MATH - SCIENCE INTEGRATION

bullet1 CALCULATING FORCES OF MOTION

bullet2 Basic Concepts

Perfect as the wing of a bird may be, it will never enable the bird to fly if unsupported by the air. Facts are the air of science. Without them a man of science can never rise.
Ivan Pavlov (1849 - 1936)


bullet3 Introduction to Basic Concepts
OVERVIEW:
How can you tell if something is moving?  
Sounds like a pretty simple question, right?  

 


Well try to explain it to someone else.  
Go ahead, write down a short explanation on how you can tell whether or not an object is moving.





  • Your Description of Motion
    In your written explanation, you should have mentioned that the object changed from one position to another and that you could tell that the position changed because the original background in which you saw your object is no longer the same.  

    For example, you can tell that a person is running in a race because you saw the person start from the starting line and now the person is moving away from the starting line and toward the finish line.  
    The starting line and the finish line are points of reference. The start and finish lines do not move and you can tell that the runner is moving in relationship to their position to the lines.  You can measure the distance the person moved from the starting line (fixed point).




     
    • Detecting Motion
      Can you describe the motion of an object?  


      Click on the link below and see if you can tell whether the teddy bears are in motion.  Using the scientific definition of motion and the correct terms for motion, jot down on your paper your arguments on whether the teddy bears are/aren't moving.


      After you finish watching the bears, hit the back arrow on your browser and return to this page.





       
      • In Your Classroom
        In your science class, you are learning about forces and their relationship to motion.

        This lesson will remind you of the basic concepts taught to you by your teacher and then you will get a chance to practice the calculations needed to solve force problems.


        It's time to look at the objective for this lesson.



         

bullet3 Objectives of this unit

When you are finished with this lesson, you should be able to write a response to each of the objectives below.  We'll give you a little quiz at the end of this lesson to see how you are doing.

  • What is motion and how is it determined?


  • What is force?

  • Define speed.


  • What is acceleration?

  • Define velocity.


  • Define momentum.




bullet3 Motion

MOTION


DEFINITION:   Motion  is the change of position or location of an object.

What do we need to know in order to determine motion?  
We must have a fixed point that is used as a point of reference. The location of the object must change in relationship to the fixed point.


In the introduction to this lesson, a runner's motion was detected by using two fixed points, the starting line and the finish line.


When you described the motion of the teddy bears, what did you use as your point of reference?  There is more than one point of reference that could be used.

Now it's time to see what causes the motion of an object.



bullet3 Force

DEFINITION:  A force is a push or a pull.

In order for motion to take place, there has to be a force applied upon the object.  But does that mean that objects that are not moving have no forces working on them?  
Does that cereal bowl sitting on your kitchen counter have any forces working on it?  

What do you think?


  • Non-Moving Objects and Force
    Do objects that are not moving have forces working on them? YES!

    Let's talk about the cereal bowl that is sitting still on a kitchen counter.  You know that gravity is working on EVERY object on earth.  So gravity is pulling the bowl toward the center of the earth.
    Why isn't it falling?  Because the kitchen counter is pushing up on the bowl.  The bowl doesn't move because the counter pushes up on the bowl at the same force as gravity is pulling it down.




     
    • Types of Force
      Scientists talk about forces by the way the forces are working.  Take a look:


      Net forces  are a combination of all of the forces acting on an object.  These net forces determine whether an object will move or not move.


      Balanced forces  are the forces that act on an object and combine to produce a net force of zero.  In other words, all of the forces on the object are equal, so there is no motion.  The forces acting on the cereal bowl are balanced forces and so the bowl is not in motion.


      Unbalanced forces  are those forces acting on an object that combine to produce a net nonzero force. This means that some forces are greater than others acting on an object, so the object will be in motion.   
         


      If you would take your hand and push the cereal bowl across the counter, the force applied by your hand is greater than the forces that hold it still.  You have applied an unbalanced force, so the bowl is in motion. Unbalanced forces do not cancel completely and can cause measureable movement in an object.
       


