Conservation of Energy

     Understanding conservation of energy was much easier than I originally thought.  If a person knows the simple rule that initial energy = final energy, then they can pretty much understand any energy problem.  In my example below, an archery business wants to make the best bow and arrow set in the business, but doesn't know what spring constant to use in their bow in order for their arrow to fly at 34 m/s.  The comic explains how to go from a simple equation like initial energy = final energy, to finding a specific variable, for example, the spring constant.

My system (I didn't have enough panels to put in in the pixton):

ATTRIBUTIONS: none (I created all of the characters)

Circular Motion & Gravitation

This is what I learned about circulation motion and gravitation.


circular motion - I have learned that uniform circular motion occurs when an object moves around the circumference of a circle at a constant (doesn't speed up or slow down) speed.  The equation to find the speed of an object in uniform circular motion is v=2πr/T. Even though the variable 'v' is used for the speed, I quickly learned that in this case the 'v' is strictly for determining the SPEED of an object, not the VELOCITY.  An object in uniform circular motion is constantly changing direction, therefore the velocity never stays the same.  The word we were taught to use to describe an object in  (uniform) circular motion is tangential.  The speed is measured in accordance to the vector that is tangential to the circle at that moment in time.


Some general facts and equations we learned about circular motion:
-the period (variable used in equations is 'T') is the time needed to complete on full rotation (or revolution) - and the units is uniformly seconds.  
-the equation for the period 'T' ---> T = 1/f (seconds).


-the frequency (variable used in equations is 'f ') is the number of rotations (or revolutions) per unit in time - the units for frequency are called Hertz (abbreviated Hz).
-the equation for 'f ' ---> f = 1/T (Hertz).


Centripetal acceleration is always found in object moving on a circular path because whenever an object changes direction (which is constantly happening in the case of traveling around the circumference of a circle), acceleration is required.  Centripetal means toward the center, so the acceleration is always pointing towards the center of the circle.  The equation we used to find the centripetal acceleration is Ac=v^2/r.  


Centripetal force, different from centripetal acceleration, is required for any object to move in a circle.  The centripetal force is the actual force that keeps the object being pulled towards the center, keeping it moving in a circle.  Some common examples of forces that can act as centripetal forces are friction, tension, and even gravity.  The equation to find the centripetal force actual comes from Newton's second law, F=ma.  When we substitue the centripetal acceleration, we get Fc=(mv^2)/r.


motion in a vertical circle -  Motion in a vertical circle still has uniform circular motion, but just at a 90 degree (or 270 degree) angle. To solve problems involving motion in a vertical circle, we use the sum of the forces combined with the new formulas concerning circular motion/circular forces.  


universal gravitation - We learned that Newton discovered that a gravitational force, similar to the one between all objects and the earth's surface, exists between any two objects.  Newton stated that the gravitational force varies inversely with the square of the distance between two objects, A.K.A the 'inverse square law'.


The Law of Universal Gravitation says that every object attracts every other object in the universe with a force that varies directly with the product of their masses, and inversely with the square of the distance between the two masses' centers.  The equation for this is Fg=Gm1m2/(r^2).  


I had to pay careful attention to this equation, because there are two different 'g's being used here.  We have first the lowercase g that we are all familiar with, representing the pretty-much-constant acceleration due to gravity on the earth's surface (9.8 m/s^2) - due to the elevation on some areas of the earth's surface - this number can vary because the surface in constantly closer/further away from the sun.  Cavendish determined the value of big 'G' is G=6.67*10^-11 N.m^2/kg^2.


and finally - gravitational acceleration - some objects, such as the earth, we generally know that the gravitational acceleration 9.8 m/s^2.  To find the gravitational acceleration of an object we use the formula mg=GmM/r^2 - the 'm's, or masses, cancel out, so we end up with the simplified equation of g=GM/r^2.  Again, you have to be careful not to confuse the lowercase g with the uppercase G.


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What I have found difficult about this unit  is mainly the conceptual idea regarding how when an object moves in circular motion it is actually being attracted towards the center of the circle.  I understand that a force like friction, tension, or gravity has to be applied to keep the object moving in a circle, but I don't understand how that force (example: friction) is always pointing toward the center of the circle.  In my head, I imagine that the friction force just keeps changing direction according to the tangential motion of the object.  For example, when an object is moving around a circle, the force of friction keeps changing a little bit at a time, in a circular motion - so that the object, in turn, also moves in a circle.  I know that the above statement is wrong, but I don't really understand why/how the friction can point towards the center of the circle.  


