If You Have Done the Previous Laboratory Extension, Motion Down an Incline with an Initial

You have designed an apparatus to measure air quality in your city. To quickly force air through the apparatus, you will launch it straight downward from the top of a tall building. A very large acceleration may destroy sensitive components in the device; the launch system’s design ensures that the apparatus is protected during its launch. You wonder what the acceleration of the apparatus will be once it exits the launcher. Does the object’s acceleration after it has left the launcher depend on its velocity when it leaves the launcher? What effect does the initial velocity have on the apparatus? You decide to model the situation by throwing balls straight down.

If you have done the previous Laboratory Extension, Motion Down an Incline with an Initial Velocity, you can reviewthe answers for questions 1-4 below. Questions 5-7 address the effect of initial velocity on constant acceleration motion.

Often, physicists will use well-understood situations to provide reasonable evidence for an extension of the system. In fact, most experiments in science are designed as an extension of the most current understanding of how the universe works.

Instead of repeating the experiment to answer this question, you will work with your group to use the previous problem to predict the initial velocity’s effect on acceleration.

Extension Questions

One helpful place to start is with limiting cases. For this problem, we will think about what is expected when the initial velocity is either very small or very large.

Acceleration with an initial velocity:

1. If you were to re-analyze the video from the earlier Mass and the Acceleration of a Falling Ball, but you started taking data points 2 frames into the ball’s motion, what would you expect the instantaneous velocity vs. time graph to look like? What is the relationship between velocity and time that would fit the function? Write this in your journal.
2. Now imagine that you dropped the ball from 50 meters and you had a video of the entire motion. If you started analyzing the data after the ball had fallen 45 meters, what would you expect the instantaneous velocity vs. time graph to look like? What is the relationship that would fit this function? What is different about the small initial velocity graph and the large initial velocity graph? What is similar about the two?
3. From your two limiting cases, do you have a sufficient answer to the prediction? As a check, think about one more case to confirm that it reasonably fits your answer. If you were to analyze the video that you made in Mass and the Acceleration of a Falling Ball, but you advanced the video to the last frames of the motion and then took data, would you expect a constant acceleration or something else?
4. Is this sufficient for predicting the behavior of the ball under different circumstances? Do you need to run the experiment in order to be sure of your prediction? Why or why not?

Effect of initial velocity in constant acceleration motion:

1. Open PracticeFitlocated in PhysLab folder on the desktop. What is the instantaneous velocity vs. time relationship with constant acceleration? What is the instantaneous position vs. time relationship with constant acceleration? Function 1 is a simple linear relationship with only integers for the coefficients. Fit the function that is given and then decide with your group how to have the same acceleration but change the initial velocity. You are comparing zero and non-zero initial velocities. You can do this no matter what the mystery fit function is. Discuss with your group how to accomplish this.
2. For the instantaneous velocity vs. time graph, what is the difference between the zero and non-zero initial velocity if the acceleration is the same? What happens to the function if the initial velocity and the acceleration have opposite signs?
3. Function 3 is a simple quadratic function that always has integers as the coefficients, and the linear coefficient is always zero (i.e. B=0). What is the physical significance of this? Fit the function given and then change the initial velocity parameter to have a non-zero initial velocity. Compare the zero and non-zero initial velocity functions. What effect does initial velocity have on the instantaneous position of the projectile? Make the signs of the initial velocity and the acceleration opposite of each other. What effect does that have on the instantaneous position?

Prediction

Sketch a graph of a ball’s acceleration as a function of time after it is launched downward with an initial velocity. Sketch a graph of the ball’s acceleration as a function of time after it is dropped from rest. Compare the two and state how your graph will change if the object's initial velocity increases or decreases.

Do you think that the acceleration increases, decreases, or stays the same as the initial velocity of the object increases? Explain your reasoning.