      Let's look at measuring movement.



       
      • The Effect of Forces on Motion
        This lesson focuses on the measurement of motion by objects. You know that unbalanced forces cause motion.  What kind of motion measurements can you take?

        Questions like, "How far?" , "How fast?" , and "How long did it   take?"   refer to values that measure the motion of an object.

        These are the values we will calculate in this lesson:

        • speed and velocity
        • acceleration
        • momentum
                                               


        All of the above values mathematically describe the motion of an object due to the forces acting on the object.  We need to look at each one separately.  Let's start with speed.



        » See also: Force Practice Problems
         

bullet3 Speed

DEFINITION:   Speed  is the distance traveled in a specific amount of time.  Speed describes how fast an object moves.
   
In order to calculate speed, you need to know two things, the distance an object traveled and the amount of time that it took the object to travel the distance.


 



  • Constant and Average Speed
    When objects move an equal distance in an equal amount of time, they are moving at a constant speed .  


    Most objects do not maintain a constant speed, they speed up and slow down as the forces acting on them change.  

    It is much more useful to measure the average speed of an object.   Average speed  is the distance covered by an object divided by the time it takes to travel that distance.


    We will calculate average speed in our lessons.  Let's look at the equation for average speed.



     
    • Speed Equation
      SPEED EQUATION:
      speed = distance          or      v = d
                       time                               t

      • v represents speed in the equation.  The SI unit for speed is meters per second (m/s).
      • d represents distance in the equation.  The SI unit for distance is meters (m).
      • t represents time in the equation.  The SI unit for time is seconds (s).




       
      • Sample Calculation
        Let's look at a sample calculation for speed.


        If a track runner sprints the 100 meter dash in 12.7 seconds, what is her speed?


        v= 100m =    7.87m/s
            12.7s

        The speed of the track runner is 7.87 m/s.


        Before we go any further into calculating speed, we need to look at velocity. They are closely related and we can learn both calculations at one time.



         

bullet3 Velocity

DEFINITION:   Velocity  is a quantity that describes both speed and direction.

Many times, the speed of an object is not enough information about the motion of the object.  Read the story on the next page and write down some possible problems with the information given by the witness of an accident.




I

  • Scene of the Crime


    A driver of a red sedan runs a red light at an intersection and hits another car.  There was only one witness who saw the accident and what happened next.  The driver of the red car left the scene of the accident and raced away.  The witness was very observent and was able to give a police officer a good deal of information. The witness told the policman the length of time since the accident and a close approximation of the car's speed.  With this information, the officer could calculate about how far the red car has gone since the accident.  


    But can you think of a piece of added scientific information that would help the officer quickly catch the driver of the car?  Think for a minute!  Hint:  The accident happened at an intersection.




     
    • Direction


      What about the direction in which the car took?  The officer might calculate that the car was 25 miles away, but is it 25 miles to the north, east, south, or west?  Direction in this case is critical.  The officer needed the velocity of the car, not just the speed.

      Time for you to look at calculating the speed and velocity of objects in motion!



       
      • Velocity Equation
        When calculating velocity, we use the same equation used for speed since distance and time are still required.  But we also add direction to our answer.  Below is an example of velocity.


        A train is traveling north at a rate of 12,879 meters in 345 seconds.  What is the velocity of the train?


        v =  d  =   12,879m  =  37.33m/s north
              t           345s


        How about some practice on calculating speed and velocity?  Click on the link below to see the steps and practice problems.



        » See also: Methods for calculating
         

bullet3 Acceleration

DEFINITION: Acceleration  is a change in velocity.  
This is calculated by dividing the velocity of an object by the time interval in which the change took place.  Positive acceleration is an increase in speed and negative acceleration is a decrease in speed.  Outside of science, we sometimes refer to negative acceleration as deceleration.


