I do no longer know what to reflect Elon Musk anymore. I indicate the SpaceX stuff is awesome, and the Tesla car has been stunning frosty. But now we hang got the Tesla pickup truck, unveiled on Thursday. (Simone Giertz did it first!) The Tesla Cybertruck appears to be like unfamiliar—one person likened it to a futuristic doorstop—but that is dazzling with me. My situation is with the revealing itself.
At the same time as you happen to overlooked it, Musk essential to display cover the truck’s ruggedness. They originate off by hitting a unparalleled 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 of us with sledgehammers.
Oh, and the windows? They’re product of “Tesla Armor Glass.” To review, Musk’s assistants drop a steel ball on unparalleled car glass, which cracks. Then they drop it on Tesla’s particular glass, and the ball bounces off. They drop a a lot bigger ball on it from higher up. Nothing. So the person tosses the ball on the driver’s window of the Cybertruck—and smashes it.
“Effectively, possibly that was a little too irritating,” Musk says. So the person picks up the ball and lobs it as softly as he can on the rear passenger window. Now there are two smashed windows. Awkward.
I don’t know, if it had been me, I’d hang tested this demo sooner than doing it reside onstage. But, to Musk’s credit, they perfect carried on with the indicate. The total leisure of the presentation was implemented in entrance of a prototype with broken windows. Immoral optics, but you would possibly must like his aplomb.
What went noxious? Why did Tesla’s admire glass reside on a dropped ball but no longer a thrown ball? To search out out, we desire some physics.
How excessive was the take a look at ball dropped?
At the same time as you happen to drop a steel ball, it accelerates because it falls. So that you would possibly know how irritating it hit the glass in the demo, we hang got to know the height from which it was launched. For the first drop, the stage assistant stands over the glass, raises his arm, and releases the ball—that appears to be like to be a distance of roughly 1 meter. The higher drops are a little trickier. It would possibly possibly had been nice if they perfect informed us, but that’s OK, we can estimate it from the length of time it takes to hit.
At the same time as you happen to drop an object, it begins with an initial tempo of zero, and the most sharp power performing on it is gravity. The gravitational power, all of us know, relies on the native gravitational topic (9.8 newtons per kilogram) and the mass of the item.
We furthermore know that the gather power must equal the product of mass and acceleration. Survey: Mass is on every aspects of the equation, so we execute out the mass, and we gather that the acceleration of a falling object is 9.8 meters per 2nd squared in the downward route.
The usage of the definition of acceleration, and rearranging, that you would possibly even gather the next semi-necessary equation exhibiting height (y) as a characteristic of time (t):
If I’d measure the autumn time for the ball, I’d perfect scurry it into that equation and gather the switch in vertical height. Alas, nothing is inconspicuous. The video would no longer appear to indicate a staunch shot of the ball falling—it cuts to but every other angle. OK, that is dazzling. There is but every other shot that presentations the ball falling. Having a see at about a frames, I gather a falling time of 0.267 seconds. This presents a drop of 0.35 meters—and or no longer it is about the the same distance as one amongst those steps on the ladder next to it. With ten steps, that locations the total drop height of spherical 3.5 meters. Not perfect, on the assorted hand or no longer it is dazzling for now.
How will we symbolize the collision?
What’s the variation between a ball dropped from a height of 1 meter and 3.5 meters? How enact you symbolize the impact with the window? In reality, here’s a tough situation. There is no longer perfect one amount that utterly describes the interplay between the ball and the window. The 2 absolute top things to calculate are the momentum and kinetic strength of the ball perfect sooner than it strikes the glass window—so I will calculate every of those.
The momentum is a product of the item’s mass and tempo. Right here is an expression for momentum (p) in one dimension (because if fact be told or no longer it is a vector amount).
So, I want the ball’s mass (m) and its tempo (v) sooner than impact. I if fact be told do no longer know great about the ball moreover that it appears to be like about the size of a baseball and I know that you would possibly even have interaction steel balls with a diameter of three inches (baseball sized). Let’s perfect crawl along with that. This one has as a weight of 4.2 kilos (1.9 kilograms).
