Newton's Three Laws of Motion

Over the past 2 weeks, we have been deriving Newton's three laws of motion by performing the hover disk lab and the fan cart lab.

Newton's First Law

• An object at rest or traveling at a constant speed will continue to do so, unless a net force acts on it.

• Any object moving at a constant speed or at rest, has no net force acting on it. (Fnet = 0). The hover disk lab allowed us to see how this law works. When the hover disk is at rest or moving at a constant speed, it will not have a change in velocity, or accelerate, because there is no net force acting on it.

• Although there is no net force acting on the object because the object is at rest, there are still many forces acting on everything. In the interaction diagram, you can see that there is a gravitational force acting down on person 1, person 2, the earth, and the hover disk. But what allows them to not fall through the ground is the normal force acting up on them.

• Here is an example where the object remains at a constant speed. Here we see that there is so net force on the object; however, there are still gravitational and normal forces acting on oerson 1, person 2, the disk, and the earth.

Newton's Second Law

• Force = mass (acceleration)

• From the fan cart lab, we derived this equation. We measured the acceleration of a 0.3 kg fan cart when turned on high with a constant force of 0.15 newtons. We then added weights of different masses to the fan cart to find different accelerations. From this we found that acceleration is the change in velocity divided by the change in time.

Collected Data

0.3 kg cart: 0.450 m/sec^2

0.4 kg cart: 0.380 m/sec^2

0.6 kg cart: 0.208 m/sec^2

1.1 kg cart: 0.146 m/sec^2

1.4 kg cart: 0.123 m/sec^2

1.7 kg cart: 0.105 m/sec^2

• To derive this equation, we found that as the mass increases, the acceleration decreases, meaning that mass and acceleration are inversely proportional. We also had to take into account that the force remains constant; therefore, we came up with the equation F = ma.

Newton's Third Law

• When two objects interact, they exert equal and opposite forces on each other.

• These forces are:

• equal in magnitude

• opposite in direction

• same type of force

• The hover disk lab helped us see how this law is true. When the hover disk is moving with a net force and is stopped by person 1's hand, the disc and the hand with exert and equal but opposite force on each other, which will be a normal force. 

Real World Connection

Here is a website that tells how Newton's laws of motion relate to a dancer.

http://physicsofballet.homestead.com/newtonlaws.html

Impulse Lab

Introduction
In this week's lab we crashed an empty red cart into a force-probe with aluminum (to slow down time) attached to a ring stand. We found the velocity of the cart before and after the collision. We then found the change in momentum, also known as impulse. We did this to measure the relationship between impulse, force, and time during a collision.

cart with aluminum

force prob with aluminum

Key Info

• impulse: a change in momentum (another way of representing the conservation of momentum)
• impulse is measured in Joules

• momentum = P

• impulse equation: J = Pfinal - Pinitial

• mass of car: 0.25 kg

• velocity is measured in meters per second (m/s)

Big Question

What is the relationship between impulse, force, and time during a collision?

After we collided the car with the aluminum ring, we found the velocity of the cart in the collision before and after using the sonic range finders. Then we found the momentum before and the momentum after to find the impulse. Then we recorded the area, also known as the integral, under the Force vs. Time graph. 



Here is what our data looked like:

From here, we did the calculations and found that the area of a force vs. time graph is impulse. So now the equation for impulse can be written as Impulse = Force (Time) or J = F(t).

Analyzing Data

Concluding Ideas
       Impulse and Are are the same! After determining the area of a Force vs. Time graph and calculating the impulse, the answers come out to be equal. Forces are equal and opposite; therefore, the impulse remains constant in a collision by increasing the time and decreasing the force. In the collision, the metal sheets increased the time and decreased the force.

Real Life Connection
        Boxing uses this same principle of minimizing the effect of a force by extending the time of the collision. When a boxer recognizes that he will be hit in the head by his opponent, the boxer often relaxes his neck and allows his head to move backward upon impact. This known as "riding the punch." A boxer rides the punch in order to extend the time of impact of the glove with their head. Extending the time results in decreasing the force and then minimizing the effect of the force in the collision. Now that is physics in action!
  
