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repository:ball_on_a_ramp [2021/03/24 23:17] porcaro1 |
repository:ball_on_a_ramp [2021/03/24 23:34] (current) porcaro1 [Answer Key] |
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| - The simulation is not realistic; When a ball rolls down a ramp, it is moved due to the force of gravity; however, it cannot fall straight down since it is restricted by the ramp. On a completely horizontal surface, gravity and the normal force perfectly balance each other out, and there is no acceleration. As the ramp becomes steeper, the less the force of gravity is resisted by the normal force. For a completely vertical surface, there will be no normal force and therefore the force of gravity pulls the ball towards the earth unimpeded. This means that increasing the ramp height should increase the speed of the ball. Additionally, changing the length of the ramp should not affect the final speed of the ball. Although a ball rolling down a steeper ramp will accelerate faster, the final speed of the ball at the end of the ramp will be the same, regardless of ramp length (ignoring frictional forces). This can be demonstrated by relating the potential and kinetic energy. We can set potential energy equation equal to the kinetic energy equation to find the speed of the ball is affected by the ramp: $$mgh=\dfrac{1}{2}mv^2$$ where $m$ is mass of the ball, $g$ is the acceleration of gravity, $h$ is the height of the ramp, and $v$ is the speed of the ball. Since the mass, force of gravity, and height of the ramp does not change when you lengthen the ramp, the velocity will be the same. | - The simulation is not realistic; When a ball rolls down a ramp, it is moved due to the force of gravity; however, it cannot fall straight down since it is restricted by the ramp. On a completely horizontal surface, gravity and the normal force perfectly balance each other out, and there is no acceleration. As the ramp becomes steeper, the less the force of gravity is resisted by the normal force. For a completely vertical surface, there will be no normal force and therefore the force of gravity pulls the ball towards the earth unimpeded. This means that increasing the ramp height should increase the speed of the ball. Additionally, changing the length of the ramp should not affect the final speed of the ball. Although a ball rolling down a steeper ramp will accelerate faster, the final speed of the ball at the end of the ramp will be the same, regardless of ramp length (ignoring frictional forces). This can be demonstrated by relating the potential and kinetic energy. We can set potential energy equation equal to the kinetic energy equation to find the speed of the ball is affected by the ramp: $$mgh=\dfrac{1}{2}mv^2$$ where $m$ is mass of the ball, $g$ is the acceleration of gravity, $h$ is the height of the ramp, and $v$ is the speed of the ball. Since the mass, force of gravity, and height of the ramp does not change when you lengthen the ramp, the velocity will be the same. | ||
| - Adding a coefficient of friction could reduce the speed of the ball. This is because frictional forces resist motion. | - Adding a coefficient of friction could reduce the speed of the ball. This is because frictional forces resist motion. | ||
| - | - See below | + | - See highlighted code below. Note that some values are in slightly different locations in the code below. |
| - | - | + | - "axis" tells us the direction that the ramp will point. In this instance, the ramp will be "R1X" units in the x-direction and "-R1Y" units in the y-direction |
| ===Code=== | ===Code=== | ||
| ==Partially Complete== | ==Partially Complete== | ||
| [[https://www.glowscript.org/#/user/porcaro1/folder/RepositoryPrograms/program/BallonRamp-Solution/edit | Link]] | [[https://www.glowscript.org/#/user/porcaro1/folder/RepositoryPrograms/program/BallonRamp-Solution/edit | Link]] | ||
| - | <code Python [enable_line_numbers="true"]> | + | <code Python [enable_line_numbers="true", highlight_lines_extra="84,85,86"]> |
| GlowScript 2.7 VPython | GlowScript 2.7 VPython | ||
| Line 251: | Line 251: | ||
| t=tFinal</code> | t=tFinal</code> | ||
| ==Complete== | ==Complete== | ||
| - | https://www.glowscript.org/#/user/porcaro1/folder/RepositoryPrograms/program/BallonRamp-Solution/edit | Link]] | + | [[https://www.glowscript.org/#/user/porcaro1/folder/RepositoryPrograms/program/BallonRamp-Solution | Link]] |
| - | <code Python [enable_line_numbers="true", highlight_lines_extra=""]> | + | <code Python [enable_line_numbers="true", highlight_lines_extra="18,19,20,21,22,23,24,30,32,38,39,40,67,68,69,93,94,100,101,102,104,105,106,107,108,109,110"]> |
| GlowScript 2.7 VPython | GlowScript 2.7 VPython | ||