Physics lab report 2 - measuring the acceleration of gravity PDF

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measuring the acceleration of gravity ...

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Lab #2: Measuring the Acceleration of Gravity Anna Hofbauer, Misheel Dolguun, Dr. Schuler Introduction The purpose of this experiment was to use a timer, photogate sensor, and picket fence to determine the velocity and acceleration of the motion of the picket fence, as well as to gain a better understanding of kinematics and projectile motion. Kinematics is defined as the study of motion of objects, and projectile motion is the motion of a falling object under the acceleration of gravity. The strength of the gravitational field near Earth’s center places a constant acceleration of 9.8 m/s2 on an object in free-fall. The timer used was a precise computer timer. The photogate sensor functions by transmitting a beam of infrared light to a detector across the gap and detects when the beam is blocked by an object. A ladder shaped object named as a “picket fence” was dropped through the photogate sensor. The picket fence is made of clear plastic and is constructed with rings of evenly spaced black bars. When the picket fence passed through the photograte, the computer software program measured the time between the 8 black bars blocking the beam. The known distance between the bars is 5 cm. Data Analysis Trial No.

1

2

3

4

5

6

Slope (9.8 m/s2)

4.49

9.65

11.4

9.85

45.6

15.56

Position vs Time Graph

The shape of the position vs time graph is a line curving upwards until it reaches 1.90 s, where it then becomes a linear line ending at 2.54 s. This shape indicates that the velocity is speeding up to the right of the graph. Velocity vs Time Graph

The shape of the velocity vs time graph is a linear line, where it increases in its slope from 1.872 s to 1.892 s. This shape indicates that the acceleration is constant. The shape of the position and time graph curving upwards, and the shape of the velocity and time graph as a linear line with a positive slope, correspond to show an increase in both acceleration and velocity of the picket fence per second. The minimum acceleration of the picket fence was 4.49 m/s2. The maximum was 45.6 2 m/s . The average acceleration was 16.09 m/s. Aave=(4.49 + 9.65 +11.4 + 9.85 +45.6 +15.56)/6 = 16.09 m/s 𝜎=

= 13.59 m/s The final experimental result is that the average acceleration of the picket fence is 16.09 ± 13.59 m/s. % uncertainty = (13.59/16.09) x 100% = 84.46% The precision percentage of the experiment is 84.46%, indicating that it was not precise. It had a high amount of variation between values of acceleration of the picket fence. The generally accepted value of g is 9.8 m/s. This falls in the range of 16.09 ± 13.59 m/s found here. Additional Data Analysis The air resistance in this experiment was small because the plastic picket fence was thin, but if a large air resistance had acted on the picket fence then the force of gravity would have to be that much stronger. Thus, the acceleration of the picket fence would increase with increased air resistance, and it would take more time to pass through the sensor. The larger air resistance would alter the position and time graph by stretching it out, and it would change the velocity and time graph by having a steeper gradient.

The position and time graph for an object with non-uniform acceleration would still be curved upwards, and it would have a varying gradient.The velocity and time graph would be curved upwards, instead of linear, and would have a varying gradient. The acceleration and time graph would be linear.

Our data reflects a constant acceleration, the position and time graph is curved upwards but the velocity and time graph is linear, not curved like shown in the changing acceleration velocity and time graph.

Lab #2: Motion in One Dimension Introduction The purpose of this portion of the experiment was to utilize an ultrasonic motion detector to measure the changing position of a ball thrown straight up, and determine the velocity and acceleration of the ball in free-fall. The ultrasonic motion detector functions by emitting a sound wave that reflects off an object in motion, and as this wave is reflected back, the sensor records the time between when the emitted and reflected waves are detected. This information is then used to determine the position of the falling object. From this position data, the computer data collection program was used to determine the velocity and acceleration.

Data Analysis Position vs. Time Graph

The ball was being tossed but still touching the hands from 7.950s - 8.200 s. The ball was rising from the moment it left the hands to its highest position: (8.555s, 0.99m). The ball was falling after it reached its peak at 8.555 s until it hit the table. The entirety of the ball’s fall was free fall. Velocity vs. Time Graph

The ball had its maximum velocity at 8.2 seconds as it was leaving the hands and being tossed upwards at 3.21 m/s. Maximum Height of the Ball During Free Fall

On the position vs. time graph, the maximum height of the ball during free fall was 0.99m at 8.600s. The exact midpoint is not represented but at (8.550s, 0.99m) the slope is 0.25 m/s and at (8.600s, 0.99m) the slope is -0.25 m/s so it’s reasonable to assume that at 8.555 s, the exact midpoint, that the slope is zero. In this context that means the velocity of the ball is zero when it reaches its maximum height. The acceleration of the ball at this point is -9.41 m/s^2. Fitting a Curve to the Position vs. Time Graph

The motion of an object in free fall is modeled by y=y0+v0t + (½)at2. The coefficient of this curve is very similar to (½)g, -4.56 and -4.9 respectively. Fitting a Line to the Velocity vs. Time Graph

The graph of velocity vs. time should be linear and modeled by v=v0+at. The value of m is very similar to the accepted value for g, with m equaling -10.4 and g equaling -9.8. Fitting a Line to the Acceleration vs. Time Graph

The graph of acceleration vs. time should appear to be more or less constant. For this data set it doesn’t appear to be constant and has a mean value of -11.26 which isn’t very similar to g.

However, if the data range is shortened a small constant area can be seen with a mean of -9.4 which is much closer to g. This short data range is most likely the result of an error where the motion sensor didn’t completely pick up on the last few seconds of the ball’s trajectory accurately. The direction of the velocity vector does have an impact on the acceleration of the object. If it’s working in the same direction or in opposition, it can increase and decrease the acceleration. Additional Analysis The effect of different coefficients on the shape of the position vs. time plot is the size of

the parabola. The shape will remain the same but the peak will have a different location. This applies to if the object was thrown with a different initial velocity or acceleration, an example is shown below.

In this trial the initial velocity was 0.86 m/s instead of 0.92 m/s and the shape remains a parabola with a different maximum height. Conclusion Both experiments in this lab followed the kinematics of projectile motion, of a picket fence in the first experiment, and a ball in the second. For the first experiment, analyzing the shapes of the position vs time and the velocity vs time, tells us the trend of velocity and acceleration of the picket fence. The curved shape of the position vs time graph, and the linear shape of the velocity vs time graph indicate that the acceleration of the picket fence was constant. Comparing these graphs to the expected shapes of an object with non-uniform acceleration confirms that the picket fence’s acceleration was constant. For the second experiment, analyzing the ball’s position, velocity, and acceleration shows the relationship between an object in free fall and gravity. It was clear that at the object’s highest point its velocity was 0m/s as it changed direction from moving upward to falling down. In each graph a line was fitted to the data: the position vs time graph was a parabola, the velocity vs time graph was linear, and the acceleration vs time graph was constant for the most part. Each equation had values that corresponded with some value of g, gravity and this is what we expected to see of an object in free fall....