Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.
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Trajectory of projectile thrown downhill
I'm teaching myself mechanics, and set out to solve a problem determining the optimum angle to throw a projectile when standing on a hill, for maximum range. My answer seems almost plausible, except ...
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Flying a toy helicopter inside an accelerating train
Scenario:
You ride in a train, you have this helicopter toy. The train is not yet running when you flew your helicopter on a constant altitude (say 1 meter above the train's floor).
Question:
What ...
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How to find the value of the parameter $a$ in this transfer function?
I am given a transfer function of a second-order system as:
$$G(s)=\frac{a}{s^{2}+4s+a}$$
and I need to find the value of the parameter $a$ that will make the damping coefficient $\zeta=.7$. I am not ...
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How could this damped oscillator ever go to infinity? Or negative infinity for that matter?
This is an ODE problem,but I cannot visualize why it can go to infinity or negative infinity.
Consider
$$x'' -6x' + 8x = 0$$
Where $x''$ is acceleration, $-6x'$ is the ...
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1answer
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Would a light or a heavy ball roll fastest down a slope?
A small, light ball and a larger, heavier ball are released from the top of a slope.
Which will move further? which will come down faster?
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What is a Free Body Diagram?
I have this problem:
A 10 kg box is resting on a frictionless table and someone drags it by a string at a 30 degree angle to the horizontal with a force of 40 Newtons. Find the acceleration of the ...
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1answer
240 views
Mass points of a Mass-spring model
Let's say I have a mass spring model like the one in the picture below:
So, there are 3 parts of the spring joined together in an equilateral triangular manner. Each of the joints has a mass of ...
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1answer
318 views
Elastic Collision And Momentum
The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = ...
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236 views
Force applied off center on an object
Assume there is a rigid body in deep space with mass $m$ and moment of inertia $I$. A force that varies with time, $F(t)$, is applied to the body off-center at a distance $r$ from its center of mass. ...
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1answer
327 views
Calculating torque in a structure
I posted this on math stack exchange but realize it is more a physics question.
I have a structure which is set up as shown in the image. A weight hangs from point A with mass $m$. Joint B is free ...
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1answer
114 views
Question about interaction between three objects
I have been thinking of Newton (insert bad words because of frustration) laws for hours and hours today, and I'm not going anywhere. I'm going insane! So, I made up this question.
Object A | ...
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History of interpretation of Newton's first law
Nowadays it seems to be popular among physics educators to present Newton's first law as a definition of inertial frames and/or a statement that such frames exist. This is clearly a modern overlay. ...
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Does juggling balls reduce the total weight of the juggler and balls?
A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that ...
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Could someone jump from the international space station and live?
Felix Baumgartner just completed his breathtaking free-fall skydiving jump from $120,000\,\text{feet} = 39\,\text{km}$ above the Earth, breaking the speed of sound during the process.
I was wondering ...
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4answers
554 views
Is there a deep reason why springs combine like capacitors?
I was solving a practice Physics GRE and there was a question about springs connected in series and parallel. I was too lazy to derive the way the spring constants add in each case. But I knew how ...
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How to explain independence of momentum and energy conservation in elementary terms?
I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
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1answer
752 views
Solving a statically indeterminate truss
I'm trying to solve the statically indeterminate truss shown below and I'm having a little trouble.
$H$, $P$ and $\beta$ are given. The material is aluminum (density is 2700 ${kg/m^3}$) and has a ...
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2answers
611 views
When does not Newton's 3rd law apply?
Is Newton's 3rd law valid in non-inertial frames?
If so, then are there other cases for which Newton's 3rd law is not applicable?
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Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph?
I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, ...
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6answers
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Why is torque not measured in Joules?
Recently, I was doing my homework and I found out that Torque can be calculated using $\tau = rF$.
This means the units of torque are Newton meters. Energy is also measured in Newton meters which are ...
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2answers
861 views
Norton's dome and its equation
Norton's dome is the curve $$h(r) = -\frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$.
Via Norton's web.
If we put ...
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3answers
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Is the normal force a conservative force?
Most of the time the normal force doesn't do any work because it's perpendicular to the direction of motion but if it does do work, would it be conservative or non-conservative?
For example, consider ...
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4answers
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Can an object accelerate to infinite speed in FINITE time (Newtonian)?
Obviously this is impossible in relativity; however, if we ignore relativity and use only Newtonian mechanics, is this possible? How (or why not)?
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Why are there both Static and Kinetic Friction?
When dragging an object, there is a greater start-up force than the force it takes to keep it moving. Why is this? Why are there two different values for friction?
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1answer
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Book suggestions for foundation of Newtonian Mechanics
I'm not looking for books which deal with the mathematical foundations of Newtonian mechanics. What I'm looking for are modern books which deal with conceptual foundations of Newtonian mechanics - by ...
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7answers
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Is Melancholia's orbit impossible?