What about the tempo? If it falls from a height (h) of three.5 meters with an initial tempo of zero m/s, I’m able to spend the next kinematic equation to calculate the final tempo. (Right here g is the gravitational topic, with a worth of about 9.8 newtons per kilogram.)
This presents an impact tempo of 8.3 m/s and a momentum of 15.7 kg * m/s. But what does that even indicate? Let’s perfect review that with the final momentum of the the same ball dropped from a height of 1 meter. The usage of the the same system, I gather an impact momentum of 8.4 kg * m/s. That is set half of the momentum.
What about the kinetic strength? Right here’s calculated as:
Survey that this one furthermore relies on every the mass (m) and the rate (v) of the ball. But with a drop height of 1 meter, the impact kinetic strength would be 18.6 Joules. At the same time as you happen to raise the ball to three.5 meters, the kinetic strength increases 65.17 Joules. Why the huge distinction? The switch in kinetic strength relies on the distance the item falls. Lengthen the distance by a component of three.5, and the kinetic strength increases by 3.5. The momentum relies on the falling time. At the same time as you happen to amplify the falling height by a component of three.5, the falling time would no longer amplify by the the same component. Right here’s since the farther the item falls, the larger the tempo and the faster it moves over that distance.
But which one better describes the impact? In reality, it if fact be told relies on the placement. For this Tesla truck window thing, I will spend the kinetic strength to indicate what went noxious.
How instant did the dude throw the mass?
The dropped ball didn’t spoil the window, however the thrown ball did. How instant did that dude throw the ball? Time for but every other rough approximation. Let’s recall about a things:
Now I perfect want two definitions of common tempo. The first is that the common tempo is the sum of the initial and final tempo divided by two (perfect love a unparalleled common). The 2nd definition is that the common tempo is the switch in location divided by the switch in time. Since the initial tempo is zero, I’m able to set these two collectively to search out the final tempo.
Plugging in my values for the distance and time, I gather a throwing tempo of seven.4 meters per 2nd (perfect 16.6 mph) with an impact momentum of 14.1 kg * m/s. That locations it perfect across the impact momentum of the ball dropped from a height of three.5 meters. So, if every little thing is determined up it must no longer spoil the window.
What went noxious?
But the window did indeed spoil. What came about? Did someone perfect put out of your mind to bolster the windows on the Tesla truck? No, I mediate there is but every other reason the truck window broke however the take a look at window didn’t. The key distinction between the two windows was the mounting. The take a look at window with the dropped ball was held in dwelling by some vogue of clamps. These clamps usually are no longer utterly rigid—they permit the take a look at glass to pass some all over impact. The truck window was held in dwelling by the door physique such that it would possibly no longer pass very great.
Right here, let me indicate this with a device.
In every conditions, the ball is touring with about the the same tempo and the ball is stopped by a power exerted on it from the glass. Within 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’re going thru forces and distance, we can spend the work-strength idea to calculate the work accomplished by the glass, the set aside the work is the product of the power and distance the ball moves. The work accomplished on the ball needs to be equal to the switch in kinetic strength of the ball. Oh, the power is pushing backwards, or no longer it is genuinely negative work.
Since every balls end, they’ve about the the same switch in kinetic strength. Nonetheless, since the truck window stops over a shorter distance, it must hang a a lot bigger power. It be tricky to estimate the distance the glass moves, but let’s perfect pretend. Supposed the mounted glass moves 1 centimeter all over impact however the truck window simplest moves 2 millimeters. Since the mounted glass moves 5 cases farther than the truck window, it would hang an impact power that is one-fifth that of the truck window. With a closer power on the truck window, or no longer it is extra seemingly to spoil.
Then how enact you fix this? Effectively, you would possibly but little little shocks or springs on the truck window, but that would possibly possibly detract from its frosty see. And even the placement is that the mounted glass and the glass on the truck had been just a few materials. Who knows.
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