Newton's 3 Laws of Motion

Last week, we studied the Newton Laws. The first basically states that an object in motion will stay in motion and an object at rest will stay at rest unless acted on by an outside force. The second comes with the equation F = ma (Force equals mass x acceleration). This complements the other equation for force that we already have: f = mg (Force equals mass x gravity).

In the lab, we first needed to find the constant force the fan-cart exerts. We then used Logger Pro to create a velocity vs. time graph as we ran trials with the fan-cart carrying various weights. We then found the slope of the velocity vs. time graphs which gave us their accelerations. What we found is that when the force is constant, the acceleration and mass have an inverse relationship. This means that when the mass of the fan-cart went up, it's acceleration decreased and visa versa.

Also we did the hover disc lab. We analyzed the effects of gravitational, frictional, and normal forces on the disc. In my opinion it was a very cool lab because it was the first time that we used all three of Newton's laws of motion together.  

1. If an object is at rest or at a constant speed, it will remain that way unless it experiences a net force.
2. A=netF/m or netF=ma
3. When two object interact, they exert equal but opposite force upon each other.

We put this knowledge to use by creating interaction and free body diagrams for the lab. Interaction diagrams show the dynamics of force within an entire system. On the other hand, a free body diagram focuses on only one object of the system and only shows the forces acting upon it. One situation we depicted with both diagrams is below. The interaction diagram is followed by the free body diagram.

Hover Disk Lab

In class last week we did the hover disc lab. We analyzed the effects of gravitational, frictional, and normal forces on the disc. In my opinion it was a very cool lab because it was the first time that we used all three of Newton's laws of motion together.  
                                 

                                 

3 Laws of Motion:

1. If an object is at rest or at a constant speed, it will remain that way unless it experiences a net force.
2. A=netF/m or netF=ma
3. When two object interact, they exert equal but opposite force upon each other.

We put this knowledge to use by creating interaction and free body diagrams for the lab. Interaction diagrams show the dynamics of force within an entire system. On the other hand, a free body diagram focuses on only one object of the system and only shows the forces acting upon it. One situation we depicted with both diagrams is below. The interaction diagram is followed by the free body diagram.

I think that being able to draw these diagrams is very helpful for visually understanding situations in the world around us. Drawing the diagrams really forces you to think about all the individual forces these objects are experiencing. It also helps explain the dynamics between the force of gravity and the normal force.

Impulse Lab

Last week, we did the impulse lab. We crashed a cart into a metal deflector to test the force created by the cart and velocity of the cart. Also, we observed the conservation of momentum within the system.

During this lab, we addressed the relationship between impulse and momentum. We found that the impulse value directly relies on the values of the final and initial momentum of the system. 

Some important equations and definitions we used today: 

1. Impulse is a change in momentum due to applied force over time
2. Impulse = final momentum - initial momentum
3. Momentum = velocity x mass

Below is a visual representation of our results: 

The graph which shows the velocity and force, and the data which shows the area and impulse of the collision is shown above. The pictures above shows that one could find the impulse, the velocities and the momentum of the system with the collected data. This is done by finding the initial and final momentum of the individual carts.

I can think of so many people who need to know about the physics of collisions for their professional lives. Just think the people who's job it is to develop car safety. For example, airbags are an excellent example of humans manipulating collisions to their benefit. First off, its a elastic collision. A lot of momentum is conserved. What this means is that the persons head will bounce off of the air bag with backwards momentum instead of most of the momentum being lost in the collision with the steering wheel. Also, the airbag increases the time of the collision which in turn decreases the force.

Collisions Lab

Last week in class we did the collision lab. We compared the conservation of momentum and energy in elastic and inelastic collisions. There was a red and a blue cart, and a motion sensor to help measure the velocity of each cart. The elastic collision resulted in the red cart colliding with the blue cart and the inelastic collision resulted in the carts sticking together with their Velcro fronts. 

Answers to the big questions: We found that elastic collisions conserve more energy than inelastic collisions do. We also calculated that momentum is more easily conserved through collisions than energy is. These patterns are shown in the picture below.

Some old and new equations and concepts we had to use today:

- Momentum = mass x force

- KE=1/2mv^2

- to calculate energy/momentum lost: final - initial divided by final x100

\We see collisions all the time but perhaps one of the most glamorous is the collision between bat and ball during a baseball game. This is an inelastic collision - neither the ball nor the bat have elastic qualities. Much of the energy from the collision travels through the bat into the hands of the batter but perhaps the most recognizable cause for the high amount of energy lost in inelastic collisions stems from the loud "crack" made when the contact occurs.

