Question about uncertainties

[DrDanger]

Homework Statement

A glider moves on a level (horizontal) air track. The motion detector records five velocities of the glider: 0.48 m/s, 0.48 m/s, 0.53 m/s, 0.48 m/s, 0.47 m/s. The average velocity, uncertainty in the velocity, and relative uncertainty are

Homework Equations

Avg velocity= V1+V2+V3+V4+V5/2

The Attempt at a Solution

For the average velocity I used the above equation and got 0.488. For the uncertainty in the velocity I did 0.53-0.47/2 to get plus or minus 3, but I'm not sure if that is right. I have no idea on how find the relative uncertainty

 

[DrDanger]

Ok so I just read that relative uncertainty is found by percent uncertainty in velocity/ avg value. Correct? but when I use that my answer is'nt one of my choices. So is there something wrong I did when finding the percent uncertainty in the velocity?

 

[tomcue]

.I would like to provide a more comprehensive explanation and approach to addressing uncertainties in this scenario.

First, let's define uncertainties in the context of science. Uncertainties refer to the potential errors or limitations in our measurements or data. These can arise from various sources such as experimental error, limitations of the equipment used, or even human error. It is important to acknowledge and address uncertainties in our data to ensure the validity and accuracy of our results.

In this scenario, we have five recorded velocities of the glider on a level air track. To calculate the average velocity, the correct equation to use would be the sum of all the velocities divided by the number of velocities, which in this case is 5. Therefore, the average velocity would be (0.48+0.48+0.53+0.48+0.47)/5 = 0.488 m/s.

Next, let's address the uncertainty in the velocity. To determine the uncertainty, we need to consider the precision and accuracy of our measurements. Precision refers to the consistency of our measurements, while accuracy refers to how close our measurements are to the true value. In this case, we have multiple measurements of the same quantity, which suggests a high precision. However, the fact that the velocities are not exactly the same suggests some level of uncertainty in our measurements.

One way to determine the uncertainty in this scenario would be to calculate the standard deviation of the velocities. This would give us a measure of how much the velocities deviate from the average velocity. Using a statistical software or calculator, we can calculate the standard deviation to be approximately 0.027 m/s. This would be our uncertainty in the velocity.

Finally, let's discuss the relative uncertainty. This refers to the uncertainty expressed as a percentage of the measured value. To calculate the relative uncertainty, we divide the uncertainty by the average velocity and multiply by 100. In this case, the relative uncertainty would be (0.027/0.488) x 100 = 5.5%. This means that our measurements have an uncertainty of 5.5% of the average velocity.

In conclusion, uncertainties are an important aspect of scientific measurements and should be considered when analyzing data. In this scenario, we have determined the average velocity, uncertainty in the velocity, and relative uncertainty using the appropriate equations and considerations. It is always important to carefully consider and address uncertainties in our data to ensure the accuracy and validity