You are in charge of an interstellar spacecraft that is investigating the planets around a faraway star system. Currently, your spacecraft is located in the region of space between two of these planets, Ursula and Triton, where the net gravitational force on the spacecraft is equal to zero. You have measured that the distance between your spacecraft and the center of Ursula, \(d_u\text{,}\) is greater than the distance between your spacecraft and the center of Triton, \(d_t\text{.}\) You want to know whether the mass of Ursula is greater than, less than, or equal to the mass of Triton.
Which of the following equations do you think will be useful or applicable in approaching this situation? For each equation, identify the corresponding physical model.
Write an explanation allowing you to defend whether \(m_u\) is greater than, less than, or equal to\(m_t\text{,}\) starting from one or more of the physical models you previously identified as being useful or applicable to this situation.
Watch the video below, then review your answers to the questions above and reflect on how your thinking has changed over the course of this activity. Generalize your thinking to identify (1) what is important to include in a scientific explanation and (2) what is unnecessary to include, and why.
This activity is intended to help you practice solving problems using the A*R*C*S format introduced in A*R*C*S Steps. This will serve as a touchpoint you can come back to if you need any assistance on working through an A*R*C*S activity. You will work through each section of the A*R*C*S format, watch a video, and reflect on your work. The videos are a little bit long, but there is a lot to explain in an A*R*C*S activity!
Shown below are two blocks connected by an ideal string that passes over a massless, frictionless pulley. The mass of the larger block sits on a flat, frictionless table, and has a larger mass than the smaller block, which hangs vertically. Determine the speed of each block when the larger block reaches the edge of the table, a distance of 0.75 m.
Make a list of the important concepts, laws, or ideas that you will use to solve the problem. (Hint: You have probably seen more than one way to approach a situation like this one. This is a good place to consider the advantages and disadvantages of each approach.)
There are many ways to solve this problem. Can you think of a way to perform this calculation that is different from the one in the video? Do you think that way would be easier or harder? What parts of the calculate portion did you find most difficult?
Convert your final numerical answer into a unit that is more familar to you (miles per hour, kilometers per hour, etc.). What else travels this fast? You may need to search to help you answer this question. Is this a reasonable speed for a falling block?
Consider the situation where mass 2 falls on it’s own, under the force of gravity. What is the velocity of mass 2 after it falls a distance of 0.75 m? How does this compare with your numerical answer found above? Does this make sense? Why or why not?
