Force Vectors Pushing Agains a Wall Gif

What happens when an object collides with a stationary wall at some incident bending? If this object is a ball, nosotros often say that it "reflects" off the wall just similar light does with the incident angle equal to the reflected bending. Ii questions:

• Is this true? Does the incident bending equal the reflected angle for a ball hitting a wall?
• Why would this "rule" exist truthful and when would information technology not work?

Let's take a look.

Does incident angle equal reflected angle?

Of course this question depends on the types of objects colliding, but permit's just do a simple test. I could toss dissimilar assurance at the flooring and look at the reflected angle---merely I'm non going to do that. The problem is that the velocity of the brawl would modify both earlier and after the collision. Oh sure, you could still practise information technology only it would be a piddling more than complicated.

Instead I am going to take this floating puck and push it along the flooring (the puck has a fan in it and so that it hovers with low friction). Using a video as recorded from above, I can get the post-obit plot for the trajectory of this puck as information technology collides (x vs. y).

The slope of the trajectory line for the incident disk is -1.sixty and the gradient of the reflected 1.133. These aren't exactly the same---but perhaps it would be easier to look at them every bit angles. The bending of incidence is 57.ix° and the reflected angle is 48.6°.

What most a few more tests? Here is that same hover deejay with the same wall but at different incident angles. This is a plot of the incident trajectory slope vs. the reflected trajectory slope.

If the constabulary of reflection worked perfectly for this disk, the gradient of this line would be 1.0---but it'due south not. But why doesn't it exactly work? Here is a plot of both the x and y position as a role of time. From the slopes of these lines we can get the x and y velocities.

First look at the horizontal position. If you fit a linear function to the data, you would see that the x-velocity before the collision is 0.7 m/south and afterwards it is 0.37 m/s. And so information technology slows down in the horizontal direction. For the vertical velocity, information technology goes from -1.09 1000/s to 0.452 thousand/southward. Oh, the disk besides spins after the collision---but permit's not worry about that right now.

If the horizontal velocity didn't change and the vertical velocity just changed directions---then you would have a perfect "reflection" standoff. Of form, the changes in velocity depend on the types of objects colliding. I suspect that I could find a different set of materials that produces a better reflection.

How does reflection piece of work?

Kickoff with a ball moving towards a wall with some initial velocity. When the ball comes in contact with the wall, there is a force exerted on the ball. Here is a diagram of the perfect collision.

When dealing with forces and momentum, we should of course consider the Momentum Principle:

In this special standoff, the strength from the wall is merely perpendicular to the wall (in the y-direction). This ways that at that place is no change in the x-component of momentum and only a modify in the y-momentum. If this is a perfectly rubberband collision such that the total kinetic energy is constant, then this y-momentum must have the aforementioned magnitude as before the collision (but in the opposite direction). This would make the reflected bending the same equally the incident bending.

Only what happens in our real collision case? Information technology'southward non a perfect standoff so that the diagram might look like this:

For the non-perfect collision, the wall exerts two forces on the brawl (or you could combine these into just one forcefulness if it made you happy). In that location is still a force pushing perpendicular to the wall, but there is as well a frictional force parallel to the wall. This friction force does 2 things. First, information technology changes the momentum in the 10-direction and second it exerts a torque on the disk. In the cease, the x-momentum of the disk (or ball) changes and the ball acquires a spin. This is exactly what we encounter in the animation above.

But how do you lot get a "perfect" collision? You need two things. Starting time, you need an rubberband collision so that there is no kinetic energy lost. If you lose kinetic free energy, there'south no style the y-velocity will remain the same. 2d, y'all need to take no frictional forces on the object. These frictional forces will just modify the x-velocity of the ball.

Modeling a Brawl-Wall Collision

You know I tin can't end without beginning making a numerical model. OK, so how do you model a ball colliding with a wall? The easiest fashion is with a spring. Here's how my adding will work.

• The ball moves along merely normally with a constant velocity.
• If the centre of the ball is closer to the wall than the radius of the ball, then there is a force pushing on the brawl perpendicular to the wall.
• The forcefulness of this forcefulness will be proportional to the amount the ball overlaps into the wall.
• When the ball is no longer "in contact" with the wall, the force goes back to zero.

What about a collision with friction? If I want to add a frictional force, I volition simply do the exact same thing except that the strength from the wall won't be completely perpendicular to the wall. In that location volition exist a small component of this force parallel to the wall and in the opposite direction to the velocity of the ball. I didn't include loss of kinetic free energy in the perpendicular management---that's a bit more complicated to model.

Just printing the "play" button to run the code. You can see that there are two balls. They are initially on superlative of each other, only later the collision they accept a dissimilar path. The model isn't perfect---simply it mostly works. Go ahead and alter the calculation a petty bit to come across if yous can make a meliorate model.

Why exercise I even care about balls colliding with walls? Trust me, in that location is a reason---but I'll get to that in a hereafter mail.

jensensence1983.blogspot.com

Source: https://www.wired.com/2016/05/swear-theres-reason-model-ball-bouncing-off-wall/

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