BFPM Challenge Problem

This is a diagram of our setup, with  the mystery weight attached to the ceiling by two points on the ceiling. It might be hard to tell, but the angles of each line are not the same. 

This is what my setup looked like when broken down into a free body diagram with every force acting on the object. I broke the two tension forces up because every force has to be on the axis of the  diagram to be equal to another force. This diagram shows that it is balanced, as every force is accounted for on the axis. 

Once I had my free body diagram, I could begin to find my predicted weight, or the Force of Gravity that is acting upon the mystery weight. I first measured the angles at which the lines were holding the weight, and they showed Line A to have an angle of 35 and Line B to have an angle of 70. With this information, I could then use Soh Cah Toa to find the exact amount of force in Newtons that FTenAy and FTenBy have. I'll start with FTenBy. Since 20+70 is equal to 90 degrees, I can use the cosine of 20 to find the amount of force in FTenBy. My math is as follows:

Cosine(20)= FTenBy/ 2.2 (N)

FTenBy= Cosine(20)(2.2 N)

FTenBy= 2.1 N

To solve for the amount of force in Newtons for FTenAy, I chose to use sin(35) to solve, because sin is equal to opposite/hypotenuse. The following is my setup and solved answer:

Sin(35)= FTenAy/0.8 (N)

FTenAy= Sin(35)(0.8 N)

FTenAy= 0.46 N

Even after all that work, I'm still not entirely finished. The two force amounts that I found still need to be added together, as both of them come together to equal the force of gravity on an object, or more commonly known as the object's weight. 

FTenBy+FTenAy=Fgravity

2.10 N + 0.46 N= Fgravity 

Fgravity= 2.56 N

CAPM Challenge Problem

This is a sketch of how our setup looks like. The green objects represent the books under the table, with the table being the black line. The orange object is our metal ball, which rolls faster when rolling down the table (look for the red arrows). We measure our spacing in centimeters, timed to half-seconds for the most accurate measurements. 

     

0	0
0.5	5
1	16
1.5	32.5
2	54
2.5	80
3	110
3.5	144

Our raw data looks like this, with the x-coordinate being the half-seconds we measured and the y-coordinate being the distance we measured in centimeters.

Our first graph shows our raw data in a position versus time graph, proving our guys correct that our object would move with an exponentially increasing speed. We were originally going to use this data and create a Velocity vs. Time then find the slope of that line. That would then give us the acceleration of our ball. However, we could easily cut down on the number of steps to do by instead using a Position vs. Time Squared graph.

This is the result of squaring our time and using the new results instead of the old time, which turns our exponential data graph into a straight line that has a slope. The equation for this line is equal to X=1/2 at^2, with the slope of this line being equal to a half of the acceleration of the object. Our slope, as seen in the graph above, is equal to 11.708 cm, or .11708 meters. we took our new slope and multiplied it by 1/2, which turned out to look like this: .11708/1*2/1. This all resulted with our acceleration being equal to .23416 meters/second squared. 

Unit Blog Summary #2

     Well, I've certainly covered a bunch of material so far, and this section has been the most rewarding so far in terms of my overall learning and growth. I went from barely understanding which forces act on an object to knowing the precise amount of force in newton’s (N). In the seven sections that I covered in class, everything built on top of the last section, making it extremely important to retain my prior knowledge. The first thing we learned was how to draw a free-body diagram showing forces acting upon an object. These forces that we learned first were gravity, normal, and friction forces. Also, by using proportionately sized force vectors (Lines used to measure the amount of a certain force), I was able to show if opposite forces were equal or different. 

     Moving forwards a couple of days and some learning opportunities, we learned about Newton's first law. It states that an object in motion will stay in motion, and an object at rest will stay at rest, until another force acts upon that object. For example, if I had a ball rolling across a frictionless floor at a constant speed, the ball wouldn't stop unless another external force is applied to the ball.

However, as soon as I apply a force such as friction, the ball would slow down and eventually stop moving all together.  A tricky example of this is a ball that I've just released from my hand upwards. The only force acting on the ball throughout it's entire flight is gravity, as it's slowing down before reaching the vertex, changing direction at the top of it's arch, and then speeding up as it travels downwards. This unit gave me the tools to realize how individual forces act upon an object.

     The third major thing I learned this unit was to realize the difference between the mass and weight of an object. The mass is the measurement of how much material an object has, while the weight is the measure of how hard gravity acts upon an object. The units for the mass are in kilograms (kg) while the weight is measured in newton’s (N). To convert from mass to weight, you need the following equation: Weight= (10)*(mass). Note that the 10 stands for Earth's gravity constant that’s actually 9.81, but 10 is okay for most problems. The mass also has to be in kilograms. One cool thing that I learned was that the only force acting on an object while it was in the air is gravity, nothing else. With critical thinking, this begins to make perfect sense, as it is the only thing acting on an object while it's slowing down, speeding up, or changing directions in the air.  

     The next thing that I learned was how to find the actual amount of friction that acts on an object. To find this, you need the weight of an object and the coefficient of friction, which is measured between the two surfaces of the interacting objects. The actual equation looks like this: F=(mx)*(weight), with mx as the coefficient of friction. An important idea that I learned was the notion that friction is not affected by the surface area of an object. The only two things that do in fact affect friction is the weight of the object and the speed that it’s traveling. Also, it's important to note that the direction of the velocity of an object is directly related to the direction of the unbalanced force in a free-body diagram. If an object has an unbalanced force going the same direction as velocity is, then the object is speeding up. The opposite occurs if they are facing opposite directions. 

            One of the most recent things I learned was to realize when to shift my axis, like in the many

ramp problems I solved. After that, I moved to Newton’s third law, which states that each action has a equal and opposite reaction. This was helpful in discovering which forces between different force diagrams act on each other, such as in the tug of war game between Asheville School and Christ School. It’s also very important to remember and draw the force vectors between the two diagrams as proportionate to one another.

            The most recent thing that I discovered was how to plug in values for each of the forces I previously had. More specifically, I looked at the force of tension and using sine, cosine, and tangent to find the specific amounts of force in newtons along lines. Using these three different equations also allowed me to find various force amounts on other forces. I also got the chance to pull together old concepts from earlier this year and add to them. For both the horizontal and vertical line equations, I can plug in numbers instead of force names and use them to check my answers. For example, if I said that the Force of Tension+ the Force of Friction= 0N, then I could take my numbers for the forces and check them to make sure they match up with everything else. Altogether, I finished up this unit with a strong understanding of how objects can be broken down into their diagrams a lot easier than I originally thought. In the BFPM challenge problem, I got a real life opportunity to apply what I learned to solve for the weight of an object. I felt very well prepared for all of my assignments, and I’m looking forward to crushing this test!