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Solutions to Non-Ideal Gyroscopic Equations

In my work with gyroscopes, I have correctly derived the Lagrangian of a 3d top or gyroscope as $L=\frac{1}{2}I_{xy}(\dot{\phi}sin^2(\theta)+\dot{\theta}^2) + \frac{1}{2}I_{zz}(\dot{\phi}cos^2(\theta)...
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3answers
49 views

Work done over a closed loop

Is it true that the work done in the motion of a body over a closed loop is zero for every force in nature?
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1answer
81 views

Why don't objects bounce infinitely?

I'm computer programmer, and I was making a little test of my “possibilities”, so to speak, so I made a small game with sort of gravity, bouncing ball and walls around. Recently I've noticed that ...
0
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1answer
51 views

Sign of the work done by dissipation forces

I don't understand this passage from the book I'm reading: Physically, it is clear that a system cannot be conservative if friction or other dissipation forces are present, because $\mathbf{F}\...
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2answers
106 views

what are the sources of energy loss for a ball rolling down slope?

I am experimenting in lab with an iron sphere rolling down a smooth aluminum ramp. The final velocity is smaller than the one predicted assuming energy conservation (see calculations below), which ...
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3answers
59 views

Potential, Kinetic, Thermal Energy?

When things move, potential energy turns into Kinetic energy, right? Then how does Kinetic energy convert to thermal energy?
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3answers
9k views

Why can't we make a perpetual motion machine by using a magnet to pull up a piece of metal, then letting it fall back down? [duplicate]

Obviously, a perpetuum mobile isn't possible by any law in physics, because energy can't be "created" or "destroyed", only transformed. This said, I've had an idea for a perpetuum mobile and can't ...
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2answers
94 views

How is the simple damper equation derived?

I know the spring is modeled as $F_{\text{elastic}} = k\cdot x$ when the displacements are small since this is empirically based, but what happens with $F_{\text{damping}}=c\cdot\dot{x}$? It is the ...
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2answers
128 views

Harmonic motion with friction [closed]

Consider an undamped mass and spring system with friction. The friction is not proportional to the velocity of the mass. If we solve the corresponding differential equation,the spring will oscillate ...
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1answer
76 views

Explanation of a spring using “Artistotle's law of motion”, $\vec{F}=m\vec{v}$

So I was watching Susskind's Classical Mechanics lectures and I didn't understand something in the second lecture. He was telling about Aristotle's Law of motion which is $$\vec F = m\vec v.$$ He ...
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2answers
213 views

Why does height affect bounce efficiency?

I recently conducted an experiment, where I dropped tennis balls from various heights and recorded their rebound heights. The higher the drop, the higher the rebound height, obviously. However, the ...
2
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2answers
107 views

Exact equation of exponential curves of underdamped harmonic motion

I was studying the underdamped harmonic motion and got curious about the fact that the decreasing exponentials $\pm Ae^{-\gamma t}$ are good approximations only for light damping $(\gamma<<\...
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1answer
214 views

Maxwell's wheel and friction

We experimented with the Maxwell's wheel today and at the end we were asked about why does this apparatus stop since there is conservation of energy. I did some research and apparently there is a type ...
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1answer
543 views

How is the rate of decay of a Newton's Cradle affected by the number of spheres in the system?

How does the number of spheres in a Newton's Cradle affect its rate of decay? (assuming only 1 sphere is released initially) From experiment, I observed that the rate of decay of a 5 sphere Newton's ...
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2answers
106 views

When you have engine at idle and turn your car, where does the kinetic energy go?

