Description
Part 3: Measuring Gravitational Acceleration
In this part of the course project, we apply what we have learned about motion as a change of position to find the gravitational acceleration of a free-falling object using the ultrasonic sensor. This data will also be used in the next module to investigate the conservation of energy. The location of an object undergoing constant acceleration, such as an object in free-fall, can be written as:
where y is position, is the initial position, is the initial velocity, t is the time of flight, and a is the acceleration.
We can use this formula to determine the acceleration of an object falling towards the ground. This acceleration is commonly referred to as the acceleration due to gravity, and is given the symbol g. The approximate magnitude of acceleration due to gravity is g = 9.80 m/s2.
If an object falls from rest ( = 0), the fall distance from a reference point as a function of time y(t) can be expressed as
where y0 is the initial distance from the reference point.
From equation (1), the distance as a function of time can be modeled using a quadratic function.
In Excel, a quadratic best fit on a graph is of the form
where ‘a’, ‘b’ and ‘c’ are constants that are determined automatically by the fitting algorithm. Comparing equations (1) and (2), by graphing our data in Excel with time (t) as the x-coordinate, we can determine the acceleration due to gravity approximately using the coefficient of x2 as
Solving for ‘g’, we find
The value calculated from the above equation should be close to the acceleration due to gravity.
Objectives
- To generate an experimental set up to observe the laws of physics
- To determine the value of the acceleration due to gravity of a free-falling object
- To train in scientific method of observation
- To acquire experience handling of electronics equipment
- To collect scientific data
- To compute reliable results and draw valid conclusions from data
Deliverables
- Complete the Course Project PowerPoint Deliverable
- Include a picture of experiment set up for the course project
- Include screenshot of serial monitor showing your name
- Include a screenshot of your table and graph in Excel for one trial
- Conduct analysis of collected data
- Answer questions to draw valid conclusions from data
