Experiment: Acceleration on an Inclined Track

Daniel Jung
Tyler Moore, Dil Querido
Physics/ 2
Mr. Elwer

Introduction
   1. Background info
      Acceleration is equal to the rate of a change of velocity. Thus, in the velocity versus time graph, the slope is acceleration (m/s^2). The coefficient of the acceleration is reveals the direction related to the sensor.
      If a cart moves on a tilted plane with the angle of θ, the force to move it along the surface is equal to mgsinθ. g is the acceleration constant of gravity on Earth. gsinθ is the actual acceleration on the tilted plane.
   2. What concept is being explored/ investigated
      The relationships between acceleration, velocity, and position. The meaning of the plus and minus signs of them. The motion of an object on a tilted plane where there is no other major forces except gravity.
   3. Purpose of the experiment
      Students will get accustommed to Xplorer GLX. Students will know the relationships between position, velocity, and acceleration by graphs measured by GLX.
   4. Hypothesis
      As the force is constant by mgsinθ, acceleration will be constant by sin θ. As the cart starts away from the sensor, comes, stops, and goes away, the velocity will start from negative value to positive value. The slope of the velocity graph will be constant. The position-time graph will be from positive(as the position is the distance from the sensor) ,and it will decrease and increase, showing u shaped graph.

Materials
   1. a mini-car
   2. a PASCO track for the car to move on
   3. a xplorer GLX
   4. a GLX motion sensor
   5. couple of books to make an inclined track
   6. a computer to save graphs from GLX

Experimental Design
   1. The experiment will measure the position of a mini-car according to time. The position should be varied only by gravity. Thus, the track should be plain and has as little, or regular friction as possible. The car will move along the track linearly, and the motion sensor that's attached to the track will measure the exact distance between itself and the car. The car will be pushed by hand softly.
   2. Controlled Variables :
     a. The angle of the inclined track, or gravitational acceleration (g sinθ).
     b. The friction of the track. The track should be dry, clean and even.
     c. The shape and mass of the mini-car
     d. The force toward the car will exist only at the first time where a hand pushes the car. Thus, the experiment will be done in an isolated room without any fan or airconditioner.
     * As this experiment is to see the relationship with position, velocity, and acceleration, there will be no independent (or manipulated ) variable.
   3. Dependent Variables :
     a. both average and instantaneous position, velocity, and acceleration.

Procedures
   1. Attach the motion sensor to GLX.
   2. Turn the GLX on.
   3. Make an inclined track using books. Beware to make the track as even as possible, so avoid using uneven books.
   4. Attach the motion sensor at the end of a track where books are located.
   5. Put the mini-car at the bottom of the track.
   6. Activate the sensor through your GLX.
   7. Push the car softly but firmly toward the sensor. Control the strength so that the car can stop no closer than 15cm to the sensor. Otherwise, the measurement will become inaccurate.
   8. Finish the measurement through your GLX when the car returns to the initial position.
   9. Repeat the measurement until the graph seems natural and without radical change.
   10. Record the position-time graph.
   11. Change the y-axis to velocity (m/s) on GLX. (check-check-menu-more-velocity)
   12. Use the arrow keys to put the cursor to the point on the graph where the linear movement started.
   13. Press F3 to open the 'Tools' menu.
   14. Select 'Linear Fit' and press the check button.
   15. Record the data and graph.
   16. Again, press F3 to open the tools menu. Deselect 'Linear Fit'.
   17. Change the y-axis to acceleration as it's done in 11.
   18. Move the cursor to the initial point of the movement.
   19. Press the check button to open the tools menu. Activate the 'Statistics'.
   20. Record the data and graph.

Data Table (Data is included in the graphs) (SI units (m, s) are used)
   1. Velocity-Time graph

2. Acceleration-Time graph



   3. Relationships
     The slope of velocity-time graph is same as the average acceleration. Both are some 1.0 .
     Also, the slope of the position-time graph is same as the velocity. The sign of the velocity shows the direction of the car.

Conclusion
   1. The slope of position-time graph was same as the velocity. The slope of the velocity-time graph was same as the acceleration.
   2. The sign of the values represented direction of the car 
   3. Visible Errors : The graph, especially acceleration-time graph, is not completely even. The error can be derived from uneven friction of the track, uneven, or rusted wheel of the mini-car, or inaccuracy of the sensor.
   4. Recommended Improvement : The most accurate, if possible, way to measure this relationship will not include a wheel. Also, it may be done on a evenly-cut ice to reduce the friction.
   5. Questions from the worksheet
       1. The sensor can calculate the distance between itself and a moving object. Thus, if the object comes toward a sensor, it means the total distance becomes shorter. That' why the distance value in the graph decreases as the object, a cart, moves up the inclined plane.
       2. The velocity was increasing. The slope of the velocity was constant.
       3. Accelaration value didn't show major change. The slight curves inside the straight line may suggest the unevenness of the surface, or inaccuracy of the sensor.
       4. The correlation between the slope of velocity and the average acceleration is very strong. They are almost same.