When you turn the front wheels to the right for example, your car will tend to continue in its original forward direction. However, there is friction between the wheel and the ground that prevents it ...
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3answers
104 views

Kinetic Energy with constant velocity

I am sorry for the question, but I am a noob in Physics. I don't understand why in the kinetic energy's formula the distance is out of the equation. Kinetic Energy formula: $$K = \frac{1}{2}m v^2 = ...
2
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0answers
43 views

Potential gravitational energy versus potential spring energy [duplicate]

My textbook points out the following predicament, and I do not know the answer, despite a lot of thinking: A spring is hanging of a ceiling and a mass is attached. As a result the spring descends to ...
-1
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1answer
47 views

Phase shift of damped mass on spring with moving source [closed]

I have a setup with a moving (upwards, downwards) board on which there is a spring mounted on the edge. The spring has a mass $m$ on its end and is damped in some sort of liquid. What methods could I ...
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2answers
503 views

Why does a ball rolling without slipping stop due to friction? [duplicate]

I'm confused on a scenario. If we roll a ball on a horizontal surface and it rolls without slipping it should eventually stop due to friction. However rolling without slipping means the velocity at ...
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1answer
40 views

Approximating mechanical systems with high friction

I remember to have read (a long time ago) that if I have a mechanical system $\ddot x=\frac1mF(x)$ with a high friction, then I can instead study the other system $$\dot x\sim F(x)$$ to get an ...
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2answers
1k views

When is mechanical energy ever conserved for inelastic collisions?

So as I was taking a test today I encountered an intriguing question, the question came in two parts. The first parts, which I answered quite easily, was about whether or not mechanical energy is ...
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1answer
79 views

Why is there no friction energy?

Can anyone briefly explain to me why is there no term for frictional energy when they often referred to work done by friction instead? Thank you
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0answers
62 views

Can torsional force be used to harvest gravity?

I am curious if an idea I have will work or if it is the result of a lack of understanding of the physics involved. I am expecting to be disproved. Please excuse any lack of understanding on my part ...
1
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4answers
546 views

Friction during pure rotation

I have already read Role of friction during pure rolling What is the direction of the friction force on a rolling ball? Rolling resistance and static friction and many others But I still have the ...
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4answers
315 views

Non-conservative forces in nature [duplicate]

We know that gravitational, electrical and magnetic forces are conservative in nature. We also know that friction is fundamentally Electromagnetic in nature. How is it then a non-conservative force?
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1answer
75 views

Potential Energy of Damped Oscillator

In the case of a simple harmonic oscillator we know that the total energy of the system is given as $$E=\frac{1}{2}m\dot{x}^2+\frac{1}{2}kx^2$$ where the potential is $$U=\frac{1}{2}kx^2$$ I read ...
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1answer
41 views

Rowing Oar - Loss of energy

Modern rowing oars for still water rowing are made of various carbon composites, during the drive phase of the stroke (force applied by the rower) the oars bend slightly as in the attached photo ...
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2answers
1k views

Where does kinetic energy go after a car crash?

More specifically, where does it go after it destroys the crumple zone? My assumption is that after a collision most of the kinetic energy will be transferred into the metal in the crumple zone (the ...
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2answers
118 views

Principle of energy conservation

I am new to physics and I hope you can help me solve this problem. When two objects collide with each other and stick, there is an internal force, so linear momentum is conserved. But when I ...
15
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4answers
2k views

What exactly makes a force conservative?

I get that forces can be classified as either conservative or non-conservative, depending on whether the work done in a round trip is zero or non-zero. What property of the force makes it to be, ...
2
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1answer
36 views

Why is energy usually concentrated on low frequency modes in dynamics?

In all structural dynamics applications I have seen, the motion is mostly governed by low frequency modes. For example, a pretty accurate approximation of buildings dynamics can be obtained with the ...
2
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4answers
797 views

Spiral trajectory under gravity?

I know that the general equation of motion for a two body problem under gravity is usually an ellipse. $$r(\theta) = \frac{R}{1-e\cos(\theta-\theta_0)}$$ where $R$ and $e$ depend on initial ...
2
votes
3answers
559 views

Lagrangian and Hamiltonian formalism for damped pendulum

Suppose I have a simplified pendulum (massless string of length $l$, ball of mass $m$ and some non-zero volume). I want to derive the equations of motion, but I want to take air resistance under ...
1
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1answer
1k views

What slows down a fidget spinner more: air resistance, or friction from the bearing?

