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m1 is the large cruise ship m2 is the tug boat The question doesn't state it explicitly, but I assume that both masses are undergoing acceleration because the tug boat is experiencing a change in velocity. I assume the system accelerates uniformly, and I assume that m1 and m2 accelerate...

Thank you for your response. To some extent, I agree with you, but to some extent I disagree. But perhaps I am wrong, I cannot say for now because I do not entirely understand the topic. Precisely speaking, the momentum of a system is conserved so long as there are no external forces acting...

Thank you for your response Is it possible to have recoil without conservation of momentum? It appears possible to me upon my first consideration, but I could not necessary precisely prove it. Perhaps, what I mean to say, is this: Is a ΔF or a ΔP or the Law of Conservation of Momentum an...

Thank you for your response. I am considering "recoil" more generally. I used the cannon example because it is one that I happened upon and it was fresh in my memory. But if "recoil" appears to have properties of force, momentum, displacement, and the the like, then can recoil be defined and...

I have a basic understanding of Newton's Third Law. This definition from KhanAcademy seems sufficient. "If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A." An object of some mass that exerts force an some...

I am having some difficulty understanding what "recoil" really is with respect to momentum, force, and and time. On the one hand, momentum is considered to be the product of mass and velocity or perhaps the product of the sum of masses and some velocity, or some variant of P=mv, where P is a...

Thank you. That is very helpful information. Is it fair to say that the angle of projection is, with respect to the position of the object, is constantly changing? Thanks

Thank you.

Dear Sir or Madam: I did all of my work, then I checked the answer in the back of the book (this does not give a solution, just a plain answer). With the wrong answer in mind, I really wanted to understandand why my reasoning was incorrect so that I understand the problem with greater depth...

My reasoning and answer is wrong, but I cannot figure out why. Perhaps it is strange, perhaps not, but I want to figure out why my initial method of solving this problem did yield an incorrect answer. I began by creating an equation and drawing a right triangle. x is the horizontal part of...

I understand this. But why not do one of two things... 1. Establish a new frame of reference that is accelerating? or 2. Simply acknowledge that, similar to time dilation, the speeds of these massive objects only appears to be traveling at the speed of light, however, the speeds that these...

But are there not such things as non-inertial reference frames? Can't we consider a reference frame in which the object is not at rest... ? Or even a reference frame of one photon to the other? I mean... is it possible to establish a reference frame in which a particle is accelerating or in...

I see. But why is it impossible for a photon to have a reference frame?

I had to look up the definition of "spurious." The question and constraints do not imply any falsehood. Let us examine the situation. I apologize, but auto-correct made a fool of me. In any case, I am constructing a diagram based on the information given and in the steps that said...

So, time only appears different relative to observer. Everything that is moving at normal speeds here on Earth might appear to move very fast relative to particle A, but in its absolute sense, time is experienced uniformly from particle to particle? But, I have read on this forum that photons do...

Thank you. I will purchase this book sometime in August when I have some free time to explore this topic. At the moment, my daylight is being consumed by the black hole that is academia.

Thanks. I have begun to read those first ten pages. I have an exam this weekend, but I will endeavor to understand those ten pages to the extent that my faculties permit.

Is there a particular source you might recommend to explain this more deeply (conceptually) for someone who is very new to physics and only has a background in single variable calculus with an introduction to integration (real variables)?

I think I understand. Both particles experience the passage of time similarly, correct?

Supposing that we have a hollow sphere of mass m and radius R. Furthermore, suppose that we attach the sphere to a rod of length L and mass M. Now, suppose we rest the rod-sphere contraption on a pyramid a distance (X+R) from the center of mass of the sphere and a distance [(L/2)-X)] from the...

If A and B are moving relative to each other, we might say that their interactions are similar to A being on a train and B being on the ground. I wanted to understand the motion of A and B relative to each other... what I mean is I wanted to understand how A and B can interact with each other...

The problem that I see is that they can never be at the same place at the same time because time is experienced differently for each particle? What I mean is... how can two particles be in the same place at the same time if both particles experience time differently? The only interaction that...

First, I am new to physics and only taking my first course in calculus based classical mechanics with topics covering thermodynamics and an introduction to general and special relativity. Everything here is pretty much a question, even if periods exist and not question marks. My teacher had...

I understand what you are saying; however, multivariable calculus goes beyond the scope of my education and the discussion. Conceptually, I understand what you getting at. Notice that the question is slotted as a beginning level calculus question, not a third semester college calculus question...

I see. I will research your notation in a bit to try to understand how they are equal to mine. I was just working on this again and I think I see where you are going... but it slipped my mind... The volume of the snowball melts at a rate proportional to the surface area. I am still struggling...

Also, I do not understand your notation. Can you please use words? It seems that you are saying that the derivative of volume at some arbitrary time for some arbitrary radius (with respect to time) is equal to some constant of proportionality multiplied by the surface area at some arbitrary...

The derivative of volume is equal to surface area?

A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. Two ratios are proportional if they change equally and are related by a constant of proportionality? Not sure about this definition, but please correct it if you can...

Thank you.

Thanks. I understand the value of checking units, but in math they are useless. I understand where you are going though, as I once had a chemistry TA make the statement "numbers without units are useless" as in... I think he was getting at something like "math without application is useless."...

Can someone help me with this? (dA/dt)=1cm/s (cm^2 whatever...leave out trivial corrections). A=pir^2 (dA/dt)=2pir(dR/dt) Multiply through by (1/2pir) (dA/dt)/(2pir)=dR/Dt What is the rate of change of the radius for a circumfrance of 2 I just used the related rates formula that I derived for...

Thank you.This problem is a practice problem to develop the quotient rule for differentiation (I have only taken calculus 1 and am waiting to take calculus 2). I decided that I would like to try to use the limit definition to find the derivative for this particular function (I usually pick...

Is this a series? I have not taken calculus 2... is there a way to simplify this limit without using a series? I am not really familiar with them...

What does it mean to "develop" the exponential? I apologize, I never really understood math terminology. Words like argument and stuff... always go beyond me Thanks

Sorry, I just took that from wolfram. It was supposed to be what I had typed in (didn't want to retype), but I see the problem. It seems I did not correctly type in what I wanted to take the limit of...I actually didn't even notice that because wolfram wasn't that helpful (it just says simplify...

lim_(h->0^-) (e^(x+h)/((x+h)^2-1)-e^(x+h)/(x^2-1))/h = -(2 e^x x)/(x^2-1)^2 I know how to differentiate the expression using the quotient rule; however, I want to use the limit definition of a derivative to practice it more.This desire to practice led me into a trap! Now I just can't simplify...