  • Example of Acceleration
    An example of acceleration:  A new car manufacturer is testing a design model and they want to know how quickly the car can accelerate.  The car goes from 0 m/s to 96 m/s in 10s.  
    You can see that there are several pieces of information in the above statement.  You know that at the beginning of the ten second time period, the car was not moving (0 m/s).  And you also know that at the end of the ten seconds the car was traveling 96 m/s.  The time interval was ten seconds.  We will use these pieces of information to calculate the rate at which the car accelerated and place them in an equation.



     
    • Acceleration Formula
      acceleration = final velocity - initial velocity         
                                          time

      OR

      a = vf – vi  =     D v
               t               t           or

      OR

      a =    D v  
               t


      • a represents acceleration.
      • D v represents a change in velocity.  The D  (delta) symbol represents "a change in..." and is followed by another symbol in an equation.  For example   DT means a change in temperature.
      • vf – vi   represents final velocity minus initial velocity.
          t represents time.






         




      » See also: Methods for Solving Problems
       
      • Acceleration of Test Car
        Let's look at the test car problem from earlier.


        A new car manufacturer is testing a design model and they want to know how quickly the car can accelerate.  The car goes from 0 m/s to 96 m/s in 10s.

        Using the information about the car above we can calculate its acceleration by putting the velocity and time into the equation:
        a = 96.0 m/s – 0 m/s =  96.0 m/s  =  9.6 m/s2
                         10 s                   10 s   
        • Notice that the unit is meters/second/second or m/s2.  This is because the object is accelerating at a rate of 9.6m/s every second.

        The acceleration of the car is 9.6 m/s2.  
        • Be careful of SI units when working with velocity and acceleration problems.  The SI unit for velocity is m/s, but the SI unit for acceleration is m/s2.   Make sure you check and see what units the problem is asking for.  You may also need to do some converting in certain problems.

        Its time to look at the steps for solving acceleration problems and to practice some calculations.



         

bullet3 Momentum

DEFINITION:  Momentum  is a quantity defined as the product of an object's mass and its velocity.


When considering the motion of an object, you not only need to look at an object's velocity, but its mass.  An object with a greater mass will move differently than an object with a lesser object.  
       
This consideration is most important when we are trying to stop the motion of objects.   


  • Example of Momentum
    Let's look at the momentum of two real objects.


    If we have two balls that are rolling down an alley at 7m/s and one is a tennis ball with a mass of .25kg and a bowling ball with a mass of 2.5kg, which one do you think would be harder to stop?  


    It will take a greater force to stop the bowling ball because its momentum is greater.  The bowling ball has greater mass, so that if both balls are moving at the same speed, the mass of the balls will make the difference.  You will better understand this if you look at the math!

    Let's look at the equation for momentum.



     
    • Momentum Equation
      momentum = mass x velocity  or
      p = mv


      Because momentum includes velocity, momentum solutions must also include a direction.  We'll use the information about the tennis ball and bowling ball and place it in the formula to calculate their momentum .

      Momentum of tennis ball:                           
      p = (.25kg) (7m/s) = 1.75m/s down the alley   
       
      Momentum of bowling ball:
      p = (2.5kg) (7m/s) = 17.5m/s down the alley

      As you can see above, the momentum of the bowling ball is ten times greater than the tennis ball.  It would take ten times the force to stop the bowling ball than it would to stop the tennis ball.  Notice that the phrase down the alley is included in the answer.  That is because momentum solutions must include direction.  Remember that directions do not have to be cardinal directions (north, east, south, west), but can be description of motion.  For instance, up the hill,  toward the wall, and across the field, are all directions of motion.  

       



      » See also: Definition of Momentum
       
      • Why Consider Momentum?
        Momentum is a serious consideration for automobile engineers who design braking systems.  The mass of vehicles is very different.  
                      
        The mass of an SUV is much greater than a compact car, so if both vehicles were traveling 35 miles per hour, it would require that the braking system of the SUV apply more force to stop it than the braking system of the compact car.

        For the steps of solving momentum problems and some practice, click below.