In the recent movie "Melancholia", a planet, also called Melancholia, enters the solar system and hits the Earth. I want to leave aside the (also unreasonable) aspect that planet "hides behind the ...
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How is distance between sun and earth calculated?
How has the distance between sun and earth been calculated by scientists?
and size of sun?
Thanks,
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Why is there this asymmetry between the two foci of an orbital ellipse?
Why does the Earth revolve with the Sun at one of its foci? Does the other focus do nothing? Why is there this asymmetry in our solar system?
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Effect of the tail of the cat in the falling cat problem
To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in
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Is there a good Modern English translation of Newton's “Philosophiæ Naturalis Principia Mathematica” available for free viewing/download?
I have found several nice versions available for purchase, but all of the free ones are either Latin, old English, or pixillated. I searched google and was only able to locate the free ones linked to ...
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Some questions about the logics of the principles of independence of motion and composition of motion
In high-school level textbooks* one encounters often the principles of independence of motion and that of composition (or superpositions) of motions. In this context this is used as "independence of ...
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1answer
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3 current loops with non-conservation of momentum, when one specifically considers SIGNs
Thought experiment I.
Consider two loops of wire, 2 small dipoles B and C , with a common axis z (facing each other) and (say) 30 cm apart B to C. At the speed of light, information (including a ...
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1answer
354 views
Countersteering a motorcycle
Everyone knows the story about countersteering. For those who don't I will explain it below and after the explanation i will ask my question.
You can watch this short video as a beginning: ...
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Using acceleration to plot position
Sorry if this question is dumb, and I know is physics 101, but I'm not that good with physics.
I'm writing an iPhone program that by collecting the acceleration data of the device tries to replicate ...
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4answers
333 views
Irreversible expansion and time reversal symmetry
Suppose there are N non-interacting classical particles in a box, so their state can be described by the $\{\mathbf{x}_i(t), \mathbf{p}_i(t) \}$. If the particles are initially at the left of the box, ...
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What is the difference between weight and mass?
My science teacher is always saying the words "weight of an object" and "mass of an object," but then my physics book (that I read on my own) tells me completely different definitions from the way ...
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4answers
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Does it matter how you order your tug-of-war participants?
In a tug-of-war match today, my summer camp students were very concerned about putting the biggest people at the back of the rope. Is there any advantage to this strategy?
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What is the maximum efficiency of a trebuchet?
Using purely gravitational potential energy, what is the highest efficiency one can achieve with a trebuchet counter-weight type of machine? Efficiency defined here as transformation of potential ...
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2answers
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What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?
I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
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2answers
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Explanation that air drag is proportional to speed or square speed?
A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the drag (air resistance) which is proportional to the object's speed. By Newton´s laws this can ...
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1answer
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Slinky base does not immediately fall due to gravity
Why does the base of this slinky not fall immediately to gravity. My guess is tension in the springs is a force > mass*gravity but even then it is dumbfounding.
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1answer
231 views
Shaping a wire such that a bead sliding on it has exactly isochronous oscillations
Let a wire be shaped according to some even function $y=f(x)$, with $f'(0)=0$ and $f''(0)>0$, and let a bead of negligible size slide frictionlessly on the wire. Let the bead oscillate ...
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3answers
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A fly in an accelerating car
A fly is flying around in a car, the fly never touches any surface in the car only fly’s around in the air inside the car. The car accelerates. does the fly slam in to the rear window. or does the fly ...
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4answers
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How Felix Baumgartner has reached the speed of sound quickly
I have watched Felix Baumgartner freefall; but I wonder how Felix has reached the speed of sound quickly, in a matter of some seconds, then we had no idea of its speed?
Any explanation please.
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2answers
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How much thrust would be needed to turn a hobbyist weather balloon into a deep space probe?
I was reading the article Weather Balloon Space Probes that says you can put your own balloon probe at 65,000 ft temporarily.
Is it even remotely possible to raise the probe high enough using ...
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3answers
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How do I calculate DC motor speed for a given load?
Suppose I have a robot of a given mass, and I'm choosing between 2 different wheels and 2 different motors to put on it. For each wheel I have the diameter, and for each motor I know the stall torque ...
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2answers
168 views
Finding optimal angle for projectile, taking into account linear (Stokes) drag
If you throw a projectile from the ground at a certain angle, it's not hard to see that, assuming we're in a vacuum, throwing it at 45º from the ground will always make it go farthest before it hits ...
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Does Earth's Rotation Affect Its Shape?
The question I am working on is, "Consider the following.
(a) Find the angular speed of Earth's rotation about its axis. rad/s
(b) How does this rotation affect the shape of Earth?"
I am fully ...
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Newton's 3rd Law: How can I break things?
If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist?
When the board breaks in two due to my force, the halves have a ...
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1answer
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What is the function of the top point of a bouncing ball?
A ball is thrown away as parallel to x axis from M(0,h) point with speed V . After each jumping on x axis , it can reach half of previous height as shown in the figure.(Assume that no any air ...
