Experiment Help: Investigating Freely Falling Bodies

In summary, the distance traveled is the area under a velocity/time graph. If you tried to compute the area of a portion of the velocity-time graph I drew you would come up with the following equation: d=\frac{(v_{f}+v_{o})*t}{2}+\frac{2v_{o}*t}{2}.
  • #1
bilalbajwa
28
0
Experiment Help!

Homework Statement


We were given this experiment in which we have to investigate the motion of a freely falling body on a fictitious planet.

2. Things we have to do
(1) the value of the acceleration due to gravity on the planet, (sucessfully did it)
(2) how the distance fallen depends on the elapsed time, and :confused:
(3) an interesting relation between the instantaneous velocity at the center of a time interval and the average velocity over that interval. :confused:

Can anybody explain me what will be the conclusion of the part (2)
and part (3).
 
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  • #2
Is there friction at the surface of the planet?
Assuming there isn't, you can still use the vector kinematics formulas.
For example, you can think about
d = vo*t + 1/2 a t^2
 
  • #3
Can you give us more information on what measurements were given?
 
  • #4
Since acceleration is constant, your acceleration vs time graph will look like this :

f_acceleratiom_9d47c19.png


Since acceleration is constant, the velocity changes at a constant rate every second and thus the velocity time graph is ALWAYS linear under constant acceleration like so:

f_velocitym_556c3b3.png


Note: these images are not to scale with each other.

For number 3, what is the equation for the midpoint of a line, can you you use this relationship to find an interesting equation for the relationship between the initial velocity, the final velocity, and the average velocity under constant acceleration?

A little bit of extra information since I made these graphs anyway, I want to show you another interesting relationship.

You probably notice that the distance traveled is the area under a velocity/time graph?

If you tried to compute the area of a portion of the velocity-time graph I drew you would come up with the following equation:

f_aream_fdbac81.png


For the red area, the area is [tex]v_{o}*t[/tex] and for the bluish area the area can be found by [tex]\frac{1}{2}(v_{f}-v_{o})*t[/tex]

Which can be combined to form [tex]d=\frac{(v_{f}-v_{o})*t}{2}+\frac{2v_{o}*t}{2}[/tex] which is equal to [tex]d=\frac{(v_{f}+v_{o})*t}{2}[/tex] which is a well known kinematics equation that you probably use ;-).

I added this in because you seem to enjoy developing a good understanding of physics in the other threads and the solution to #3 of your problem is very similiar. :wink:
 
Last edited:
  • #5
Thanks a lot for reply and this wonderfull equation relationship!
Please be tune i am going to show u a lab experiment!
 
  • #6
Did you get #2 and #3 solved? :smile:
 

1. What is the purpose of investigating freely falling bodies in an experiment?

The purpose of investigating freely falling bodies is to understand the laws of motion and gravity. By studying the motion of objects as they fall, we can gain knowledge about the forces acting on them and how they behave in different environments.

2. How do you set up an experiment to investigate freely falling bodies?

To set up an experiment, you will need a tall, open space and a timer. First, drop a small object (such as a ball) from a known height and measure the time it takes to reach the ground. Repeat this multiple times and record the data. Then, repeat the experiment with different heights and objects to gather more data.

3. What variables should be controlled in an experiment investigating freely falling bodies?

The variables that should be controlled include the mass and shape of the objects being dropped, the height from which they are dropped, and the environment (such as air resistance). By keeping these variables constant, we can accurately measure the effects of gravity on freely falling bodies.

4. How can you calculate the acceleration of a freely falling body using experimental data?

To calculate the acceleration of a freely falling body, you can use the equation a = (2d)/t^2, where a is the acceleration, d is the distance the object falls, and t is the time it takes to fall. By plugging in the values from your experiment, you can determine the acceleration due to gravity.

5. What are some possible sources of error in an experiment investigating freely falling bodies?

Some sources of error in this experiment may include human error in timing the fall of the object, variations in the height from which the object is dropped, and air resistance. It is important to repeat the experiment multiple times and average the results to minimize the impact of these errors.

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