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Topic: Physics question please help or at least lead me in the right direction!?**Question:**
A small boat anchor is cast from 0.001m3 of iron alloy. The iron alloy has a specific gravity of 8 (so, its density is 8 times greater than the density of water = 1000kg/m3). How hard will the anchor pull on the rope attaching it to the boat when it is gently lowered to the bottom of a lake?
please answer in newtons.
I am stumped by this, any help would be appreciated!

June 16, 2019 / By Alma

First lets solve an easier problem. If you were just holding the anchor in air, it would pull down on the rope with a force equal to the mass times gravitational acceleration. But what is the mass of the anchor be? Well, you know the volume and density, so the mass is .001 m^3 * (8 * 1000 kg/m^3) = 8 kg so the force the anchor would pull in air would be F=m*a= 8 kg * 9.8 m/s^2 = 80 N (remember 1 N = 1 kg m/s^2 ) Now, how does the water change the answer? Well, the anchor will displace an amount of water equal to its volume, so the force on the rope will be a little less, by the weight of the water displaced. The weight of the water is 1/8 that of the anchor, so the force on the rope will be 80N - 10N = 70 N If you think about it, you should be able to see that you didn't need to find the force on the rope in air, if you just knew that the force would be reduced by the water displaced, so you could have just solved the first two equations using 7 instead of 8. Hopefully you can see that, as that makes the problem much faster to solve on a test. PLEASE NOTE that I did not solve the problem exactly, since I approximated 8*9.8 as 80. You can solve it more exactly. I hope this helps!

👍 240 | 👎 6

Did you like the answer? There are several ways to do this. I actually started writing out the loong way using calculus when I actually finished reading your question and realized you don't need the equations of motion *sigh* :( Well this problem is actually quite simple then.. you could hardly call anyone a physics god for solving it.. but anyways.. Just use conservation of energy. If the pendulums length is 0.91m and it is pulled back 7.6° then the height is: height = 0.91m - (x component of distance from rotation point) height = 0.91m - 0.91m*cos(7.6°) h = 0.91m * [1 - cos(7.6°)] Gravitational potential energy is given by: U = mgh So: U = 0.73kg * 9.8m/s^2 * 0.91m *[1-cos(7.6°)] U = 0.0572 Joules Using conservation of energy we know that the sum of kinetic energy and potential energy in an isolated system is constant. BTW: this constant is called "mechanical energy" *hint* ME = T + U where ME="mechanical energy" T="kinetic energy" U="potential energy" At the bottom all of the potential energy is now converted into kinetic energy, so we have T = "kinetic energy" = 0.0572J = (1/2)mv^2 (1/2)0.73kg * v^2 = 0.0572J v = 0.396 m/s Oops, guess I solved part C first.. whatever.. Part B is easy to go from here, because ME = T+U ME = 0.0572J <---answer to part B Now, part A is a little trickier... or not.. depends on how you do it.. most people just like to memorize the equation for this case: w = sqrt(g/r) But I can explain this in more depth... which I will because I already wrote it out the first time I was writing this message. But you don't have to read the rest, everything above this paragraph is all you need. just substitute in w = sqrt(9.8 / 0.91) = 3.28Hz <---answer to part A Here is the explanation of WHY w = sqrt(g/r) in my own words... which most people don't care about anyways.. I'm just copying and pasting it from my earlier explanation so it may sound out of context: ======================================... ======================================... So the pendulum is going to have a torque of I*(θ..) where (θ..) = second derivative of theta with respect to time, similarly (θ.) = first derivative of theta with respect to time and I = moment of inertia (capitol "i" not a lower case "L") The torque can also be given by: rxF, or simply r*F*sinθ and F of course is -m*g so we have: I*(θ..) = -m*g*r*sinθ I (moment of inertia) for a single particle is: I = m*r^2 m*r^2*(θ..) = -m*g*r*sinθ now eliminate m and 1 r to get: r*(θ..) + g*sinθ = 0 OR dividing by r: (θ..) + (g/r)*sinθ = 0 You will find later that the g/r part determines the frequency.. specifically sqrt(g/r) which is why most books/teacher will simply tell you to solve this problem by giving you these: (θ..) + w^2 * sinθ = 0 where: w = sqrt(g/r) if you substitute in w you see it is the same as what I got above. At this point you can use either one, I suppose I will continue on using w^2 instead of g/r as it is the customary way, but if you do it with g/r instead you will get the same answer and also see why it is that w^2 = g/r BTW: w = "angular frequency" = 2*pi*frequency = 2*pi / period Next we need to make the assumption that this is for SMALL angles. The problem becomes very very complex (perhaps impossible to do by hand?) without making this approximation. So under this assumption we say: sinθ is about equal to θ itself. So now the problem is to solve the differential equation: (θ..) + w^2 * θ = 0 which as I said is the same as: dθ/dt + w^2*θ = 0 The way this is done is actually quite simple so if you want to know then send me a message, for unfortunately most books will just tell you the solution to an equation of this form, so that is what I will do. The solution is given by: θ(t) = A*e^(iwt) + B*e^(-iwt) Which can be shown to be equivalent to: θ(t) = A*cos(wt) + B*sin(wt) Now we have to find the coefficients A and B. It starts at 7.6 degrees, so we will call this t=0. θ(0) = A*cos(wt) because sin(w0) = sin(0) = 0 and clearly w = "angular frequency" which is sqrt(g/r).

