly outdoors the expected range. The difference between the equator and the poles is just about zero.05, and these values differ from 9.eighty by solely 0.02 to 0.03. The values from the literature account for centrifugal drive, but not altitude. A quick calculation would show that this is additionally negligible. If we recalculate the value of g from the speculation section by including 10 km to the Earth’s radius, we acquire a price that differs by only 0.03. The calculation of g from our measurements may be very sensitive to time since it is squared in the calculation. We can recalculate g using the gap from run 1 to see the means it may affect the reply. If we differ the time for 1 / 4 oscillation of the pendulum by simply zero.03 s, we obtain

Time, s (at h=1.609 m)
Calculated g, m/s2
zero.572
9.84
zero.575
9.73
0.578
9.63

A difference of 0.003 s would correspond to a distinction of zero.003 ×4×5=0.06 seconds within the measurement of 5 oscillations. The measurement of time clearly deserves more attention in future experiments. Human response time is already a couple of tenths of a second. Future experimental designs ought to search to measure the time more precisely. More oscillations would make this measurement more correct, but damping may become as issue. This means that an electronic technique must be used. A good future experiment could be to measure the altitude variation of g, however this is ready to require better accuracy than the current experiment.

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