Here's a clip from the final fighting scene in the movie Rocky Balboa 

Collisions Lab

The BIG Question
   
    What is the difference between the amount of energy lost in an elastic collision vs. inelastic collision?
    What is a better conserved quantity- momentum or energy?

Background

• scalar quantities: magnitude (mass, energy, temperature)
• vector quantities: magnitude and direction ( + rightward, - leftward)
• types of collisions:
• elastic- objects bounce off each other
• inelastic: objects stick together
• momentum: p = m (v)
• mass (velocity)
• mass is measured in kilograms (kg)
• velocity is measured in meters per second (m/s)

• In this week's lab, our goal was to find the difference between the amount of energy lost in an elastic collision and inelastic collision. To test this, we put two cars of the same mass on opposite sides of a track, one red and one blue. We set two range finders on the ends of the track, which measure the velocity of the cars. These range finders were plugged into the electronic force probe, which was then plugged into the computer. The application on the computer graphed the velocity of both cars before, during, and after the collision.

• For the inelastic collision, we pushed the red car to the right toward the blue car, which then stuck together with velcro. Both cars continued to move together to the right. 

• For the elastic collision, we pushed the red car with a spring toward the blue car to the right. In this collision, the red car followed the blue car at a much slower pace once they hit, while the blue car continued to move to the right.

• We recorded our data and found the total momentum (p = mv) and the total kinetic energy (KE = 1/2mv^2) of both collisions.

• Then we found the percent difference of both the amount of energy and momentum that left or entered the system for both elastic and inelastic collisions.

• Percent difference: 

• Kinetic energy: (Total after - Total before)/(Total after + Total before / 2) (100)

• Momentum: (Total after - Total before)/(Total after + Total before / 2) (100) 

• We found that momentum is a better conserved quantity rather than energy because more energy is given off during a collision. Momentum has a smaller percent difference.

• We also found that inelastic collisions lose more energy than elastic collisions

Real Life Connection: 

      The game of pool uses the exact same concepts of momentum in collisions. When the white ball hits another colored ball, the hit and the colored ball keeps moving. The goal of the game is to get all the colored balls in the holes without knocking the white ball in with them. The velocity of the balls plays a key part in strategizing. 

       

Rubber Band Cart Launcher Lab

The BIG Question
      How are energy and velocity related?

• In Physics class this week, we tested to see how energy and velocity are related. To do this, we launched a glider at different distances on an air track. We measured the velocity using a Photogate Sensor, which detects the speed of the glider as it passes through. It works by creating an infrared beam and timing how long this beam is blocked by the glider. In order to get the most accurate data we possibly could, we leveled out the air track so that there no spontaneous movement of the glider. By turning the screw under the air track, we leveled the slope of the air track to make it flat.

• During the experiment we measured the velocity at 5 amounts of the rubber band stretched. Here are our calculations and data:                                                                                                                          

• Then we graphed our data using our Graphical Analysis App on our Ipads. Here's what our graph looked like:

• Post Analysis Questions:

1. The mass of the red cart is 0.38kg. How do you think the slope and the mass of the glider relate? 

• We found that the slope of the line, 0.147 v^2/J, is about 1/2 the mass of the cart. 

1. Can you derive an equation relating energy (KE), mass (m, and velocity (v^2)?

• To find our equation, we started the y = mx +b, the equation of a line. Then we plugged in the information we had with the variables we're supposed to use and got KE = .147 (v^2) + 0. Then using the answer to our first analysis question, we saw that mass has to be related. So we plugged 1/2 (mass) in for the slope and got KE = 1/2 (m) (v^2) as our final equation.

• Real Life Connection: In physics, the phrase "kinetic energy" is used to describe the energy of motion. Any object in motion possesses kinetic energy, and this energy can be controlled, transferred, and transformed to do work. A dancer holds much kinetic energy. Moving in a constant direction creates momentum. Momentum is mass in motion. The amount of momentum depends on the amount of mass moving and how fast that mass is moving. This shows how much or how little a dancer can have while performing. Momentum and speed, or mass and velocity, make up kinetic energy in a dancer.

