Car Velocity Lab

 Conclusions:

How do the predicted velocity and the measured velocity compare in each case?  Did your measurements agree with your initial prediction?  If not, why?  

We used the equation above to determine our predicted initial velocity. The predicted velocity and measured velocity were very similar in comparison. As always, there is uncertainty when using Video Analysis to measure data. The measurements we calculated did agree with our initial predictions within uncertainty. I believe the variation in our data came from the fact that the model we used to make our predictions was "ideal", meaning we did not account for the friction of the system (only the two masses and distance) or the effective mass of the pulley.

Does the launch velocity of the car depend on its mass?  The mass of the block?  The distance the block falls?  Is there a choice of distance and block mass for which the mass of the car does not make much difference to its launch velocity?

The launch velocity depends on: the hanging mass, the mass of the car, and the distance the hanging mass falls before reaching the ground. The mass of the hanging object affects the initial acceleration by the amount of tension it creates. The larger the mass of the hanging object, the more tension in the system, and thus a larger magnitude of initial velocity. The distance the hanging mass falls also affects the initial velocity. If the distance is smaller then the tension being applied only lasts a short amount of time; whereas if the distance (between the ground and the object) is large, then the force applied by the hanging mass will last a longer amount of time. Finally, the mass of the car is also a factor in initial velocity, because if the mass of the car is large, then it will take a considerable amount of force to move the car initially. With a large enough hanging mass at a high enough distance, the mass of the cart would be negligible.

If the same mass block falls through the same distance, but you change the mass of the cart, does the force that the string exerts on the cart change?  In other words, is the force of the string on object A always equal to the weight of object A?  Is it ever equal to the weight of object A?  Explain your reasoning. 

The tension force of the string is not always equal to the weight of the object. In a static system (when the acceleration is 0), the tension force will be equal to the weight. However, in a dynamic system the tension must also account for the objects acceleration and mass.

Was the frictional force the same whether or not the string exerted a force on it?  Does this agree with your initial prediction?  If not, why?

No, the frictional force varies based on the system. The frictional force that the car experiences while the hanging mass is still falling is less than the frictional force the car experiences when the hanging mass reaches the ground. This is because at the point where the hanging mass is still falling, the system has the force of hanging mass (creating the tension that acts on the cart) and kinetic energy of the cart to oppose friction. Once the mass is no longer acting on the system, the friction is only opposing the kinetic energy of the cart, and eventually slows it down. So, we can say that the magnitude of frictional force is changing throughout the duration of motion. This does not agree with our prediction of friction being a constant force.

Hanging Bridge Lab

 

Hanging Bridge Lab

Post Lab Write Up:

1. The graphs should match early on when the weight of the masses is less, but as you increase the masses the graphs start to diverge.
2. The limitations that my group observed were the lack of precise tools. For example taking measurements with a meter stick and "eyeballing" measurements. Our system is also not ideal, meaning that things like the string, the pulley, and how we arrange the masses must be taken into account.
3. The vertical displacement increases as the mass of the center object increases. However, the model created is really only useful for smaller masses (because the curves diverge the more mass you add).
4. My groups predictions somewhat agreed with the results of the lab. As you add more mass to object B the displacement becomes larger. The predicted equation for the model assumes ideal string and pulley, which we know not to be true.
5. No, the pulley doesn't behave in a frictionless way throughout the experiment. The less mass there is the closer the curves match, which means the pulley can be neglected (considered frictionless). However, this does not hold true as you begin to add more mass to object B. Therefore, the pulley can't always be considered frictionless. We also know that string itself is light and shouldn't interfere with experiment. As explained in class, a heavy string is more unpredictable compared to a light string.
6. The information needed would be: length of the walkway, mass of the walkway, mass of object on the walkway, density of rope (cable), effective mass of the pulleys, hanging mass on either side of the walkways.

