Simulation Of Freefalling of a body in Motion Solve
OBJECTIVE :
To Simulate and plot a freefalling body(point mass) of mass 1 kg and inertial properties 1 kgm2 in the y-axis with simulation time of 2sec
THEORY :
Free Falling Object : The term \'free fall\' means that an object is falling freely with no forces acting upon it except gravity.
Mathematical equation for free falling object
`h = 1/2*(\"gt\"^2)`
here,
h - Distance travelled by object in m
g - Acceleration due to gravity in m/s2
t - time elapsed
SIMULATION :
* Before creating the point mass, the gravity and units in the motionview User Interface is modified to the requirement
![\"Gravity\"](\"//edxengine-live-courses-files.s3.amazonaws.com/1577029708.png\")
![\"Units\"](\"//edxengine-live-courses-files.s3.amazonaws.com/1577029725.png\")
* Now, A point mass is created in the motion view graphic user interface with mass 1kg and inertial properties of 1kgm2 in Ixx, Iyy and Izz directions and the global origin is taken as the origin point within the center of mass co-ordinate system.
![\"Body\"](\"//edxengine-live-courses-files.s3.amazonaws.com/1577029796.png\")
* Next, the simulation is run after setting the simulation end time as 2 seconds.
* After the simulation is solved, the plot option is used and the required graph (Disp of point mass in Y-direction against Time) is plotted with which we can determine the distance travelled by the body after 2sec time period.
![\"graph\"](\"//edxengine-live-courses-files.s3.amazonaws.com/1577030070.png\")
QUESTIONS :
Q - Does the mass and inertial properties of the body depend on the rate of fall?
From the above equation it is clear that the rate of fall is independent of mass and inertial properties.
Assume two bodies, one of mass 1 kg and inertial properties of 1kgm2 and the other 10 kg and 12 kgm2 inertia
Substituting in equation
`h = 1/2*(\"gt\"^2)`
`h = 1/2*9.81*2^2`
`h = 19.62` m
Hence for both bodies, the rate of fall would be constant which is evident from the fact that the distance travelled for the same time interval is same.
Using Motion Solve Graphic User Interface, the same simulation was carried out for the second body, and the graph is shown below
![\"graph2\"](\"//edxengine-live-courses-files.s3.amazonaws.com/1577030486.png\")
The graph simulated for both bodies are the same with the displacement of the bodies for time interval of 2 seconds as 19.62m.
Q - In what case will the mass have an effect on the rate of fall? In the same case what other physical characteristics will affect the rate of fall?
For the mass to have an effect on the rate of fall, the case of air resistance needs to be taken into account.
The two most common factors that have a direct effect on air resistance are
- The speed of the object
- The cross-sectional area of object
REFERENCE :
https://www.physicsclassroom.com/class/newtlaws/Lesson-3/Free-Fall-and-Air-Resistance