Glider on air-track: Quantitative Observational Experiment

Aim

To establish a relationship between the acceleration of a glider and the force exerted on the glider by the spring.

Prior Knowledge

• Kinematics: position, velocity and acceleration.
• Graphing skills.
• Elementary knowledge of springs

Description of the Experiment

A glider is set up on a level air track. A spring scale is mounted on top of the glider. The spring scale will indicate the amount of force exerted on the glider. A string is attached to the spring scale and then hung via a pulley over the end of the track. Objects of various masses are hung on the end of the string so as to exert a constant force on the glider. For various objects, the glider is released and allowed to move under the influence of the force exerted on it by the spring scale.

Addtional Information

There are two things you should focus on. One is the reading on the spring scale when the glider is moving. The second is the motion of the glider relative to the ruler attached to the side of the air-track. You may observe that the cart appears to be going ``backwards'' (relative to the camera) at some points. This is because the camera is panning faster than the cart is moving. Do not be confused by this: the motion of the cart relative to the ruler mounted on the airtrack is what is important.

The spring scale is quite hard to read. The readings on the scale are provided below.

Force readings (unknown units)
Trial 1	1
Trial 2	1.3
Trial 3	1.6
Trial 4	1.9
Trial 5	3.1

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Questions

1. Analysing the motion of the glider.

   • For one particular force reading, draw a motion diagram of the glider, analysing the video frame by frame.
   
   
   
   • Is the glider's speed constant or changing? How can you tell?
   
   
   
   • Next, plot a graph of the glider's position as a function of time.
   
   
   
   • What is the shape of the curve that you get?
   
   
   
   • What does this tell you about the acceleration of the glider?
   
   
   
   • Using the position and time data that you have, what sort of graph could you plot in order to determine the acceleration of the ball most accurately?
     
     
     • Consider the different variables you might choose to get a straight line graph whose slope would yield the acceleration.
     • What problems might arise? Consider particularly possible sources of systematic error in your analysis. Where do they come from? Can you eliminate all of them?
   
   
   
   • The end result of this discussion is that it is possible to eliminate the systematic errors if you are careful, but it is going to be extremely difficult. It is easier to fit the correct polynomial curve to a graph of position versus time and obtain the acceleration from the best fit curve. This can be done using excel or your favourite data analysis software.
   
   
   
   • Repeat this process finding the acceleration of the glider for each of the different forces exerted on the glider by the spring scale.

2. The force

   • From the discussion on Newton's first law, you should understand that an object changes its velocity only due t the interactions with other objects (for observers in inertial reference frames).
   
   
   
   • Focus your attention on the spring scale. The stretch of the spring will indicate the net force exerted on the glider.
   
   
   
   • Note: Only read the force when the glider is moving, not when it is being held.

3. Relationship between force and acceleration

   • First decide which variable is the dependent one and which is the independent one. If you are unsure, ask yourself: ``Does a change in force cause a change in acceleration?'' (Acceleration depends on force.) Or, ``does a change in acceleration cause a change in force?'' (Force depends on acceleration.)
   
   
   
   • Next, plot a graph of force vs acceleration or acceleration vs force according to which variable is the dependent one. Do you get a straight line?
   
   
   
   • If you get a straight line, how are force and acceleration related?
   
   
   
   • If you did not get a straight line, what sort of relationship would you guess between force and acceleration, based on the shape of the curve?
   
   
   
   • Test your guess by plotting the new variables and seeing if you get a straight line.
   
   
   
   • If a straight line is not obtained, try again.