Newton's Laws of Motion

Lab #1: Hover Disc:

In the Hover Disc Lab, we went down to the gym foyet and discovered what gives rise to a change in motion. We observed the disco at rest, in motion, and while it was being pushed. Then, we took note of the change in motion and documented it in an interaction diagram and a free body diagram.

When the disc was at rest and in motion, there was a gravitational and normal force between each person and the earth and the disc and the earth. The normal force was going upward and the gravitational force downward in the free body diagram. When the disc was being pushed by either person, there was a gravitational and normal force between each person and the earth and the disc and the earth. There was also a normal force between the disc and the person pushing it. In the free body diagram, there was a normal force going upward and to the right, and a gravitational force going downward.

Newton's 3rd Law of Motion:

This lab allows us to act upon Newton's 3rd Law of Motion, which states that when two objects interact, they exert equal and opposite force on each other.These objects are equal magnitude, opposite in direction, and the same type of force.

Lab #2: Fan Cart:

In our Fan Cart Lab, we discovered the relationship between mass, force, and acceleration. First, we found our slope, or constant force of .15 N. Then, we added mass to our fan cart to observe the affect on the acceleration. Below is an image of our data:

Newton's 1st and 2nd Laws of Motion:

From our data, we derived the equation: force= mass x acceleration. This equation happens to be Newton's 2nd Law of Motion. This affects Newton's 1st Law of Motion, which states that an object at rest or traveling at a constant speed will continue to do so, unless a net force acts on it. 

Real World Connection:

Below is a video, which describes Newton's three laws of motion, and involves connections to our everyday life:  http://www.youtube.com/watch?v=UVdqxYyFRKY

Impulse Lab

In this week's lab, we performed a collision to determine the relationship between force, distance, and time. First, we attached our force probe and zeroed it. Then, we performed a collision between the red cart and the aluminum ring and found the momentum and measured the velocity before and after the collision. We found the velocity before to be 0.2625 m/s and after to be -0.2997 m/s. We measured our force as -.2100 N. Below is an image of our data in LoggerPro:

Through our data and class discussion, we came to the conclusion that impulse is the area of a force vs. time graph. In a collision, the momentum changes because of the impulse, measured in NxS (or force x time). No matter the mass, there is always an equal and opposite force--in any collision. When you increase time, force is always decreased. We found the equation for impulse to be J= Pf - Pi, or impulse= final momentum - initial momentum. Below is an image of our white board:

Real World Connection:

In the real world, the physics behind bowling relate to momentum and impulse. When the bowling ball comes in contact with the pins, a collision takes place. The momentum of the ball, however, changes because of the impulse. The article below further explains this theory:
http://www.topendsports.com/sport/tenpin/physics.htm

Collisions Lab

In this week's lab, we studied the difference between energy lost in an Elastic Collison vs. an Inelastic Collison. To do so, we set up two carts so that their spring launches were facing one another, so ensure that they would bounce off each other for an elastic collision.  Our carts weighed .25 kg. We measured the speed of the red cart to be .472 m/s and the blue cart to be 0 m/s before the collison. After the collision, the red cart had a velocity of .323 m/s and the blue cart to be .243 m/s. Then, we set up the carts so that their velcro sides were facing one another so that they would stick together, for an inelastic collision. We recorded the red cart to have a speed of .667 m/s and the blue cart of 0 m/s before the collision.
After the collision, the red cart had a velocity of
.031m/s and the blue cart of .431 m/s. A table with
our data is shown below:

After our experiment, we calculated the amount of energy for the elastic and inelastic collisions by finding the percent difference, which is the total energy before x the total energy after / the average of total energy before and after x 100.  We calculated the percent difference of energy in the elastic collision to be 19.608 %. The momentum in the elastic collison was 1.709 %. For the inelastic collision, the energy had a percent difference of 94.737 %, and the momentum of 16.181 %. For both types of collisions, momentum had a lower percent difference, so momentum is more conserved and momentum can help us analyze collisions.

