I completely agree. There is a movement to dumb down the schools (K-16) so that no one feels stupid and failing is not possible. I teach physics and engineering courses at the college level and the standard abilities in math and physics coming out of high schools is downright poor! One of your statements really rings true: The new method is just to teach the basic idea. I good example of this that I have observed many times is the skill to perform the algebraic operations to solve several equations and several unknowns. When I ask did they cover this in their [College] Algebra course the answer is usually 'yes', sometimes 'I think so.' After asking enough questions and observing skills I conclude that in fact this topic and many others are not being stressed. Students need lots of practice to master these skills...but somehow that is not happening. I can't always blame the instructors of these classes... just like me they have to work with what they get. And no offense to anyone here, but in general students produced by public high schools in the U.S. have been pampered way too much.
That the shape of a cantilever beam changes the angle of twist (the number of degrees that the end twists through) of the beam due to an applied torque is a well known mechanical/civil engineering fact. Basically a beams angle of twist (all else being equal) is inversely proportional to something called the polar moment of interia, which is just the distance of each differential piece of the beam shape from some central point squared and added up for all differential pieces. For the same order of magnitude size of a V shape versus say a flat shape there is no question in my mind that the V shape would twist more under the same torque. In this case the torque could be provided by the force differing in direction or magnitude on each side of the cantilever.
I have no experience working with AFM so I do not know whether the torsion is significant enough to change measurements.
So there... it definitely does not need to be verified experimentally since this fact is well known amongst engineers. Just consult any sophomore level text on mechanics of materials.
Have not seen the show, but...
I just looked at the bios (pun intended) of the mostly biologists that make up the cast. It's no real surprise that they are either rabid environmentalists or mostly biologists. These fashionable scientists make a young and photogenic crew with neat CVs that sound cool to many folks that watch PBS. Surely there are more qualified candidates... since usually engineers solve applied science problems... and engineers usually have backgrounds in physics, which only two of the seven appear to have, and normally physics (and it's application in mechanical engineering) is pretty important in solving the types of problems one would encounter if stranded in the middle of nowhere... you know like building shelter, water transport, and using mechanical advantage whenever possible. Don't get me wrong, I recognize that often mechanical engineers (in particular academics) are not always great at solving practical problems, but come on PBS!!!
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I completely agree. There is a movement to dumb down the schools (K-16) so that no one feels stupid and failing is not possible. I teach physics and engineering courses at the college level and the standard abilities in math and physics coming out of high schools is downright poor! One of your statements really rings true: The new method is just to teach the basic idea. I good example of this that I have observed many times is the skill to perform the algebraic operations to solve several equations and several unknowns. When I ask did they cover this in their [College] Algebra course the answer is usually 'yes', sometimes 'I think so.' After asking enough questions and observing skills I conclude that in fact this topic and many others are not being stressed. Students need lots of practice to master these skills...but somehow that is not happening. I can't always blame the instructors of these classes... just like me they have to work with what they get. And no offense to anyone here, but in general students produced by public high schools in the U.S. have been pampered way too much.
That the shape of a cantilever beam changes the angle of twist (the number of degrees that the end twists through) of the beam due to an applied torque is a well known mechanical/civil engineering fact. Basically a beams angle of twist (all else being equal) is inversely proportional to something called the polar moment of interia, which is just the distance of each differential piece of the beam shape from some central point squared and added up for all differential pieces. For the same order of magnitude size of a V shape versus say a flat shape there is no question in my mind that the V shape would twist more under the same torque. In this case the torque could be provided by the force differing in direction or magnitude on each side of the cantilever.
I have no experience working with AFM so I do not know whether the torsion is significant enough to change measurements.
So there... it definitely does not need to be verified experimentally since this fact is well known amongst engineers. Just consult any sophomore level text on mechanics of materials.
Have not seen the show, but... I just looked at the bios (pun intended) of the mostly biologists that make up the cast. It's no real surprise that they are either rabid environmentalists or mostly biologists. These fashionable scientists make a young and photogenic crew with neat CVs that sound cool to many folks that watch PBS. Surely there are more qualified candidates... since usually engineers solve applied science problems... and engineers usually have backgrounds in physics, which only two of the seven appear to have, and normally physics (and it's application in mechanical engineering) is pretty important in solving the types of problems one would encounter if stranded in the middle of nowhere... you know like building shelter, water transport, and using mechanical advantage whenever possible. Don't get me wrong, I recognize that often mechanical engineers (in particular academics) are not always great at solving practical problems, but come on PBS!!!
And I quote from my University Physics text:
The weight of a body is a force, a vector quantity, and we can write as a vector equation:
weight(vector)= mass x gravtity (vector)
Note that gravity is your local value of acceleration due to gravity (which for most of us does not vary too much from 9.81 m/s^2).