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Distance and Constant Acceleration

Difficulty
Time Required Short (2-5 days)
Prerequisites None
Material Availability Readily available
Cost Low ($20 - $50)
Safety No issues

Abstract

This project is an experiment in classical physics. You'll be following in Galileo's footsteps, and investigating Newton's laws of motion, using a metronome as your timing device. Sure, it's been done before, but if you do it yourself, you can get a firm understanding of these important concepts.

Objective

The objective of this project is to determine the relation between elapsed time and distance traveled when a moving object is under constant acceleration.

Credits

Andrew Olson, Ph.D., Science Buddies

Cite This Page

MLA Style

Science Buddies Staff. "Distance and Constant Acceleration" Science Buddies. Science Buddies, 30 June 2014. Web. 2 Sep. 2014 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p026.shtml>

APA Style

Science Buddies Staff. (2014, June 30). Distance and Constant Acceleration. Retrieved September 2, 2014 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p026.shtml

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Last edit date: 2014-06-30

Introduction

You know from experience that when you ride your bike down a hill, it's easy to go fast. Gravity is giving you an extra push, so you don't have to do all the work with the pedals. You also know from experience that the longer the hill, the faster you go. The longer you feel that push from gravity, the faster it makes you go. Finally, you also know that the steeper the hill, the faster you go.

The maximum steepness is a sheer vertical drop-free fall-when gravity gives the biggest push of all. You wouldn't want to try that on your bicycle!

In free fall, with every passing second, gravity accelerates the object (increases its velocity) by 9.8 meters (32 feet) per second. So after one second, the object would be falling at 9.8 m/s (32 ft/s). After two seconds, the object would be falling at 19.5 m/s (64 ft/s). After three seconds, the object would be falling at 29 m/s (96 ft/s), and so on.

Measuring the speed of objects in free fall is not easy, because they fall so quickly. There is another way to make measurements of objects in motion under constant acceleration: use an inclined plane. An inclined plane is simply a ramp. You're making a hill with a constant, known slope. With a more shallow slope, the acceleration due to gravity is small, and the object will move at a speed that is more easily measured.

This project will help you make some scientific measurements of the "push" from gravity, using a marble rolling down an inclined plane, with a metronome for measuring time.

Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:

  • velocity,
  • acceleration,
  • inclined plane,
  • mass,
  • gravity.

Questions

  • What is the formula for velocity as a function of time when an object is subject to constant acceleration?
  • What is the formula for distance traveled as a function of time when an object is subject to constant acceleration?

Bibliography

Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • inclined plane:
    • you'll need a flat board, about 2 m long (longer is better unless you are using a video camera);
    • cut a groove straight down the middle to guide the rolling marble, or
    • glue a straight piece of wood along the length of the board to act as a guide;
    • mark a starting line across one end;
    • you will also need some wood blocks (about 2.5 cm thickness) to raise up one end of the board.
  • tape measure (for measuring height and length of inclined plane),
  • marble,
  • metronome,
  • helper,
  • pencil.

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Experimental Procedure

In this experiment, the goal is to measure the distance the marble travels in equal time intervals as it rolls down an inclined plane.

  1. Set up your inclined plane on a single block, so that it has a low slope. If the slope is too high, the marble will roll too fast, and it will be too hard to make accurate measurements.
  2. Hold a marble in place at the starting line.
  3. Use a metronome to keep track of equal time intervals.
    1. You can set the number of beats per minute that the metronome will sound.
    2. 60 beats per minute would give you one tick every second.
    3. 120 beats per minute gives you two ticks every second, or one tick every half-second.
    4. We suggest that you start with one tick every second.
  4. In time with a tick, release the marble, being careful not to give it a push as you let go.
  5. Have your helper mark where the marble is at the first tick after release.
  6. Measure and record the distance (cm) from the starting line.
  7. Repeat this 10 times.
  8. Next your helper will mark where the marble is at the second tick.
  9. Measure and record the distance (cm) from the starting line.
  10. Repeat this 10 times.
  11. Keep repeating the process for each successive tick, making 10 measurements for each tick, until the tick when the ball goes past the end of the inclined plane.
  12. Calculate the average distance the marble traveled over 10 trials for each tick.
  13. Graph the average distance traveled (y-axis) vs. time (x-axis) in terms of the number of metronome ticks (for example, 1 second or 1/2 second).
  14. Graph the average distance traveled (y-axis) vs. time squared. Compare the two graphs.
  15. Another way to see the relationship between time and distance traveled with constant acceleration is is to use the distance traveled during the first "tick" as the distance unit instead of centimeters. How many of these distance units has the ball traveled by the second tick? By the third tick? By the fourth tick? By the fifth tick?

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Variations

  • Does the mass of the marble affect its acceleration? Try the experiment with marbles of different masses. Or, even better, compare a steel marble (e.g., a pinball or a large ball bearing) with a glass marble of the same diameter. Use a gram balance to weigh each marble (you can always weigh them at the post office if you don't have a gram balance available at home or school). Is the acceleration the same or different for the marbles with different masses?
  • For another method of measuring distance traveled and velocity of an object rolling down an inclined plane, see the Science Buddies project, Distance and Speed of Rolling Objects Measured from Video Recordings.
  • Use your measurements to calculate the approximate velocity of the marble at each tick. As an example, to calculate the average velocity at the second metronome tick, take the distance the marble has traveled by the second tick, and subtract the distance the marble traveled by the previous tick. Divide the result by the amount of time per tick. Repeat this calculation for several successive time points to see how velocity changes as the marble rolls down the ramp. Make a graph of velocity (y-axis) vs. time (x-axis). Does this graph look more like the distance vs. time or the distance vs. time squared graph?
  • One reason a marble was chosen for this experiment was to minimize the frictional forces which counteract the acceleration of gravity. Try repeating the experiment with other rolling objects (e.g., a toy car with the same mass as the marble) or different surface treatments (e.g., smooth, waxed surface, vs. rough, sandpapered surface). Can you detect a decrease in acceleration due to increased friction?
  • For more advanced students:
    • If you have studied trigonometry, you should be able to derive a formula that describes the acceleration, a, of the marble as function of the angle, θ, of the inclined plane (see Henderson, 2004).
    • If you have studied calculus, you should be able to explain both velocity and acceleration as the first and second derivatives, respectively, of distance traveled with respect to time. Conversely, you should be able to explain velocity and distance traveled at a given time as the first and second integrals, respectively, of acceleration with respect to time.

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