Vector problems from physics 6a Spring 2018.

Understanding vectors will be important in physics 6c. Here is the solution to one vector problem; I think this is from one of the first homework sets. I believe there is also a video solution to this problem linked in an earlier post on this blog. (link also added below in this post)

You may go through the earlier posts on this blog from last Spring, if you like, and find solutions to other vector problems we did (for example, in the post "Homework 3. due Friday" from April 16). Feel free to share your knowledge, insights and questions with other students by posting here about what you find.

Below the break there are some video solutions to vector problem from 6a.

practice problem notes

For 1a. The friction force is 20 N** and is opposing the motion. So the net force in the first time frame is 35-20=15 N.  Ultimately, via our kinematic equations, that leads to v= 6 m/s at t=2 s...
Also, one can use the area under the velocity curved to obtain the distance travelled. (That is, the position of the block.) As an example of this, to find the distance travelled between t=0 and t=2 s, you can use the area under the v(t) curve, which is, A=(6 m/s * 2 s)/2 = 6m. This method becomes particularly useful when the velocity curve gets complicated due to changes in acceleration. It is good to know how to calculate the area of rectangles, triangles (and a triangle on top of a rectangle).

**you don't need to know about mu for our exam tomorrow. You will be given friction forces in newtons.

Final notes and equation sheet.

Here is the equation sheet for the final exam. Please let me know if you find any mistakes. Thanks.

Notes. 

Oscillations: Being able to visualize the cosine equation and to think about the effect of the phase constant on the cosine function is an important part of understanding oscillations. The nature of a particular oscillation depends on information you will be given or that you can infer. Generally that information involves position and velocity at particular times. Frequency, period, m and k can also be relevant.

Collisions: Collisions occur very quickly and nothing matters in a collision except how the velocity and momentum of each block is instantaneously changed! Total momentum is conserved. That is, it has to be the same before and after. The time scale of a collision is much shorter than any oscillator-related time scale.  Basically during a collision, nothing moves, because delta t is so short, and the velocity is the only thing to change.

Gravity involves force,  potential energy, g, circular orbits. You will be given equations such as a=v^2/r, U=-GMm/r, F=GMm/r^2.  You will want to really understand those equations and how to use them, as well as the definition of little g. Don't get the equations for U and F mixed up! The negative sign in the equation for the potential energy is important!

In problems where something moves on a horizontal surface, the force is a key place to start.  a=F/m. Use intuition, visualization and math together to keep things continuous at time boundaries where the net force changes. Friction forces always oppose motion and disappears when the motion stops.

Final Instructions

If you last name begins with A-L, you take your exam in our regular room, E&M B206.

If you last name begins with M-Z, then you take your exam in Humanities 206.
(the large Humanities Lecture Hall.)

Please bring blank paper to do your work on and hand in (with your name on it).

Calculators are allowed; phones are not allowed (please turn phones off).

Midterm 1 & 2 solutions

I am not top posting these for any special reason. It is just that a student mentioned that they couldn't find them, and then neither could I, so I am (re)posting them now.

Practice problems

Practice problems.

For 1a, the friction force is -20 Newtons. Treat that as given and don't worry about mu.
The push force is 35 N. So the net force is 15 N.
After 4 seconds the pushing stops and the only force is the -20 N friction force. Does that help?

ClassNotesJune6

Notes are here.

Midterm2 solutions

Midterm 2 solutions:

Final Review Section: Next Monday 3:00 - 5:30 PM in ISB 235

Hello Physics Friends,

Finals preparation is upon us! Though I'm sure you're already studiously reviewing notes and pondering the universe, here's a reminder to
a) Study early and often to increase your efficiency and reduce the burnout of cramming!
b) Take some time for your self and remember that you're still a human being. Skipping sleep and meals feel necessary sometimes, but can hurt both your health and grades.
c) Attend the final review section if possible!

Essential details about the section:

• LOCATION: ISB 231/235 (rooms will be joined)
• DATE: Monday, June 11
• TIME: 3:00 - 5:30 PM
• BAGELS: FREE

If you have any questions beforehand, feel free to comment below, email me, or attend regularly scheduled section. Thank you for all the fantastic energy you've put into this class! Summer's only a few exams away 😎.

Happy learning,
Michael

P.S. -- As discussed previously, come to section to pick up your exams if you have not done so already.

Homework 9. Due Wednesday, June 6.

This homework is a pretty long one and involves at least 3 different sorts of problems, so I thinking it could be best not to try to do them all at once?
1. One type involves calculations of little g, the acceleration near the surface of a planet, using G and M, the mass of the planet. (Also R)
2. Another type involves orbital motion and the relationship between the acceleration need to maintain a circular orbit and the force of gravity (e.g., exerted by the sun on an orbiting planet).  (see video below)
3. A third type of problem involves gravitational force vectors, and how to calculate components and add them. (see other video below).
4. Problem 13.73 involves negative gravitational potential energy (-GMm/r). When the comet is closer to the sun, its potential energy is lower and it will speed up as it gets closer to keep the total energy of the comet-Sun system unchanged. (Don't accidentally use -GMm/r^2 by mistake like i did the first time.) Roughly, U=-5... at the far location, and U= -25... at the close-to-the-sun location, so the KE must increase by +20... in order to keep the total energy constant. Does that make sense?
Problem 13.17 also involves gravitational potential energy. Weirdly, the potential energy of the rocket-earth system is highest when the rocket is very far away from the earth (at which point, its value is basically zero!) Zero potential energy, however, is higher than the large negative potential energy that the system has when the rocket is closer to the earth.
Solutions follow:

Video on orbital motion

Consider a planet in a circular orbit around the sun. There is a particular amount of force needed to maintain the needed curvature for that orbit. This video examines how one can understand and use a particular relationship between orbital radius, speed and acceleration that is valid for circular orbits.
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Video on calculating gravity force vector components.

Here is a video on calculating gravity force vector components.  Note that whether you use sin or cos for the x-component depends on context and geometry.
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