Tesla’s Shattered Cybertruck Windows

A Physics Analysis.

 

I don’t know what to think about Elon Musk anymore. I mean the SpaceX stuff is awesome, and the Tesla car has been pretty cool. But now we have the Tesla pickup truck, unveiled on Thursday. (Simone Giertz did it first!) The Tesla Cybertruck looks odd—one person likened it to a futuristic doorstop—but that’s fine with me. My problem is with the unveiling itself.

In case you missed it, Musk wanted to demonstrate the truck’s ruggedness. They start off by hitting a normal truck door with a sledgehammer. Yes, it makes a dent. What about the Tesla truck? Bam! Not a scratch. It has a thicker steel exterior that makes it impervious to people with sledgehammers.

Oh, and the windows? They’re made of “Tesla Armor Glass.” To compare, Musk’s assistants drop a metal ball on normal car glass, which cracks. Then they drop it on Tesla’s special glass, and the ball bounces off. They drop a bigger ball on it from higher up. Nothing. So the guy tosses the ball at the driver’s window of the Cybertruck—and smashes it.

“Well, maybe that was a little too hard,” Musk says. So the guy picks up the ball and lobs it as softly as he can at the rear passenger window. Now there are two smashed windows. Awkward.

I don’t know, if it were me, I’d have tested this demo before doing it live onstage. But, to Musk’s credit, they just carried on with the show. The whole rest of the presentation was carried out in front of a prototype with broken windows. Bad optics, but you have to admire his aplomb.

What went wrong? Why did Tesla’s fancy glass survive a dropped ball but not a thrown ball? To find out, we need some physics.

How high was the test ball dropped?

If you drop a metal ball, it speeds up as it falls. So to know how hard it hit the glass in the demo, we need to know the height from which it was released. For the first drop, the stage assistant stands over the glass, raises his arm, and releases the ball—that looks to be a distance of roughly 1 meter. The higher drops are a little trickier. It would have been nice if they just told us, but that’s OK, we can estimate it from the amount of time it takes to hit.

If you drop an object, it starts with an initial velocity of zero, and the only force acting on it is gravity. The gravitational force, we know, depends on the local gravitational field (9.8 newtons per kilogram) and the mass of the object.

We also know that the net force must equal the product of mass and acceleration. Notice: Mass is on both sides of the equation, so we cancel out the mass, and we get that the acceleration of a falling object is 9.8 meters per second squared in the downward direction.

Using the definition of acceleration, and rearranging, you can get the following semi-famous equation showing height (y) as a function of time (t):

y equals initial y plus velocity times t plus acceleration times t squared divided by 2

If I could measure the fall time for the ball, I could just plug it into that equation and get the change in vertical height. Alas, nothing is easy. The video doesn’t seem to show a continuous shot of the ball falling—it cuts to another angle. OK, that’s fine. There is another shot that shows the ball falling. Looking at a few frames, I get a falling time of 0.267 seconds. This gives a drop of 0.35 meters—and it’s about the same distance as one of those steps on the ladder next to it. With ten steps, that puts the total drop height of around 3.5 meters. Not perfect, but it’s fine for now.

How can we characterize the collision?

What’s the difference between a ball dropped from a height of 1 meter and 3.5 meters? How do you characterize the impact with the window? Honestly, this is a tough problem. There’s not just one number that completely describes the interaction between the ball and the window. The two easiest things to calculate are the momentum and kinetic energy of the ball right before it strikes the glass window—so I will calculate both of those.

The momentum is a product of the object’s mass and velocity. Here is an expression for momentum (p) in one dimension (because really it’s a vector quantity).

p equals m times v

So, I need the ball’s mass (m) and its velocity (v) before impact. I really don’t know much about the ball except that it looks about the size of a baseball and I know you can buy steel balls with a diameter of 3 inches (baseball sized). Let’s just go with that. This one has as a weight of 4.2 pounds (1.9 kilograms).

What about the speed? If it falls from a height (h) of 3.5 meters with an initial velocity of zero m/s, I can use the following kinematic equation to calculate the final speed. (Here g is the gravitational field, with a value of about 9.8 newtons per kilogram.)

velocity squared equals 2 times gravity times h

This gives an impact speed of 8.3 m/s and a momentum of 15.7 kg * m/s. But what does that even mean? Let’s just compare that with the final momentum of the same ball dropped from a height of 1 meter. Using the same method, I get an impact momentum of 8.4 kg * m/s. That’s about half the momentum.

What about the kinetic energy? This is calculated as:

K equals mass times velocity squared over two

Notice that this one also depends on both the mass (m) and the velocity (v) of the ball. But with a drop height of 1 meter, the impact kinetic energy would be 18.6 Joules. If you raise the ball to 3.5 meters, the kinetic energy increases 65.17 Joules. Why the big difference? The change in kinetic energy depends on the distance the object falls. Increase the distance by a factor of 3.5, and the kinetic energy increases by 3.5. The momentum depends on the falling time. If you increase the falling height by a factor of 3.5, the falling time doesn’t increase by the same factor. This is because the farther the object falls, the greater the speed and the quicker it moves over that distance.