So "fidget spinners" are now massively popular. I got one, and it occurred to me that I'm not sure which force is more important in slowing them: friction in the bearing, or air resistance acting on ...
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1answer
395 views

Mechanical energy when ball is falling

I could not understand why mechanical energy of ball is not constant when time passes when a ball is falling in liquid with terminal velocity.
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2answers
141 views

Elastic or inelastic collision?

When two billiard balls collide in normal situation (on earth) we hear the sound due to their impact. This is a sufficient proof that the collision is inelastic in nature due to loss of energy in the ...
2
votes
2answers
749 views

What is the difference between damping and elasticity forces?

From DYNAMICS OF STRUCTURES, Third edition, by Ray W. Clough and Joseph Penzien Damping has much less importance in controlling the maximum response of a structure to impulsive loads than for ...
5
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1answer
3k views

Why does a rolling sphere stop?

I've just started studying Rotational Mechanics and one thing I'm confused about is that if friction is equal to zero when a body is rolling purely.. then why does a rolling body e.g. sphere.. stop ...
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2answers
71 views

Is it true that an object, in course of its motion, always seeks the position of minimum potential energy?

I have heard the statement, in a Classical mechanics course, that the motion of an object is always toward the position of minimum potential energy. I don't think that this statement correct because I ...
1
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3answers
198 views

Energy doesn't get lost? Basic understanding, please [duplicate]

If its true that energy isn't lost, its just transferred, where did the energy go from a falling object that hits the floor and stays there? It started with the most gravitational potential energy, a ...
1
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2answers
226 views

Which period should be used to determine average speed of a damped oscillator? [closed]

For a damped, driven oscillator, show that the average kinetic energy is the same at a frequency of a given number of octaves* above the kinetic energy resonance as at a frequency of the same number ...
4
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3answers
2k views

If string is stretched just by weight, where does the gravitational potential energy goes if only half is converted to elastic potential energy?

If a spring is stretched by a weight of mass m, (so the extension is $\Delta x$) then $ k = \frac W{\Delta x} = \frac {mg}{\Delta x}$. So $ k\Delta x= mg $. When the Spring is stretched by distance $\...
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2answers
843 views

How to calculate energy loss in a rotating shaft?

Please help me with proper formula for below example. Imagine a rotating shaft 'X' with 2 gear wheels 'a' and 'b' of same dimensions. If energy applied to gear 'a' on the shaft through source A ...
-4
votes
2answers
564 views

If I spinned a fan in a vacuum it will keep spinning forever. Why can we not make energy out of it? [duplicate]

Suppose we created a vacuum and spinned a turbine inside it with some amount of force. According to newton's second law it will keep spinning as there is no air resistance, so why can we not make ...
2
votes
4answers
745 views

Where does the energy go when engine braking?

If you're in gear in a car and not accelerating, the car slows down faster than it would from just air resistance and tire deformation. In normal braking, the energy is turned into heat from the brake ...
0
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1answer
53 views

Change of energy into friction?

If I am pushing a car and it does not move, I am doing no mechanical work. However, I am changing the energy that was stored in my cells into heat energy (maybe sound energy if my hand slips off the ...
1
vote
1answer
80 views

Help with my bouncy ball lab (I know the factors just not how to approach them) [closed]

In my physics lab we need to determine the factors that account for the energy "loss" during a high bounce ball bounce. I know that energy is "lost" (not really) to heat, air resistance, and sound. ...
0
votes
3answers
840 views

A moving bus suddenly stops. Is its momentum destroyed?

Absolutely not but how does momentum transfer to surrounding (ground, air particles)?
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2answers
761 views

Appearance of the Jerk Term in Dynamics of Mass-Spring-Damper System

I am coming from the computer science territory and have not a long trace in mechanics. My background in derivation of the system dynamics could be summarized with utilization of the ...
1
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5answers
6k views

What happens to the kinetic energy of a dropped ball when it comes to rest on the ground?

If we want to drop a ball from a height, we calculated that potential energy at bottom is zero and we say it is converted into kinetic energy. At that movement, if it is a kind of sand, we find it ...