2 Stones
Your task is to determine collisions between moving circular objects given a starting scenario.
Here is an example:
Three in row
The arrows indicate velocity, and the darkness of the green circles is indicative of the mass of the object.
2.1 Starting scenario
The objects are specified by entering the following information into cin: the mass, radius x/y position, x/y velocity and name of each stone
All the values are in SI units: kg, m, and m/s.
The location information (x/y coordinates in meters) and velocity (x/y coordinates, in meters/second) is the initial values for time t=0t=0.
Here is an example of the input format:
10 1 0 0 1 0 one
30 2 10 0 0.2 0 three
1 1 20 0 0 0 two
Stone three has a mass of 30 kg, a radius of 2 m. It starts out at (10,0)(10,0) with a velocity of (0.2,0)(0.2,0).
2.2 Motion model
The objects travel on a two-dimensional surface. Each object travels in a straight line at a constant velocity. Each object will continue travelling in this direction forever, unless it collides with another object.
2.3 Collision model
Two objects collide at the moment the distance between them becomes equal to the collision distance. For this problem, the collision distance will be the sum of the radii of the colliding stones.
2.3.1 Elastic Collisions
These equations are from https://en.wikipedia.org/wiki/Elastic_collision in section “Two-dimensional collision with two moving objects”.
2.3.2 Collision prediction
3 Program
A working version of the program is provided here stones and a partial copy of the source code is provided here stones_template.cpp
代写Stones stones_template C+作业
The executable is compiled on the devbox, so it must be run there.
You may use all or none of the template file.
3.1 Program behavior
The program starts off by prompting for the starting scenario:
Please enter the mass, radius, x/y position, x/y velocity
and name of each stone
When complete, use EOF / Ctrl-D to stop entering
It will then print out the initial positioning, together with the initial energy of the system and the total momentum:
Here are the initial stones.
one m=10 R=1 p=(0,0) v=(1,0)
three m=30 R=2 p=(10,0) v=(0.2,0)
two m=1 R=1 p=(20,0) v=(0,0)
energy: 5.6
momentum: (16,0)
Finally, the program will print a report about each collision event until there are no more collisions.
This is what the report should look like:
Here are the collision events.
time of event: 8.75
colliding one three
one m=10 R=1 p=(8.75,0) v=(-0.2,0)
three m=30 R=2 p=(11.75,0) v=(0.6,0)
two m=1 R=1 p=(20,0) v=(0,0)
energy: 5.6
momentum: (16,0)
time of event: 17.5
colliding three two
one m=10 R=1 p=(7,0) v=(-0.2,0)
three m=30 R=2 p=(17,0) v=(0.56129,0)
two m=1 R=1 p=(20,0) v=(1.16129,0)
energy: 5.6
momentum: (16,0)
4 The visualizers
4.1 Input visualizer
You can make an image of the starting scenario using visualize (link below)
visualize example2.txt 100 10
The output will be a file example2.png showing the starting positions and velocities. The parameters 100 and 10 are to set the size of the plane to draw (-100 to 100 in this case) and the scaling factor for the arrows.
5 Grading
There will be points for
• correctness
• good program design
• readability
• appropriate use of comments
6 Downloads
Here are all of the relevant files:
• stones the executable
• stones_template.cpp the starter file
• vector2d_class.cpp a partial implementation of the vector2d class
• stones_examples.zip all text files for testing inputs.
• visualize creates image file (PNG) from input scenario
For the executables, you need to make them executable when downloaded, like this in terminal:
chmod 755 stones
chmod 755 visualize
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