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g During the semester, you have performed four experiments that either determined the acceleration due to gravity or whose results could have been used to determine it: The sphere drop, the inclined air-track and glider, the pendulum, and now standing waves on a string. Compare these four methods and make a case for which one is optimal if you conclude there is such a one.

Respuesta :

Comparing the different methods for measuring the gravity acceleration, we can conclude that the method that gives less errors is:

  • Simple pendulum measurement.

The gravity acceleration is the outside attraction of the planet on all the bodies that are in it, this gives a preferential direction of movement, the bodies fall towards the surface of the Earth. Determining the value of the gravity acceleration is very important to understand the motion of bodies.

Let's analyze the proposed methods with their benefits and problems, in all cases we will assume that friction losses are negligible.

Method 1. Drop a sphere.

In this method we use conservation of energy and find that the velocity of the body is:

           v² = 2 g h

           [tex]g = \frac{v^2}{2h}[/tex]  

For this measurement of the gravity acceleration, the average velocity is taken from the expression

          v = [tex]\frac{\Delta x}{\Delta t}[/tex]

Therefore, to achieve better precision, we must have small distance intervals, so that the average speed is close to the final speed. The measurement times are very short that they are difficult to measure, therefore the method does not give very accurate results.

Method 2. slide glider down a ramp

Using conservation of energy.

          v = g sin θ t

This method is a bit more precise since as the angle of the ramp decreases, the average speed of the car is closer to the final speed and the time measurements are not short.  This method it gives better result than method 1.

Method 3. Movement of a simple pendulum.

We use the expressions of simple harmonic motion.

           T = [tex]2\pi \ \frac{L}{g} \\g = 4\pi ^2 \ \frac{L}{t^2}[/tex]  

This method must measure the length before the start of the movement and measure the time, which can be long, measuring several oscillations and making an average, this process is more precise since when measuring several oscillations the error in time decreases and the parameter obtained gravity acceleration is more accurate.

You can also measure time for various lengths, plot T² vs L, and calculate the gravity acceleration form the slope.

This is the best method since graphical analysis allows statistical meting to reduce errors.

Method 4. Standing waves in a string.

In this case the length of the waves is;

               [tex]\lambda = \frac{2L}{n} \\v= \sqrt{\frac{T}{\mu } }[/tex]

This method has no dependence on the gravity acceleration and cannot be used to perform its calculation.

Consequently, comparing the different methods for measuring the gravity acceleration, we can conclude that the method that gives less errors is:

  • Simple pendulum measurement.

Learn more here:  brainly.com/question/24159297

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