Rubber Band Cart Launcher

In this week's lab we launched a glider from a rubber band using an air track, and used a photo gate sensor to measure the velocity. We changed the distance of the rubber band being stretched for each trial. There were five trials, with the distance  from 1-5cm, or 0.1, 0.2, 0.3, 0.4, and 0.5 meters. We recorded the velocity of the cart (dependent variable) in a data table, and then repeated the experiment to get the most accurate statistics possible.

Units used:
m = meters
v = velocity
J = Jules (Energy)
K = Kinetic Energy
Us = elastic potential energy

Data:

Using the Vernier Graphical Analysis app, I created a best-fit line for all of the data we collected, using the Energy as our Y-axis, while the average of the velocity was our x-axis.

 Based on our graph, we noticed that the slope was half the mass of the cart. all of this allowed us to derive the equation for kinetic energy! KE=1/2(m)(V^2)

 In the LOL chart below, energy is transferred from elastic potential energy (rubber band) to kinetic energy (motion). When something is in motion, kinetic energy is being used. Because potential energy is transferred into kinetic energy, energy and velocity are directly proportional.

Real-World Connection: 

For example (slingshot), as the person pulls back on the slingshot, they increase the distance stretched. Therefore, there is an increase with the elastic potential energy. As the slingshot is released, the elastic potential energy is transferred into kinetic energy, which puts the ball in motion. The velocity of the ball is proportional to the kinetic energy. Therefore the more distance being pulled back on the sling, the greater the kinetic energy will be, and the faster the ball will go. 

Rubber Band Lab

This week we used a rubber band and a force probe to find how we can store energy to do work for us later. We experimented with two different trails to find force (Fs) in terms of distance stretched (X). For the first trial, we used a single loop and stretched the rubber band to various lengths, while recording the force needed with the electronic force probe. Next, we had a double loop on the rubber band and repeated the experiment.

Units used:
m = metersN = newtons (force)K = elastic constantFs = force needed to stretchX = distance stretchedUs = elastic potential energy

Single loop data:
1 cm = .285 N
2 cm = .728 N
3 cm = 1.434 N
4 cm = 1.85 N
5 cm = 2.797 N
Double loop data:
1 cm = 2.31 N
2 cm = 3.866 N
3 cm = 6.22 N
4 cm = 8.32 N
5 cm = 11.72 N

In our graph we used  y=mx+b. In our graph force was on the y-axis and distance was on the x-axis, so we knew that the y variable would become Fs (force stretched) and the x variable would become X (distance stretched). We then found the slope of the line, which was 60 n/m. This was also the elastic constant (K). Because b=0, we derived the equation Fs=KX.

Real World Connection: 

The greater the distance the bow and arrow is stretched, then the greater the force needed to stretch, and the greater the potential energy. If you use a lot of force to pull the object back, the farther the object will go.

Pyramid Lab

In class last week, we did the pyramid lab. We pulled weights up a ramp to a specific height. After each trial, we changed the length of the ramp. The height remained the same. We used the lab probe to figure out how much force was required to pull the weights up the various lengths of the ramp.Our group found out that it is impossible to decrease the force required to move something without increasing the distance required to do it. 




While the force and distance changed, the area of all the graphs were the same. This is because the height that the weight is being lifted is constant and therefore, the amount of work or energy required for the task is constant as well. The ramp only manipulates the levels of distance and force required.



Simple machines are everywhere in our day today lives. For homework, we had to watch a theory that showed the Egyptians creating simple machines to build their pyramids. To me, it seems like people prefer less force over shorter distances. We would rather walk up a long ramp than a short flight of steps. It seems that you can find the formula "work=fd" in almost every motion of our lives.

Pulley Lab

For our pulley assignment, we created 3 different pulleys. My group created a simple pulley, a two-string pulley, and a four-string pulley. For each pulley, we measured a 200g weight and measured the force required to hold the mass steady. It took 20 cm of string to raise the weight 10 cm, which shows the increased distance and decrease of force being used.

In the picture, it shows the force required to hold the 200 g mass steady, and the string required to move the 200 g.

                                                                                  

The area all equaled .01 m/n which showed their inverse relationship. Force x Distance together are constant. Also, F x D = Work, and newtons x mass = joules. 

Simple machines have an impact on our lives because it makes it easier for us. Objects such as the pulley and hammer makes work require less energy because of the less distance required to complete the job.

Force Vs. Mass

In the Force vs. Mass lab, we measured the different amounts of force caused by different weights. The force was measure in Newtons while the mass was in grams and kilograms. In the picture, the force (dependent variable) is on the y-axis, while the mass (independent variable) is on the x-axis. As my group calculated the line graph with the information we had, we noticed a consistent upward trend, as the mass increases, the force increases. For example, the heavier an object, the more force is required to push the object. We plugged in our calculations to find the slope of the experiment, using the equation "y=mx+b." After doing the work, we concluded that Force is equal to 10x the amount of mass. In the equation, 1 kg = 10 newtons.