But which one better describes the impact? Honestly, it really depends on the situation. For this Tesla truck window thing, I’m going to use the kinetic energy to explain what went wrong.

How fast did the dude throw the mass?

The dropped ball didn’t break the window, but the thrown ball did. How fast did that dude throw the ball? Time for another rough approximation. Let’s assume a few things:

  • The guy’s throwing motion moved the ball from rest to the final speed over a distance of about 1 meter (roughly).
  • The ball increased in speed with a constant acceleration.
  • The throwing time is about 0.27 seconds (I can get that from the video). This is the time he takes to move the ball forward, not the wind-up time.

Now I just need two definitions of average velocity. The first is that the average velocity is the sum of the initial and final velocity divided by two (just like a normal average). The second definition is that the average velocity is the change in position divided by the change in time. Since the initial velocity is zero, I can put these two together to find the final velocity.

Plugging in my values for the distance and time, I get a throwing speed of 7.4 meters per second (just 16.6 mph) with an impact momentum of 14.1 kg * m/s. That puts it right around the impact momentum of the ball dropped from a height of 3.5 meters. So, if everything is set up it shouldn’t break the window.

What went wrong?

But the window did indeed break. What happened? Did someone just forget to upgrade the windows on the Tesla truck? No, I think there is another reason the truck window broke but the test window didn’t. The key difference between the two windows was the mounting. The test window with the dropped ball was held in place by some type of clamps. These clamps are not completely rigid—they allow the test glass to move some during impact. The truck window was held in place by the door frame such that it couldn’t move very much.

Here, let me show this with a diagram.

diagram with two blue rectangles

In both cases, the ball is traveling with about the same speed and the ball is stopped by a force exerted on it from the glass. In the case of the truck window, the stopping distance is shorter (labeled sT with the T for truck) than in the case of the mounted glass (sg). Since we are dealing with forces and distance, we can use the work-energy principle to calculate the work done by the glass, where the work is the product of the force and distance the ball moves. The work done on the ball must be equal to the change in kinetic energy of the ball. Oh, the force is pushing backwards, it’s actually negative work.

W equals negative Fs with is the change of K

Since both balls stop, they have about the same change in kinetic energy. However, since the truck window stops over a shorter distance, it must have a greater force. It’s tough to estimate the distance the glass moves, but let’s just pretend. Supposed the mounted glass moves 1 centimeter during impact but the truck window only moves 2 millimeters. Since the mounted glass moves 5 times farther than the truck window, it would have an impact force that is one-fifth that of the truck window. With a larger force on the truck window, it’s more likely to break.

Then how do you fix this? Well, you could but tiny little shocks or springs on the truck window, but that might detract from its cool look. Or maybe the problem is that the mounted glass and the glass on the truck were different materials. Who knows.

 

Hat tip smiley  WIRED

We Build the Wall…

Texas Monthly

We Build the Wall ordered to Stop Construction of Private Border Wall in South Texas

The group that is relying on crowdfunding to pay for construction of a private border wall in South Texas has been ordered to stop the construction they began last week by U.S. officials who monitor compliance of an international water treaty.

“We sent a letter on Friday requesting they submit additional information about their activities and asked them to stop construction until we review that information,” said Sally Spener, a spokeswoman for the International Boundary and Water Commission. She did not indicate how long it would take to review the project, but did say the group informed her agency that it would provide the requested information.

The letter went to a controversial Florida-based group called We Build the Wall, Inc., which earlier this year built a one-mile stretch of wall on private property in New Mexico just across the border from El Paso. Their construction efforts there were also briefly put on hold because the city of Sunland Park, where they were building, said they did not get the proper building permits. Eventually they were allowed to complete the wall.

The group claimed last week that it was moving forward on the crowdfunded project along the Rio Grande in South Texas. On Thursday, heavy equipment could be seen clearing brush and cane along the river on private property near the town of Mission and adjacent to the National Butterfly Center. In a now-deleted video on Facebook, a man calling himself “Foreman Mike” with We Build the Wall, the Florida-based group behind the project in New Mexico, said the clear-cutting was the first step in building three-and-a-half miles of wall to help President Trump in his efforts to secure the border.

The brush removal began on Monday, the group said in its video. This would have marked the first known activity by We Build the Wall in Texas. Local environmentalists claimed a wall in the area would worsen flooding in Mexico, violating an international treaty and create additional hazards by building in a floodplain. “Private entities are not free to violate the treaty and endanger lives and property in Mexico,” said Scott Nicol, with the Sierra Club’s Borderlands Campaign. Nicol also noted that environmental regulations—waived by the U.S. Department of Homeland Security for federal wall construction—would still apply to private entities like We Build the Wall.

