How to do Vector Addition to get Net Force

One basic skill we use over and over in physics and engineering is adding vectors to find the total, or resultant or net, vector.  Vectors are those quantities with BOTH magnitude and DIRECTION, such as forces.  Obviously, gravity has a direction of 'down' and is therefore a vector.

The easiest problem is when there are two vectors on the same line, called colinear vectors.  These we just add, if in the same direction, or subtract, if in opposite directions.  The trickier problems are when forces are pulling in multiple dimensions.  This is where the rules for right triangles are needed.  We can use sine, cosine, and tangent to figure out how much of each individual force is in the x and y directions.  We can also use these functions to determine the direction of the net force, and therefore the direction the object will actually start moving.  Remember Chief SOH-CAH-TOA for the definitions of these trig functions!

Check out this example with three force vectors.  Keep in mind to use a table of x and y components in all your problems to keep things organized - it will help.

Great Example of Computational Thinking/Modeling for an Everyday Physics Problem

Check out how mathematical modeling is applied to solving the motion of a rotating fan blade slowing down. It outlines the thought process and methods used to solve this commonly observed event.  Check it out! 

Femto-Photography is Here - 1 Trillion frames per second!

Modern technology has revolutionized many facets of life, but as much as any area, photography has gone bananas with high-speed photos and films.  As long ago as the 1960s, scientists and engineers figured out how to take pictures at one million frames per second.  Now, fifty years later, there is a camera that is one million times faster than that!   Yes, one trillion frames per second.  Check out this TED talk to see what it can do, where is actually follows a pulse of light itself...you can see a light pulse move.  I find this unbelievable, and truly fascinating.  Our ability to view Nature at this level has opened our eyes to details of all sorts of phenomena we could not dream of just a few years ago.

Big Day in Particle Physics - The HIGGS!!

The Higgs is here! After decades of looking for the bugger, confirming experimental results from Fermilab and CERN show that the Higgs boson is a real particle, which satisfies the prediction from the Standard Model.  It is also cool to see comments from two old friends from my Fermilab days, Rob Roser and Tom LeCompte, in this article.  Here is another article, and also an interview on CNBC below.  There are also a couple former students from Chem-Phys out at CERN (shout-out to Edmund and Dan!), who have helped keep me in the loop the past couple years.  Congrats to everyone involved!!

Visit msnbc.com for breaking news, world news, and news about the economy

High-speed Camera Fun

I just wanted to share this video of two guys (the Slo Mo Guys) buzzing their lips, simply because I find it hilarious!  Enjoy.

Einstein Still On Top - Neutrinos Not Faster Than Light

Just about all physicists, including this one, were skeptical about a year ago when a neutrino experiment in Europe announced it had evidence that neutrinos move a bit faster than light.  The OPERA collaboration is similar to an experiment at Fermilab, where neutrino beams are shot through the Earth to detectors hundreds of miles away.  This experiment published its results and wanted the scientific community to try to figure out if any mistakes were made, knowing that the significance of this result did nothing short of suggesting Einstein's theory of relativity was flawed.

But now, five independent groups have reproduced the experiment and verify neutrinos obey relativity and move slower than light.  A likely problem with the OPERA experiment is in its fiber optic timing system.

This is a wonderful example of how science is supposed to work.  Results are published, and other scientists need to be skeptical and open-minded about the results.  Repetition and reproducibility lie at the heart of the process of science, where ideally independent groups repeat experiments to confirm results.  Science works through observation and experimentation, where physical evidence rules the day.  So the foundational theories of physics, relativity and quantum mechanics, still come through in the heat of tests.

CONGRATULATIONS TO THE CLASS OF 2012!

The Class of 2012 is now done, and my heartfelt congratulations to all of you! This is a tremendous group of young women and men who are set to take on the top colleges in the country, and make their mark on the world! I am truly proud to have worked with each and every one of these students.

If you want a 3-D simulation that will allow you to view electric fields for a wide variety of charged systems, check out this Falstad simulation site. It is really a useful visual display!

Charged Particles in B-fields

Here's a case of charged particle flying through magnetic fields, and what happens to those particles. We know that fundamentally magnetism is formed by moving charges. So the moving charged particle has its own magnetic field. This field interacts with any external magnetic field, thus creating a magnetic force. We know this goes as F = qv x B. It is a cross product. But this then means the force is perpendicular to the motion of the particle. The consequence of this condition is circular motion, or mv^2/R = qvB. This video will show ActivPhysics simulations to get a sense of the 3-D nature of this motion. If the particle comes in 90-degrees to the magnetic field, we get a circular orbit. If the particle comes in at any angle other than 90-degrees or 0-degrees (parallel) to the field, then there is a component of motion perpendicular to the field (circular motion), as well as a component parallel to the field, which means no force and it keeps moving in that direction. A spiral/helix/corkscrew results! I also show a simulation of a mass spectrometer, where we use the circular motion to measure the mass of particles or ions. Check it out.

Check out Rotating Pulleys

Check out how to find the TWO tensions in the same rope for a real, spinning pulley problem. The video is here. Also, check out small oscillations (like a pendulum) here, or a more complicated one here.