Preliminary Questions and Ponderings
With your hand, can you change the path of a ball in the air without touching the ball?
If a ball had a strong manget on it and you had a strong magnet in your hand, could you change the path of the ball in the air without touching the ball?
Define force.
What is necessary to have a force?
Do most force interactions employ contact forces or noncontact forces?
How do you tell if a force is present?
Consider the force called "weight" or force of gravity.
Why is there weight? (Hint, change something and imagine the effect it has, e. g., remove the earth or change the separation.)Obtain items of different mass, e.g., a penny and a quarter.
How do their weights compare? How can you tell?Drop the items at the same time from rest.
Make a strobe photograph sketch and describe the motion until it hits the ground.
Did weight affect the motion?
If one of the objects was a sheet of paper, why would this be or would not be a good investigation of "weight"?
Did mass affect weight?
Does the weight change if an object sits on a table? If so, how /why? If not, why doesn't it fall? What if the table top was changed to 3 pieces of a spider web?
You are standing on a board suspended between two chairs.
Do you have any motion, i. e., what is your velocity? What is your acceleration?
Do you have a "weight" interaction?
Are there any other forces interacting with your body?
If the board breaks, what forces are interacting with your body?
Do you have any motion, i. e., what is your velocity? What is your acceleration?
Is it more difficult to make a bike role or an automobile (both in neutral and stopped on a flat road)?
Background
Newton presented 3 laws of motion and a law of gravitation to explain motion. These laws have been supported by all the measurements taken to test them upto the twentieth century. With the twentieth century, there have been some refinements to account for very fast speeds (approaching the speed of light). They still work for every day situations.
Newton's First Law
This law is sometimes called the law of inertia. It is better to think of this law as a qualifier for the second law. It coorelates balanced forces (sum of forces = 0) with uniform motion (constant velocity which includes velocity = 0). If this situation isn't true, then Newton's Second Law won't work without modifications. It accounts for rotating and accelerating coordinate axii, which are called non-inertial coordinate systems. For example, there is an amusement park ride called the Rotor among other things. In the ride, you stand against the wall while the room spins. Eventually, the floor drops, but you "stick" to the wall.Imagine you put a ruler next to you on the wall to define your coordinate system. Compared to the ruler, you don't move, yet you feel like there is a force "pushing" you into the wall. There is nothing to cause this force. Vertically, you sense weight pullling you down and friction with the wall pushing you up canceling each other out. Horizontally, nothing is there to provide the "push" into the wall. This is called a centrifugal force, a fictious force. Someone above you would explain the forces you feel in terms of the rotating room. But, in your coordinate system the room isn't rotating.
In fact, the earth is a non-inertial coordinate system since it is spinning, but it is small. You must look at something for a long time or on a very large scale to see the effect. Storms and wind patterns go around in circles because of the earth's rotation effects. Large projectiles sent large distances (at least several miles) curve like the storms as well. Pendulums spin around (look up references on a Foulcault Pendulum).
Newton's Second Law
This law is the calculation law. The first law lets you test your coordinate system to see if you can use this law. The second lets you describe why there is motion and then use the results to predict the motion. A force is a an interaction between two objects. The force interaction may change the motion (start, stop, prevent, redirect,... ) of the objects. Often we are interested in one particular object. We look at all the things interacting with it through forces, but are only conerned at the interaction at the object of interest. For example, a person on the earth has weight because of an interaction between the person and the earth. But, weight only looks at the effect of the interaction on the person from the earth, not vise versa.
Newton recognized this effect. He also noted that forces vary in amount (magnitude) and direction. The interaction of weight on your body is down into the earth not horizontal to the surface. Newton recognized that the more mass an object has, the more force required to change the motion. And, Newton recognized that accleration measures the change in motion (velocity). So, for the same mass the large the force the larger the possible accleration. This was put together in equation form often seen as F=ma (bold means it has amount and direction). That form is misleading. The "F" in the equation is actually the net force or the sum (with direction) of all the forces interacting with the object. The Equation is the sum of the forces on an object equals the mass of the object times its accleration. In equation form
To apply this law, you first choose and object or group of objects which is called the system. You then identify all the other objects which interact with the system (producing a force interaction on the system). You then apply the pieces of information known and solve for the unknown quantities. Often the accleration is found and then motion can be predicted using the motion relations. It could be you have a desired accleration and a known mass. Then you would calculate the required force for these knowns. Or, you may have known forces and accleration and need to calcuate the mass.
Newton's Third Law
This law describes the interaction. It has nothing to do with the motion. It says the force interaction between two objects is equal in amount but opposite in direction. Push your right and left hand together. The right hand experiences a push from the left hand. The left hand experiences a push from the right hand. The amount of the push is the same because they are mutually interacting. Only the direction of the push seems different - opposite each other.
Whether or not a motion occurs depends upon the other interactions occuring on the object which Newton's Second Law addresses. You could think of Newton's Third law as a sharing law - you give to me, I give back to you equally or object 1 interacts with object 2 and object 2 interacts with object 1equally. Nothing is said about motion or any other interactions which are occurring. This is done in Newton's Second law which could be thought of as a selfish law. In that case a system is defined and the only question asked is "what is everything else doing to the system?", i. e. from the system's perspective, "what are you giving me?"
Apparatus
low friction car and track, smart pulley, ULI interface, computer, string, hanging masses, ruler, balance
Suggested Procedure
To investigate the relationship between motion, mass, and force stated in Newton's Second Law, we will perform the following experiment.
A cart will be pulled by a hanging mass. The two will be tied together with a string. The force pulling the two masses will be measured (calculated), the mass of the two masses will be measured (and kept constant), and the acceleration of the two masses will be measured. We will see if there is any relationship between the moving mass (car and hanging), acceleration, and the net (unbalanced) force.
Since the car, the mass in it, and the hanging mass are tied together by a string, they move as a unit. In the above diagram, the car can't go left while the hangin mass goes down. If one is moving at 10 m/s the other must be too. If one acclerates, the other one must too. The pulley can be thought of as "bending" the x axis to keep it along the string and keeping the motion compared to the string direction as one axis. Thus, the system we will use for Newton's second law to determine forces and mass and accleration are the car, string and hanging mass together.
What forces from outside the system are there interacting on the car, the string, and hanging mass?
Do they affect the measurement, i. e., are there other forces which are in opposite direction and balancing the two (why or why not)?
Measure the mass of the car.
Place at least 10 "5 g" masses in the car.
Begin Logger Pro and begin the N2Law experiment (requires the Pasco rotational motion probe plugged into port 2 of the the ULI).
With the 50 g mass holder hanging over the pulley, pull the car back on the track. (Place a large object near the end of the track to stop the car.)
Begin collecting data.
Let the car go.
Record the average acceleration, the hanging mass, the mass of the car (including what is in it).
Move one mass from the car to the mass hanger.
Repeat the acceleration measurement.
Repeat this until all the mass is out of the car.
Complete the calculations based on the data.
Plot the variables for Newton's Second Law to see if there is a relationship between moving mass (system mass, car and hanging mass), acceleration, and net (unbalanced) force. It may help to rearange Newton's Second law equation so it is in the form of y=mx+b matchingwhat you plotted.
What relationship did you find? How do the statistics support this?