How fast can my gliding speed increase?

Well, you would think I was an ice skate racer, but instead I am a simple little cart on a simple table.

Like I said, I am only a little cart  trying to figure out how fast I can accelerate. So my proud renter took me, and put me on a track, measured every half second, and then took data to see first my change in position over time, which lead to velocity, and then solved for acceleration. 

This looked like the initial chart of:

This gave us the following graph. Note the curve upward.

We had to take the following formula, y=mx+b, and change it into a line that more closely resembles the formula's we are dealing with. The following formula is x=slope*t^2+xo. When you notice that the t is squared, it is because the time must be squared to fit into a graph to solve for acceleration.

This produced the following graph:

Note the slope of 0.070747.

In order to solve for Acceleration, we use the formula V=1/2a

Thus, as our slope is velocity, we can multiply it by 2 and solve for the acceleration. 

Our acceleration is 0.070747*2=0.141494. 

However, when we checked it with the motion detector, it found .22 as the slope. I do not know why, but will continue to ponder why I (the cart) am not accelerating at the indicated pace.

CAPM A summary of learning

Welcome to my new readers, and hello to the old.

CAPM stands for Constant Acceleration Particle Models, wherein we built from our former understanding to develop a knowledge and appreciation of what constant acceleration means.

This added acceleration graphs to our chart in contrast with velocity, showing how they intermingled. Then we worked on how we could translate from a motion graph, to a velocity graph, and then to one for acceleration. 

CAPM.1

Instantaneous velocity:

This is the velocity at any precise, given, point in time. It can be calculated in several ways from either charts or graphs. If at a graph, one can tell the velocity by using exactly where it is on a v vs t graph, such as the one below that is both constant velocity and constant acceleration.

http://www.thetrc.org/pda_content/texasphysics/e-BookData/Images/SB/57/LR/ConstAccelConstVelComparisons.png

Thus, by finding the exact position of an object which is its data points on a v vs t graph, we can see what the exact instantaneous velocity is. 

The second way to solve  for velocity is by taking mirroring in time data points on both sides of what you are looking for, and then inputting them into the formula V= Change in position/ Change in time.

Capm.2

Solving for displacement can be solved for either with formula's or with a graph. 

The formula is Change in x= xfinal-Xinitial on a x vs t graph, however on a velocity vs time graph the formula becomes change in x= 1/2*a(change in t)^2+ Vi(total time)

On a graph, we can use the position vs time graph to see where it is by subtracting the initial data points from the final coordinates.

Capm.3 

Solving for acceleration can be done in four ways.

The first is looking at a velocity vs time graph, where we can input our data into the formula a=Change in v/ change in t.

The second is solving for it in other formula's, such as solving for a in the following formula Change in x= 1/2 a (change in t)^2 + Vit.

The third is simply looking at an acceleration vs time graph and seeing where it is. 

The fourth is solving for it in the second formula:

Vf=a(change in time)+V(initial)

CAPM.4

If you look at the following position vs time graph, you may note:

This is taken from http://gradeelevenphysics.weebly.com/speed-velocity-and-acceleration.html

 You may note that it is constantly decreasing its velocity, however the acceleration is constant. It is travelling in a positive direction though the velocity and acceleration are negative as it is slowing down. 

The corresponding v vs t graph would resemble the one above, with it constantly decreasing. The acceleration is steady but nonetheless negative as it is slowing.

CAPM.5

If we take the same graph as above, we can draw a position vs time graph based on our initial understanding of what the motion means. Because our velocity vs time graph is starting positive, and never becomes negative, we know that our position vs time graph will be positive. We also know that initially it will be going faster, as our velocity graph starts from a higher position on the y (Velocity) axis. Then, as our velocity slopes downward, we know that our position vs time graph line needs to lessen its upward motion, gradually curving out until it is almost going straight.

Due to the constant nature of our velocity going towards the x (time) axis, we know that it is heading in a negative direction and thus our acceleration will be negative and a straight line.

CAPM.6

In order to construct a graph, we must see that there are 4 particles. 

The 4 particles are:

What direction is it going?

Is it constant?

What variables are we given, and what do they apply to? 

Is it possible for it to become negative?

From this, we can draw any graph we wish. 

CAPM.7

To solve for time, we can take the average formula x=1/2 a(t^2)+Vi(total time).

From this, we can solve using algebra to isolate our t. 

Please note the image below to see the process. 

 

Weight Challenge

Good day,

Today in Physics, we were asked to solve a challenge for a mystery weight suspended by two cords which provided the tension.

