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74 Chapter 2 | Kinematics
Figure 2.56
We need to solve for acceleration . Note that in this case, displacement is downward and therefore negative, as is acceleration.
Solution
1. Identify the knowns. ; ; ; .
2. Choose the equation that allows you to solve for using the known values.
3. Substitute 0 for and rearrange the equation to solve for . Substituting 0 for yields
(2.83)
(2.84)
(2.85)
(2.86)
(2.87)
Solving for gives
4. Substitute known values yields
so, because with the directions we have chosen,
Discussion
The negative value for indicates that the gravitational acceleration is downward, as expected. We expect the value to be somewhere around the average value of , so makes sense. Since the data going into the
calculation are relatively precise, this value for is more precise than the average value of ; it represents the local value for the acceleration due to gravity.
Applying the Science Practices: Finding Acceleration Due to Gravity
While it is well established that the acceleration due to gravity is quite nearly 9.8 m/s2 at all locations on Earth, you can verify this for yourself with some basic materials.
Your task is to find the acceleration due to gravity at your location. Achieving an acceleration of precisely 9.8 m/s2 will be difficult. However, with good preparation and attention to detail, you should be able to get close. Before you begin working, consider the following questions.
What measurements will you need to take in order to find the acceleration due to gravity?
What relationships and equations found in this chapter may be useful in calculating the acceleration?
What variables will you need to hold constant?
What materials will you use to record your measurements?
Upon completing these four questions, record your procedure. Once recorded, you may carry out the experiment. If you find that your experiment cannot be carried out, you may revise your procedure.
Once you have found your experimental acceleration, compare it to the assumed value of 9.8 m/s2. If error exists, what were the likely sources of this error? How could you change your procedure in order to improve the accuracy of your findings?
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