Questions that I need help with. 100 xcash to those who answer it for me

Okay I am at school right now and there are two questions that I absolutly can not find. I need the answers by tomorrow and whoever gets them gets 100 xcash per question. Thanks.

Light travels at 186,000 miles per second. How long does it take for light to travel for Pluto to Earth?

When glass breaks how fast does it move? To photograph this how fast must the camera shoot?

[unicycler]

All you need for the first question is the distance between pluto and earth.

Yeah I tried finding that, but I couldn't.

[Diamond187]

Well, Pluto's orbit is extremely eccentric, meaning that it's distance from the sun will vary greatly depending on when you are sending out the signal. Whether the difference is substantial enough to warrant a change in the time light takes to get there from Earth, I don't know, cuz I can't find any values for distance, try PMing Fiz, he'd have better references for this than I do.

As for the glass breaking question, I'm not entirely sure what it's getting at. I'm assuming it's the rate of developement of a crack along a plane of glass. I find it extremely suspect that there would only be one speed this occurs at, so I really don't know how to answer it. I'll try looking it up though, and if I find anything I'll post again.

[Liokae]

More than just the eccentricity of Pluto's orbit, there's the fact that the two planets don't cross equal degrees of their orbit in the same amount of time. The distance can vary dramatically because of this, since it's possible for one of the planets to be on one side of their orbit, and the other on the opposite side. That would affect the distance by a minimum of 2AU, causing a time difference of 16 minutes or more.

EDIT: Your best bet is to look up the average distance of both planet's orbits and compare that.

[Fiz]

The Pluto Question:

Okay, the best way to answer this question is not to think of it in every possible situation, otherwise you will never be able to answer it. When you are given a problem like this, present the solution in your own terms. Always give the line "Assume that..." and follow it up with your condition. If the problem is like this one, you should always make the marker aware that you know what you're talking about. For instance, you know that Pluto has an irregular orbit that's not perfectly circular. Say that in your answer. They can't mark you wrong if you can prove that your solution is valid. I would answer it like this:

Question: Light travels at 186,000 miles per second. How long does it take for light to travel for Pluto to Earth?

Solution:

Speed of light = 186 000 miles/second

We know that Pluto has an orbit that is not perfectly circular, so for the purposes of this problem, assume that Pluto's distance to the Sun is its mean (average) distance.

Pluto's mean distance from the Sun = 3 670 000 000 miles
Earth's mean distance from the Sun = 92 955 807 miles

Therefore, the distance between Pluto and Earth is 3 577 044 193 miles.

If light travels at 186 000 miles per second:

t = 3 577 044 193 / 186 000

t = 19 231 seconds = 5.34 hours

The average time it takes light to travel from Pluto to Earth is 5.34 hours.

I'll double check that in a little while. Gotta step out for a bit. I'll think about the second question.

[Fiz]

On second glance, its kind of a silly question. Light takes just 8 minutes to reach Earth from the Sun, so that extra eight minutes is negligible. :lol: Don't know why I didn't see that before I did the subtraction. Hehe...

In essence, the amount of time it takes for light to get from the Sun to Pluto is just eight minutes more than it takes light to travel from Earth to Pluto or the other way around. Its a matter of 500 seconds or so in the answer. It you want to be precise though, it is 19 231 seconds.

[Fiz]

The glass breaking question is, in my opinion, unanswerable, unless your teacher wants a general answer. You could read it in two ways. It could either mean how fast does the glass move after its been broken (meaning the velocity of the individual shards after the breakage) or it could mean how long does it take for the glass to actually break, or the velocity of the crack moving down the piece of glass.

Since we're talking about a camera taking a picture, I would assume we're talking about taking a picture of the crack developing. If we take the shot too soon, we will miss the crack and capture the glass in its whole state. If we shoot too late, we will capture the shards seperating.

Okay. So far so good. In my opinion, this is a classic example of the action-reaction law. If a force is applied on an object, the object must produce an equal and opposite force. If I push on the wall with a force of X Newtons, the wall pushes back at X Newtons.

I could be wrong here, but I think we could use this theory to solve this question. If you drop a piece of glass and it breaks, the force at which it hits the ground would equal a certain value. This force produced would be equal and opposite to the force propogating through the piece of glass, which would tell you how fast the crack moves down the glass.

So, when you drop something, gravity pulls it down with an acceleration of 9.81 meters/second. (Sorry for the metric units, but its scientific. Hehe...) We can use this information in the following formula:

F = ma

Which is force equals mass times acceleration. If we know the mass of the piece of glass, we can figure out the force acting on it. This force, upon impact, will be transferred to the ground, which will transfer the same force back through the piece of glass, producing the crack.

I don't know if this is logic is correct, but think about it this way. If I drop a rubber ball to the floor and it is a perfectly elastic collision, the ball will bounce right back up to my hand. That means that the force that the ball hit the ground with is the same force applied to the ball by the ground to send it back up to me. The ball recieves the force elastically and is sent back up to my hand. The piece of glass, on the other hand, does not elastically bounce back up to me, but the crack sent through the glass could be seen as the same kind of phenomenon. Instead of the energy transfer sending the glass back up to my hand, it is transferred in creating the crack.

This could be total BS, but it makes sense while I'm typing it.

So, if we had values for the force and the mass, we could theoretically figure out the velocity of the crack.

Of course, the velocity of the crack will be much less than the velocity of light, so the camera would just have to take the picture within a certain time interval. We could figure this time interval out once we know the velocity of the crack going through the glass, also knowing how big the piece of glass is. We could then figure out how long it takes the crack to travel from one end of the glass to the other, assuming it travels in a straight line, and from this, we would know how long we have to to press the button on the camera the instant the crack develops up until the time the crack seperates the glass. Of course, we would have to factor in the shutter speed of the camera. This value would tell us how long before the actual collision between the ground and the glass we would have to press the shutter button.

Its quite complicated, now that I think about it. Hehe...

In conclusion, as long as the camera button is pressed a certain number of milliseconds or microseconds instantly after the crack develops, we can take the picture. The amount of time it takes for the glass to break depends on the velocity of the crack as it goes through the glass, which we cannot figure out unless we have some numbers.

Therefore, the problem is unsolvable, but there's my attempt at the theory.

[Diamond187]

For the Pluto question, I wouldn't use the mean value. All I'd do is give the range of possibilities. The greatest value would be when Pluto is at it's Apogee (I hope I'm not getting these terms backwards) and Earth (assuming circular orbit) is on the opposite side of the Sun, and the lowest possible value when Earth and Pluto are on the same side of the Sun and Pluto is at it's Perigee (if you feel like being very technical, I guess it's Apohelion and Perihelion). And if you really wanted to impress your teacher you could, based on there trajectories, come up with a functional expression which would give you the time at any given position of Pluto.

As for the glass question, I concur with Fiz. It's unsolvable unless you know way more about solid state physics than I do, or more details are given.

Well Fiz's answers satisfy me. He gets the 200 xcash.