Rubber Band Lab

The BIG Question??
    - How can we store energy to do work for us later?
    - How does the force it takes to stretch a rubber band depend on the AMOUNT by which you stretch it?

 

• This week in Physics class, we tested how we are able to store energy that allows work to be done later. To test this, we used a rubber band and an air track that hooks up to an air vacuum. We took two trials, one with a single loop and another with a dooble loop. In order to answer our second big question, we had to measure the force in terms of distance. Once we put the rubber band on the air track, we hooked the electric force probe over both strands of the rubber band. Then we stretched the rubber band five different lengths and held it there for about ten seconds. To calculate the force, we averaged the values using "analyzing statistics." Then we recorded our data and repeated this process for both trials.

• Trial #1 with single loop:
• 1) 1 cm = 0.01 m = 0.538 N
• 2) 2 cm = 0.02 m = 1.341 N
• 3) 3 cm = 0.03 m = 1.710 N
• 4) 4 cm = 0.04 m = 2.693 N
• 5) 5 cm = 0.05 m = 3. 372 N

• Trial #2 with double loop:
• 1) 1 cm = 0.01 m = 3.835 N
• 2) 2cm = 0.02 m = 6. 375 N
• 3) 3cm = 0.03 m = 8.605 N
• 4) 4cm = 0.04 m = 11.313 N
• 5) 5cm = 0.05 m = 12.782 N

• In order to analyze our data, we graphed these points on a line graph for Trial #1. The force, measured in Newtons, went along the y-axis, and the amount of stretch, measured in meters, along the x-axis.

• Once we graphed our data, we had to derive an equation from y = mx + b, using the variables F, K, and X.  So we found the slope of our line, which was 70.85 (Newtons/Meters). We found that the slope of our line is our elastic constant "K". We found that Force (F) and the distance stretched (X) were directly proportional. Then we plugged in variables and got F = KX.

• Now we had to find the energy. As we saw in the Pulley Lab, to find the energy, we need to find the area of a certain part on our graph. In the Pulley Lab we found the area of a rectangle (A = LH) or (W = FD). Now in this lab, we have one line, so to find the area we created a triangle from that one line, using it  as our hypotenuse.

• The area of a triangle is A = (1/2) BH. To relate the equation to our experiment, We plugged in "U" for "A" which stands for the elastic potential energy. The base of our triangle is "X", the distance stretched, and the height would appear to be Force "F"

• U = (1/2)  XF

• Since we already found what the equation for Force is, all we have to do is plug that equation in for F in our new equation.

• U = (1/2)  X (KX)
• or U = (1/2)  K (Xsquared)

• In conclusion, we found that potential energy is the energy stored that does work for us later. In this case, as we pull back the rubber band, potential energy is stored, which enables us to flig the rubber band after we let go.

• Watch this video about potential energy!

• Real World Connection: Ever jump on a trampoline before?? If you have, ever wonder what allows you to jump so high? Trampolines contain springs in them. When pressed down upon, elastic potential energy is stored and it releases. It allows you to jump higher and higher and you put more force on the trampoline. Elastic potential energy is what makes a trampoline so fun to be on!

Pyramid Lab

The BIG Question?
        - Is the product of force and distance universally conserved? (a constant in systems other than pulleys?)

• In Physics class this week, we tested force and distance to see if the product, which is energy, is universally conserved. To do this, we stacked three books on a table and placed a ramp at a diagonal on top of the books. We then placed a 750g car at the bottom of the ramp. We pulled the car with an electric force probe up the ramp at different distances to get our results:

• Trial #1-pulled the car up the ramp to the edge of the books
• 153 cm at 0.4 N = 1.53 M (0.4 N) = 0.612 J
• Trial #2- changed the ramp to a larger angle and pulled car to the edge of the books
• 120 cm at 0.5 N = 1.20 M (0.5 N) = 0.600 J
• Trial #3- changed the ramp to a smaller angle than the first trial and pulled car to the edge of the books
• 184 cm at 0.35 N = 1.84 M (0.35N) = 0.644 J

• We converted the distance from centimeters into meters. Force is measured in Newtons, and the total energy is measured in Joules.