In the now deleted five-minute video, “Foreman Mike” said We Build the Wall needed to raise at least $1,000 a day to just pay for the fuel for the heavy equipment now clearing the land. Their overall fundraising goal was not immediately clear, and an email to the organization seeking elaboration went unanswered.

“Their wall is just a publicity stunt meant to fire up donors and pull in cash, but if they actually build a wall on the riverbank, it will be tremendously destructive,” Nicol warned. “They are building on a sandy riverbank, so when the first strong flood hits, the wall will wash away, sending a mass of concrete and steel downriver that will slam into homes and businesses. Their wall could not only destroy property, it could kill people.”

The construction was slated to happen in the congressional district of Congressman Henry Cuellar, D-Laredo. “No wall, whether funded by public dollars or private funding, is wanted on the border,” he told Texas Monthly.

Hidalgo County tax records show that the clear-cutting was on land—more than one thousand acres—owned by Neuhaus & Sons. Lance Neuhaus, the grandson of the founder of Texas State Bank, confirmed to Border Report that he had allowed We Build the Wall on his land, but wouldn’t elaborate.

On Thursday, to get a better look at the construction activity, I took a boat tour of the Rio Grande with Marianna Treviño-Wright, executive director of the National Butterfly Center, and Father Roy Snipes, whose La Lomita Chapel was also briefly threatened by federal wall construction plans before Congress intervened to protect that historic landmark.

From the river, it was evident that the clear-cutting came right down to the bank of the river, suggesting that the wall would be built much closer to the Rio Grande than much of the existing and planned border barriers. In the video, “Foreman Mike” says the wall would be built 25 to 30 feet from the Rio Grande. “Clearly they’re going to build on the banks of the river, but it will end up in the river when we have another tropical storm,” Treviño-Wright said. Snipes also questioned how stable the structure would be given the shallow water table that exists along the river.

In the video, We Build the Wall founder Brian Kolfage said they expected to complete the private wall in a month-and-a-half. He didn’t explain anything else about the design of the wall, and it was unclear how a private wall would integrate with the Trump administration’s plans for at least 88 miles of border barrier in the Rio Grande Valley. The Neuhaus property does not appear to be part of publicly disclosed maps depicting future border wall. Federal contractors have begun clear-cutting land about five miles west of the Neuhaus property, but construction has yet to begin. In contrast, two wall panels have been put into place at a site about thirty miles east of Mission, just south of Donna. An email seeking comment from Customs and Border Protection about We Build the Wall’s activities went unanswered. “Foreman Mike” appears in another Facebook video criticizing the federal effort.

We Build the Wall started as a GoFundMe effort last December when Kolfage, an Iraq veteran and triple amputee, sought to raise $1 billion. Within a month, the crowd-sourcing campaign had brought in more than $20 million from nearly 340,000 donors. In August, authorities in Florida said they had launched a criminal investigation into the nonprofit group. The status of that investigation is unknown, and Kolfage has denied any wrongdoing. The group’s efforts at building the wall near El Paso were temporarily halted because of city permitting issues. But construction of the half-mile barrier was eventually allowed when the group appeared to be in compliance with local ordinances.

Former White House advisor Steve Bannon and former Kansas secretary of state and outspoken immigration critic Kris Kobach are members of the group’s advisory board, according to We Build the Wall’s website.

This story was updated throughout on November 19, 2019, to reflect that We Build the Wall had been ordered to stop construction. 

Schrödinger’s Dick

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Hillorita Clintonez


 

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The World’s Deadliest Predator

BearassThe one on the left.

 


 

Schrödinger’s Dick

The name of the famous thought experiment commonly used in the explanation of Quantum Mechanics; Schrödinger’s Dick touches on the fundamentals of dual states of matter, and their effects on a macroscopic system.

Schrödinger’s Dick outlines a scenario where, since both the position and velocity of a dick cannot be known, it is said to be in a state of both cumming and not cumming whilst receiving fellatio.

 


 

What kind of motorcycle does Trump ride?

Victory

 


 

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ALIEN ALLIANCE

Rumors are rampant in Washington, after an unauthorized white house leak confirmed that president Barack Obama was working with representatives from a hidden planet between and Jupiter and Saturn since the early days of his first term in office. This source said that top scientist from this planet advised the president that the earth was on the verge of destruction because of the unregulated burning of fossil fuels. Top EPA officials working with the aliens have worked out a solution that would not only stop, but totally reverse the effects of global warming. This simple plan calls for the immediate extermination of 99% of the world’s population and the relocation of the remaining 1% to alien controlled reservations where the aliens will make sure all of their needs will be provided for, much like the Native Americans in the 19th century.  Cradle to grave care will be provided by the great green alien father who will be assisted by a select group of native earthlings.  As of this time Obama has not denied or confirmed these rumors.  However, when white house spokesman, Josh Earnest was asked about this he said the goal of the democratic party had always been cradle to grave care for all Americans regardless of race, color, creed or national origin.

Stupider