Real World Connection: 

Above is an image of a collision in real life and this article desribes the relationship of energy and momentum that causes it. http://toppers-club.com/iit-physics/be-careful-in-applying-law-of-conservation-of-energy/

Rubber Band Cart Launcher

     In this week's lab, we were asked to determine the relationship between energy and velocity. To do so, we detained the velocity of our red glider cart, using the electronic force probe. We stretched the rubber band to a distance of .01 m, .02 m, .03 m, .04 m, and .05 m. According to the electronic force probe, we documented the velocity of the cart at each distance. We did two trials for each distance and then found the average velocity, the average velocity squared, and we noted the energy measured in joules from our experiment last week. We used our graphical analysis app to determine the graph of our data, using the average velocity squared as the x-axis and the energy as the y-axis. Our graph is shown in the image below:

Using two points on our graph, we found the slope to be 1/2. We converted our y= mx+ b formula into Energy= 1/2 mass x velocity squared.  With K as the elastic constant and Us as the potential energy, we were able to determine that Us = 1/2 k x squared.

We determined that energy in a system always stays the same and that energy and velocity are directly related, and if energy increases velocity must increase. If velocity increases, so will energy.

Real World Connection:

http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/shawna_sastamoinen/Velocity&Kinetic.htm

A rollar coaster can demonstrate the relationship between velocity and energy because if the mass is constant, and the velocity is increased, the kinetic energy must also increase. The article linked above clearly demonstrates this principle as well.

Rubber Band Lab

In this week's lab, we figured out if the force it takes to stretch a rubber band depends on the amount by which you stretch it. To solve this, we stretched a rubber band to different lengths of .01cm, .02 cm, .03 cm, .04 cm, and .05 cm with the electronic force probe. With one rubber band loop, we measured the following:

.01 m = .4 N

.02 m = 1 N

.03 m = 1.9 N

.04 m = 2.7 N

.05 m  = 3.2 N

We repeated the process with a double rubber band loop and got the following data:

.01 m = 1.6 N

.02 m = 2.2 N

.03 m = 5.5 N

.04 m = 5.6 N

.05 m  = 6 N

We notice that when we stretched the band farther, the force increased. Then, we graphed our data using a best fit line. We were given Fs as the force needed to stretch the band, K as the elastic constant, and X as the distance pulled. We discovered the equation Fs=KX, also known as Hooke's Law. Our graph is shown below:

We measured our energy, area, in the shape of a triangle. Area was represented by Us, the elastic potential energy. Using the standard equation of the triangle, our equation became Us = 1/2 ( base x height). With X as the base, Fs as the height, and using K as the constant, our equation turned into Us = 1/2 (K) (Xsquared). We discovered that distance and force are directly proportional, when one increases so does the other. Here is a picture of our white board:

Real World Connection:

An example of the effects of force and distance is a slingshot. The more force used to pull back, the greater distance it will reach. Therefore, the g reater distance you would like to reach, the more force needed as well. This use of force and distance is a great example of elastic potential energy. Below is an image of a slingshot you could use:

Pyramid Lab

In this week's lab, we tested the relationship between force and distance to see if energy is universally conserved as a constant of systems other than pulleys. To experiment this, we placed three books on a ramp with a car at the bottom of the ramp being pulled up by an electronic force probe. In our first trial, it took .1 Newtons to pull the 250 g car up a ramp of 166 cm. so 1.66 meters (.1 Newtons) = .166 Joules.

In our second trial, it took .12 Newtons of force to pull the car up a shortened ramp of 132 cm. so .132 meters (.12 Newtons) = .158 Joules. Below is a picture of our ramp:

More force, Less distance = Same energy

Less force, More distance = Same energy

We continued to adjust the measurement of the ramp and add mass to our car, but we ultimately came to the conclusion that despite the measurement of force and distance, the amount of work or energy will always stay the same. Whether there is more force and less distance or less force and more distance, they same amount of energy is always conserved. In conclusion, the product of force and distance is universally conserved because the amount of energy remains the same always.

Real World Connection:

In the real world, skate ramps are built in the same structure as the ramp we built for our car. Ramps in our everyday lives are simple machines which reduce force, with the trade-off being distance, however, the amount of work, or energy, used is the same.