The first sentence of the problem statement says "The figure shows an overhead view".
It is purely a matter of convention. If you are working in two dimensions with one of them vertical (for instance, a child carrying a sled up a hill) then one would normally use x for horizontal and y for...
Nope. I am out as well. I asked for an explanation and got nothing but a regurgitation.
Your response to "how does that work" was:?
That is not an answer. That is an assertion of possibility. But I do not understand what you are even describing. I am asking you to describe it.
Your response...
I will try my hand. But, like @Dale, I do not understand the arrangement.
We seem to have a wheel on a frictionless axle anchored to the ground. We seem to have an array of disks somehow bound to the wheel. Perhaps there are spokes holding them in.
There is no friction between wheel and disks...
Right. Those are a third law pair. Particle on spring and spring on particle.
The point was that the force of particle on spring and floor on spring are not a third law pair. The fact that those are equal and opposite is a consequence of the second law: ##\sum F = ma##. If ##ma## is negligible...
That's a property, not a definition.
Edit: I take it back. It is a definition:
|x| denotes the unique non-negative number that, when squared, yields ##x^2##.
Although, if you have a definition of "non-negative" in hand and are working in a field, it seems simpler to just do the definition by...
But it's not the definition of ##|a|##. It's the definition of ##\sqrt{a^2}##. There is nothing in taking a square root that demands that the result be positive or negative. We have decided by fiat that the ##\sqrt{}## notation denotes the positive square root.
A cyclist adopting a reasonably fixed cadence will be in twice as high a gear at 20 mph as at 10 mph. At a consistent effort, this means half the torque delivered to wheels rotating at twice the speed.
Gaining an incremental 5 miles per hour takes twice as long because the available torque is...
Using radians per second gets rid of a mildly annoying conversion factor if you try to use torque and rotation rate to compute power. Or when you try to use rotation rate and wheel radius to compute linear speed.
Us math types get used to radians and have trouble imagining any other way to do...
In principle, this is a curve-fitting problem. You have three data points that you are using to fit a quadratic equation.
There are three unknowns in a quadratic equation (the "a", "b" and "c" in f(x) = ax^2 + bx + c). There are three data points that you have been asked to use (0.5, 0.1)...
Doing it is fine. Expecting it to be useful in a computation of energy needed to escape is questionable. If you need infinite energy to escape to infinity and you have infinite energy coming from the centrifugal field, how is a little bit of a boost to start with supposed to help?
I do not think that it is helpful to adopt the rotating frame and consider potential resulting from the centrifugal force field. That potential diverges as one gets far from the Earth, so any conservation of energy argument is wasted.
Like positive y = north, negative y = south, positive x = east, negative x = west.
You can choose to encode the direction in the sign that way. Or you can explicitly state the direction. Leaving the direction indication out entirely leaves us guessing at your intent. You should be writing for...
As I read it, you start by obtaining the components for the first flight leg, ##d_1##.
You evaluate 618 km times the sin of 58 degrees for the x component to obtain 524 km. This seems correct. However, I see no attempt to try to apply a sign convention.
You evaluate 618 times the cosine of 58...
In general, you would start with one compass direction. Due North, East, South or West. In this case, east. Then you would shift by the indicated number of degrees in one of the two compass directions at right angles to the first. In this case, southward. So E35S is 35 degrees south of due east.
You are fine. @PeroK is just going through the mathematical underpinnings of the fact that the two formulas for gravitational potential difference: ##PE=g(h_1 - h_0)## and ##PE=-GM(\frac{1}{r_1}-\frac{1}{r_0})## are excellent approximations to each other as long as ##h=r_1-r_0## is much smaller...
There is a complication that we may do well to explore. This is not an ivory tower thought experiment. This is a real physical experiment.
As drawn, the width of the vertical support post holding the platform up is similar to the diameter of the irregular object. That support post displaces...
It is unhelpful to mention everything that could be mentioned every time that thing could be mentioned.
It is useful to derive the fact of simple harmonic motion from a situation where mass is constant and force is directly proportional to displacement from an equilibrium position. Mentioning...
Are you trying to ask which is correct, whether acceleration in simple harmonic motion is really a function of time or really a function of position?
The answer is yes. In this case it really is a function of both. There is no underlying "true nature", whatever that term is supposed to mean.
Normally, the best use of fuel is to extract all of its energy and use that energy to hurl it out the back -- the spent fuel becomes the reaction mass.
If that approach is used, the relevant figure of merit is exhaust velocity. Sometimes it is expressed as "specific impulse": the length of time...
Well, there is good news and bad news. The good news is that it takes less and less force as you burn fuel. The bad news is that for a fixed payload, you need to have started with an exponentially large tank full.