• From this lab, I concluded that conserved means maintaining at a constance. When distance and force are inversely proportional, the energy should be the same; therefore...

• More force, less distance = same energy
• Less force, more distance = same energy

• Real Life Connection: Ramps are used in many places in our lives. We use them to ride bikes over. We use them so a disabled person in a wheelchair can get around without stairs. We use them on freeways. We use them in the mall. We use them in parking garages. There are countless examples we use ramps in our everyday lives. Ramps make life easier on us. Even though they usually take up more distance, less force is being exerted. AND the amount of energy we use stays the same!

Pulley Lab

The BIG Question?

       - How can force be manipulated using a simple machine?
       - What pattern do you observe regarding the relationship between force and distance in a simple machine?

• In the Pulley lab, we were asked to figure out how force can be manipulated using a simple machine. To find this, we first found that it takes 2 Newtons to lift the brass mass 10 cm off the ground without using the pulley system. Then we used the pulley and found that it only takes about 1.2 Newtons to lift the same brass mass 10 cm off the ground. The length of the string came out to be 27.5 cm. We found out that the force can be manipulated by the distance and the angle of the string you pull to lift the weight. 

• In comparison to Part 1, we noticed that the amount of force you have to apply is less when you have to use a greater amount of string to pull using the pulley system.

• HOWEVER, we also learned that there's alway a trade off in life... according to this experiement, the more distance you use, the less force is needed to apply. 

• To graph our data, we had to convert the distance from centimeters to meters.
• 10 CM = 0.10 M
• 27.5 CM = 0.275 M

• Here is a picture of my group's bar graph:

• Once we graphed our data, we saw a relationship between the two areas. It fits the pattern of the more distance you use, the less force there is. The area shown on the graph measuring force vs. distance with out a pulley has a higher yet shorter bar, showing greater force and less distance. The area shown on the graph measuring force vs. length with a pulley has a lower, but longer bar showing greater distance and less force.

• To write the area as an equation, we started with Area = Base (Height), which would be Area = Distance (D) x Force (F). In the data we found that 1/2 F = 2x D. The units this equation would be represented by would be Newtons (Force). Soooo.....
• (2N)(0.1M) = 0.2
• A = 0.2NM
• A= F(D)

• We also learned that energy is measured in Joules (J), and work (W) is energy transferred by applying a force over a distance. Therefore, energy (J) is the ability to do work.

• W = FD

***No matter how big the distance or the force is, you always use the same amount of energy***

• Real Life Connection: Elevators
• Imagine what it would be like to work in a 100 floor building and you worked on the one hundredth floor. Each flight you had to walk up stairs every morning and every night... That's what your day would consist of if elevators weren't invented, specifically the pulley system! Elevators use the pulley system to take you up and down to get to the floor you need to be on.

Mass vs. Force Lab

The BIG Question?

        What is the relationship between the mass of an object and the force needed to hold it in place?

• This week in Physics, we measured the amount of force on different amounts of masses using manual and electronic force probes. The force was measured in Newtons and we changed the brass masses from grams to kilograms. To analyze our data, we made a line graph connecting the two variables, mass and force, with the equation y = mx + b. 

• Here is an illustration of what our graph looked like:

• We found the slope to be 10 and developed an equation that relates force and mass. Using y = mx + b, we plugged in our variables to form the equation F = Mg. The force (F) took the place of (y) because the force was our dependent variable. The mass (M) took the place of (x) because the mass was our independent variable. 10 was plugged into (m) because 10 was our slope. The (g) in our equation stands for earth's gravitational constant. (g) is always equal to 10 Newtons per kilogram.

• We concluded that the force due to gravity (N) on Earth is about 10 times the mass (kg).

• Real life connection: Here is an article about how gravity has an effect on dancers. http://www.livestrong.com/article/507653-physics-dance-movements/
• It shows the connection between the gravitational force on a dancer, the upward force of using the floor, and the strength and mass needed to counter the gravitational force in order  to dance.