Also, I don't really understand what pi is used for/why we use it in our equations regarding circles.


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My problem solving skills have improved GREATLY by studying this unit.  At the beginning of the unit, I was so lost and confused about the concepts of centripetal acceleration/centripetal force, it was just overwhelming.  I think it was because all of the concepts we had previously studied I had somehow previously picked up information about/known a little about the unit coming into it.  Starting this unit, I had a blank slate that was expected to fill up very quickly.  After a couple of classes being completely lost, I   reread the notes at the beginning of each section (which in previous units I hadn't really studied except for some quick skimming), which turned out to help me immensely.  


By doing this I learned that I had to make an effort to understand things that were confusing to me, and not just sit back and wait have things explained to me - because the rest of the class was moving on.  I think I learned this unit that achievement comes with effort, which hopefully shows when I get my test grade back.


Strengths - My strengths in this unit, I think, were my connections I made (more effortlessly than before) about how different concepts connect to each other.  For example, the forces we had just learned about (like friction, tension, etc.) were the same forces that caused centripetal force.


Weaknesses - I think my weaknesses in this unit were mostly all related to problems involving scientific notation.  I'm still not very confident in how to multiply/divide scientific notation, but that turned out to be a small problem because we were allowed to use calculators on every problem.  Still, I think I should be able to do those problems by hand.


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Overall, this unit presented new concepts to me that I hadn't already known about before, and as a result, improved my problem solving skills.

MYTHBUSTERS LAB

  For this lab, we had to disprove two commonly accepted myths. If you asked most people if they thought the myths we were presented were true or not, most people would believe that they were.  Even at first, our lab group had trouble disagreeing with these simple misconceptions.  After a while, we discovered that both myths were actually false in many situations.  

Myth 1: An object always moves in the direction of the net force exerted on it.

If an object always moves in the direction of the net force exerted on it, and we roll a bowling ball across a level carpet surface with friction acting against the ball, then the bowling ball will continue to move in the same direction that it was originally travelling in.

Our procedure for myth one was simple: Roll the bowling ball across the carpet surface.

The small arrow represents the direction of motion.

ΣFx = -Ff

ΣFy= Fn-Fg

The ball is not moving in the way the only horizontal force, friction, is being applied to it.  It still moves to the right, when the force of friction is moving to the left, so the myth is busted!

Myth 2: An object always changes its motion if there is a force exerted on it by other objects.

If an object always changes its motion if there is a force exerted on it by other objects and we swing a tennis ball into a bowling ball while in motion, the bowling ball's path/direction it is going in will not be affected.

Procedure:

1.   Suspend tennis ball from the ceiling with a piece of string.

2.  Hold tennis ball in air while still attached to string.

3.  Roll bowling ball into tennis ball's path.

4.  Release tennis ball from hand, allowing it to swing directly into the bowling ball while it is moving.

 

The small arrow represents direction of motion.

ΣFx = -Fa

ΣFy = Fn-Fg

The ball is moving to the right, but the only force (the applied force of the tennis ball) is moving to the left.  Even though the bowling ball has a left force pushing on it, it is not strong enough to change the direction of the already moving bowling ball (going to the right).  Busted!

CONCLUSION:

We ended up disproving both myths.  But even if we hadn't disproved both, the myth still wouldn't have been proven because we wouldn't have tried every experiment/lab possible.  People believe myth one is true because most people assume the object being forced upon is starting at rest.  For example, a ball at rest gets hit by a foot.  The ball resultantly moves in the same direction as the foot was when it hit the ball.  Most people don't even consider or think about smaller forces like friction.  Because the bowling ball already had enough speed/momentum, the friction acting in the opposite direction did not have any effect on the bowling ball's direction.  People usually believe myth two is correct because they automatically assume the opposing force is stronger than the original object, which is not true in many cases.  For example, in our experiment, the tennis ball had much less force than the moving bowling ball, so the bowling ball's path was not affected at all by the strike of the tennis ball.  Both myths were BUSTED!!!