What a team of horse dung! incredibly! How does Heisenberg uncertainty concept (which extra or less states that when you pinpoint an electron as to the place this is you may now no longer tell the place it is going and in case you be attentive to the place it is going you may no longer tell the place this is.) have something to do with the universe being undetermined and random? The uncertainty isn't that that is random or undetermined the uncertainty is which you may't be attentive to the the place this is and the place it is going on the comparable time, yet those are the two parts which could be had at separate circumstances. how are you able to logically bounce from electrons to the universe? If what you assert is actual and electrons are random and subsequently the universe is then that randomness turns right into a trend and not something interior the universe might desire to make any experience. like the improbability force on Zaphod's spaceship interior the Hitchhikers instruction manual if issues are relatively random then whales might desire to be appearing in mid air and crashing to the earth. additionally your Schrodinger equation this could be a quantum concept of ways a photon (gentle waves) can function as a particle and a as a wave on the comparable time. alongside with this concept you have over a dozen extra that are contradictory to Schrodinger's and yet answer the comparable issue. So how does that disprove there's a God? It would not clarify the place the photons got here from interior the 1st place, it would not clarify the existence of self, will, morals, supernatural, etc. incredibly throwing up this vomit is relatively poor. purely because of the fact maximum Christians don't be attentive to quantum physics, and in case you published this you needless to say do no longer the two.

The mass of the anchor is its density times its volume. Density of anchor = 8000 kg/m^3 Volume of anchor = 0.001 m^3 Mass of anchor = (8000 kg/m^3) * (0.001 m^3) = 8 kg The force pulling on the rope will be equal to the weight of the anchor, which is its mass times the acceleration of gravity. Force pulling on rope = (8 kg) * (9.8 m/s^2) = 78.4 N Therefore, the anchor pulls on the rope with a force of 78.4 N.

👍 100 | 👎 -1

Oh god...In my college some years in the past I had to do some thing alongside those lines different than development a style vehicle...i might say your superb guess is to commence out your music at an exceedingly first rate top so as that the marble can benefit adequate mommentum to maintain going for 60 seconds alongside with the jumps and all i might say in all probability the bounce and the 360 loop could be early on interior the music in the different case that's going to be working out of velocity through the time it gets to it and could no longer make it to the top, plus if on the top of your bounce you upload on yet another slant interior the downwards place you could p.c.. up slightly extra action from it. good good fortune!

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Not at all. I don't consider one's religious faith or beliefs as true mark of one's capabilities or intelligence. For example, while Sarah Palin is a creationist, she still believes that BOTH evolution and creationism should be taught in school side by side. When it comes down to it, you should judge a candidate based on their actions and past experiences, that is the only true indicator.

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