Project 1 - Projectile Motion Modeling

Individual Contributions:

    For the first part of this project, I modeled projectile motion using Video Analysis and then calculated the uncertainty of the range and initial velocity. Then I found the average spring constant with uncertainty by using multiple masses to stretch the rubber band.  I used the average spring constant to calculate the initial velocity using a Work-Energy equation. Next, I found the max height of the rocket launched at a 90 degree angle by doing 2 trials. I used these measurements to find the initial velocity using a different Work-Energy equation. I combined all of these values into one table that showed each initial velocity using a certain stretch. I made graphs of both of these initial velocities vs. stretch. I then helped to start writing the basic code of the projectile motion. As we progressed, I calculated the value for "C" (using the spring Work-Energy equation) to accurately compute the initial velocity in the code. After the code was finished, I helped to start and finish the project slides. Overall I believe all of my group mates did equal and accurate work to complete our project. 

Project 1 Slides

Contributions to Project 1

    For the first part of this project, I modeled projectile motion using Video Analysis and then calculated the uncertainty of the range and initial velocity. Then I found the average spring constant with uncertainty by using multiple masses to stretch the rubber band.  I used the average spring constant to calculate the initial velocity using a Work-Energy equation. Next, I found the max height of the rocket launched at a 90 degree angle by doing 2 trials. I used these measurements to find the initial velocity using a different Work-Energy equation. I combined all of these values into one table that showed each initial velocity using a certain stretch. I made graphs of both of these initial velocities vs. stretch. I then helped to start writing the basic code of the projectile motion. As we progressed, I calculated the value for "C" (using the spring Work-Energy equation) to accurately compute the initial velocity in the code. After the code was finished, I helped to start and finish the project slides. Overall I believe all of my group mates did equal and accurate work to complete our project. 

Motion Detector & Video Analysis Lab

 1. Measuring acceleration due to gravity using a motion detector.

        a) My group used the motion detector to measure the acceleration due to gravity of a falling ball.

        b) We did this by using the motion detector to track the balls motion and use that motion to plot two graphs: a velocity vs time graph and a position vs time graph. Then, we zoomed into the portion of graph that we wanted to analyze, and then applied a curve fit. Next, we obtained the equations of each curve to find the acceleration due to gravity using both curves. We found acceleration by taking the second derivative of the position function with respect to time and the first derivative of the velocity function with respect to time.

        c) We found the acceleration using the position vs time graph to be -9.644 m/s^2.

             We found the acceleration using the velocity vs time graph to be -9.568 m/s^2.

        d) The standard deviation is 0.127 m/s^2.

2. Measurement of acceleration due to gravity using video analysis.

        a) I used vernier to track the motion of a ball and measure the acceleration due to gravity.

        b) I took a video of myself dropping a ball and used Vernier's motion tracking to plot two graphs: a position vs. time graph and a velocity vs. time graph. Again, I zoomed into the portions of the graphs that I wanted to analyze, applied a curve fit, and then obtained each of the curve's respective equations. Using the equations, I found acceleration from second derivative of the position function with respect to time and the first derivative of the velocity function with respect to time.

        c) I found the acceleration using the position vs. time graph to be -10.036 m/s^2.

            I found the acceleration using the velocity vs. time graph to be -9.443 m/s^2.

        d) The standard deviation is 0.275 m/s^2.

3. Write-up on measurement variability.

        a) The percent difference that I calculated between the measurements of both experiments using                 the velocity vs. time graphs is 1.32%.

        b) Yes, both of my measurements agree with the uncertainty determined by standard deviation.

        c) The measurements that have uncertainty when using the motion detector are: change in position from external interference (such as the table or something/someone being in the way), and all of the measurements (including time, position, and velocity) stemming from human error in the setup or capture of data.

        d) The measurements that have uncertainty when using the video analysis could be: time due to the frame rate, the change in position due to a bad scale of reference, and most importantly both the velocity and position from inaccurately plotting the points on the ball.

        e) The estimated uncertainty for each of the measurements in the first and second experiments is:

                Motion Detector - +/- 0.05m  (height)  &  +/- 0.2s (time)

                Video Analysis -  +/- 0.1m (height)  &  +/- 0.3s (time)

        f) The uncertainty propagation that I calculated is:

                Motion Detector - +/- 0.052

                Video Analysis -  +/- 0.112

        g) The measurements do seem to agree with my estimated uncertainty.

        h) I believe the data taken from the motion detector experiment is way more useful compared to the data taken from video analysis. This is because almost every aspect of video analysis (plotting points on the ball, scale for reference, etc.) seems much more inaccurate in my opinion.