The diagram was similar to the one below:

This resulted in the use of our formula SohCahToa.

Sin= opposite/hypotenuse

Cos=adjacent/hypotenuse

Tan=opposite/ adjacent

This resulted in a diagram resembling the one below:

The corresponding free body diagram resembles the one below:

The calculations to accompany this diagram are:

Ft1y + Ft2y= Fg  

Sin( beta)= Opp/Hypotenuse

Sin38=Ft1y/ 0.9

0.9n*sin(38)=Ft1y

Ft1y= 0.5540953277934n

Sin( beta)= Opp/Hypotenuse

sin (70)= Ft2y/2.2n

2.2n*sin(70)=Ft2y

Ft2y= 2.0673237657292n

Due to Ft1y + Ft2y= Fg 

Then, 0.5540953277934n+2.0673237657292n=Fg

Thus, Fg=2.6214190935226n

Hello,
To my Dearly appreciated Readers,

May I wish you a wonderful day amidst the chaos of the year.

Now, on to the point of my blog, let me address the concept of today. This post will discuss free body diagrams, as well as the parts that make them up.

Concept 1: Force diagrams (AKA Free body Diagrams AKA FBD's)

What are force diagrams?

Well, they are the diagrams that explain how the forces (such as tension, gravity, pull, push, and friction) interact with objects on our planet. A free body diagram is composed of multiple parts. The central part is a dot or circle, which represents the item that forces are acting upon, and only that one item.
Please note the example below:

Image taken from: wikipedia

The f weight in this example ends up actually being Fg in all that we do, however it does show us what a free body diagram looks like for an object sitting at a table


 On our planet, the force of gravity is labeled as g= 9.81 (or less precisely 10).

Concept 2: newton's 1st law.

There are three laws that govern forces as we know it  so far, but we have only covered 2. These laws are Newton's 1st law, and Newton's 3rd law.

Newton's 1st law is that "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force." (physics classroom.)

This means that any object such as a ball, a bike, anything really wants to do what it is currently doing. This means that any object moving will stay moving but any object that is not moving (at rest) will stay at rest. The only exception is if an outside (aka unbalanced) force acts upon it which means that something affects it such as pushing or pulling, blowing, moving it, etc...

This applies to life in that a ball won't move unless you touch or kick it, a ball won't fly through the air unless you throw it. 

In fact , a ball flying through the air is only affected by one force the whole time, that is the force of gravity. From the start of the throw the ball goes through 3 stages, going up, being perfectly in the middle, and coming down but no matter what the only aspect that matters is that gravity is the only thing acting on it. 
Thus the free body diagram is:

In another example, a skydiver is also only affected by gravity until they open their parachute up. In the first few seconds, the speed of the man is steady, but once they open their parachute, their descent slows  as the air resistance of the parachute starts to try and counter-balance gravity. Thus we see the chronicle of events, with first their initial jump from the plane, then when they have just opened their parachute but it is not fully expanded, to when it has slowed their descent considerably but not halted it.

All objects on the earth, at rest, or experiencing constant velocity have balanced forces. The FBD for at rest and at constant velocity look the same. They are shown below. 

Concept 3. 
The relationship between mass and weight (g=9.81n/ kg but we tend to use 10 for basic problems).

Weight in Newtons is the result of mass times the force of gravity. This is depicted in the formula:
w=mg.

We tend to use 10 for the force of gravity, but the exact number allowed is 9.81. Mass is only taken in kg thus any weight in grams must be multiplied by .01 to then become in kilograms which we can convert to newtons.

Thus if an object has a mass 2.5 kg, we can solve for weight by inserting the mass into our formula (w=mg) as w=10*2.5 or alternatively w=2.5*10.
Thus weight equals 25 newtons for the object.



Concept 4. Friction force and normal force on objects.
Friction force is the force that stops us from endlessly accelerating from one single push, as it helps slow us down. Normal force is what is counter to gravity, stopping us from sinking straight into the earth.

Friction is affected by surface material and weight, surface area doesn't matter.


Concept 5. Here is an example of a balanced force diagram. The umbrella is perched atop the bike and weighs 40 newtons. The bike weighs 200 newtons. The action reaction pairs are:

found via google images, umbrella on bike.

The umbrella 

Umbrella pulls bike up.
Bike pulls umbrella down.

Bike pulls earth up.
Earth pulls bike down.


The formula for an action reaction pair is:
Object 1 exerts force on object 2 in a direction.
Object 2 exerts equal force on object 1 in opposite direction.