Experiment 4 The Competition Between Brownian Motion and Directed Forces 1 The goal of this experiment is to observe random and directed motion at the same time Imagine starting with the setup from lab 3 (where we saw purely random motion) What would you have to change in the setup to introduce directed motion 2 What forces dominate when mostly random motion is observed 3 What forces dominate when mostly vertical directed motion is observed If you graph the log log plot of a power law function y ax n , what would you expect the slope of the log log graph to be proportional to What shape should the log log plot be (linear, exponential, etc ) Suppose you start with the equation y ax 2 where a is a constant If you take the log of both sides of the equation, what does your new equation become (Expand this equation so that it is the sum of logs) Starting with your answer to the previous question, what is the value of your slope if you were to graph this new equation In lab 4, if the slope of your log(R 2 ) vs log(t) graph is equal to 2, you have purely directed motion What does this suggest about the shape of your R 2 vs t graph in this case (Is it linear, exponential, etc ) In lab 4, if the slope of your log(R 2 ) vs log(t) graph is equal to 1, you have purely random motion What does this suggest about the shape of your R 2 vs t graph in this case (Is it linear, exponential, etc )

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Sep 27, 2024

Experiment 4 - The Competition Between Brownian Motion and Directed Forces
1. The goal of this experiment is to observe random and directed motion at the same time.Imagine starting with the setup from lab 3 (where we saw purely random motion).What would you have to change in the setup to introduce directed motion?
2. What forces dominate when mostly random motion is observed?
3. What forces dominate when mostly vertical-directed motion is observed?
If you graph the log-log plot of a power law function y=axⁿ, what would you expect the slope of the log-log graph to be proportional to? What shape should the log-log plot be? (linear, exponential, etc.)
Suppose you start with the equationy=ax² where a is a constant. If you take the log of both sides of the equation, what does your new equation become? (Expand this equation so that it is the sum of logs)
Starting with your answer to the previous question, what is the value of your slope if you were to graph this new equation?
In lab 4, if the slope of your log(R²) vs. log(t) graph is equal to 2, you have purely directed motion. What does this suggest about the shape of your R²vs. t graph in this case? (Is it linear, exponential, etc.)
In lab 4, if the slope of your log(R²) vs. log(t) graph is equal to 1, you have purely random motion. What does this suggest about the shape of your R²vs. t graph in this case? (Is it linear, exponential, etc.)