New answers tagged newtonian-mechanics
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Why does that screw-propelled vehicle steers opposite to common sense?
I can only offer some comments, which may or may not be useful. According to the offscreen voice in Russian, initially the vehicle's control was poor, but it improved when they started to use a screw ...
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Pivoting rod analyzed about a rotating axis
Two mistakes were made. First, the translational work done by the pin was neglected. By performing similar calculations as was done for the rotational work by the pin, the translation work is found to ...
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What is the relation between bicycle rear wheel path and front wheel path?
We can gain some insight into this relation if we note that the velocity vector of the rear wheel must be at every instant proportional to the vector pointing along the body of the bike itself:
$$ \...
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Finding the accelerations and tension of a pully wedge system
It seems tedious but not very complicated.
You don't show what is your answer or how you arrive to it. So if you are making a mistake for example in the the forces you put in the 2nd law equation, we ...
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Motion of fragments
If we assume that all the fragments have the energy, then for three fragments, we have that the momentum vectors have equal lengths, and their sum is zero. The sum of vectors is geometrically ...
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Looking for an intuitive understanding of normal force
Here is my idea for what the intuition is behind the normal force. Forces come in pairs. I have seen online that this is true of gravity. Gravity pulls me towards the Earth, but it also pulls the ...
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Gravitation satellite orbiting earth
Your statements are consistent because they are answering two different questions.
The first case, where you keep the angular momentum fixed, $v \propto r^{-1}$. Consider a planet orbiting in circular ...
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Is the $\Sigma$ in Newton's second law the sum operator or an "arbitrary" notation?
This is not a physics question, it's a notation question. In most books, you'll find
$$\sum \vec{F} =m\vec{a}, $$
where $\sum$ is the summation symbol. The expression
$$\Sigma \vec{F}=m\vec{a} $$
...
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Is the $\Sigma$ in Newton's second law the sum operator or an "arbitrary" notation?
The sum operator $\sum$ is just the greek letter $\Sigma$ (= S in our alphabet) but bigger. It's not an accident. It's just the first S of the word "Sum". It's the same reason why we use a &...
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Is the $\Sigma$ in Newton's second law the sum operator or an "arbitrary" notation?
Newton’s law, correctly stated with a summation, is
$$\sum_{i=0}^{n-1}F_i=ma$$
for mass $m$, acceleration of the system $a$, and all $n$ forces considered $F_0,F_1,…,F_{n-1}$.
I don’t know why someone ...
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Motion of fragments
is it even possible to accurately predict the motion of the fragments of an ideal body given that it splits into equal masses?
No, at least, not if all we are given is that the system conserves ...
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What is the relation between bicycle rear wheel path and front wheel path?
The equation is an approximation to the wheel path - it ignores factors such as rake and the natural tilt that a bicycle takes when turning.
A reasonable model of a bicycle path is to consider the ...
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What is the relation between bicycle rear wheel path and front wheel path?
$\frac{R'(t)}{|R'(t)|}$ is a unit direction vector in the direction the rear wheel is moving.
Your formula basically says that the front wheel is exactly distance $L$ in front of the rear wheel, and &...
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Motion of fragments
In a nutshell, is it even possible to accurately predict the motion of
the fragments of an ideal body given that it splits into equal masses?
Why wouldn't it?
For conservation of momentum, if the ...
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Motion of fragments
Yes, it is possible to predict the movement of fragments that break apart in parts of equal mass. Consider that the energy must be evenly divided among the bodies, which results in all bodies having ...
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Motion of fragments
In general, you would need very precise, and often unattainable, information about the internal structure of the fragmented body, the exact nature of the stresses that caused it to fracture, and a ...
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How does the steering wheel return to the centre after turning (and letting go)? What forces are causing the self centreing torque?
Stability of steering is complicated and not completely understood.
You might watch this video from MinutePhysics - How Do Bikes Stay Up?. Or this from Veritasium - Most People Don't Know How Bikes ...
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How does the steering wheel return to the centre after turning (and letting go)? What forces are causing the self centreing torque?
The simplest instance of using caster angle to give a wheel a tendency to return to a particular orientation is with the type of caster wheel that a shopping cart has, but with the pivot axis at a (...
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Work-energy Confusion
It could have been stored in any form:
Kinetic energy (KE): a golf club hitting a golf ball loses KE to do work accelerating the ball.
Gravitational potential energy (PE): a sky diver falling at ...
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Work-energy Confusion
The question overloads the word "system", so I am going to plow ahead assuming I know what you mean. but first:
When addressing these conservation/symmetry type question, it's really ...
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Inconsistent result when finding the minimum speed to reach the highest point of a circular road
The minimum of $v_A$ makes $v_B=0$
The problem is that a car can't reach B and have zero velocity. If it has some tangential velocity, then it can't get rid of it at B since the only forces on it ...
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Trouble with the concept of external force on a system
There are many ways to show that there is another external force acting on the two mass and string system other than the two gravitational forces on the masses and the normal force on mass $m_1$, the ...
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What is the maximum displacement at which a series of blocks can be displaced vertically?
I remember such a problem, the displacement of cubes placed one on another was only in one direction. The total displacement could be arbitrarily large, and maximum displacements formed the harmonic ...
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How to understand the work-energy theorem?
In this answer I will derive the work-energy theorem twice: Section 1 presents a derivation that straightaway adresses the case of an arbitrary acceleration profile. This approach requires integration....
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Is there a principle that determines the tension in this system?
Apologies for posting a second answer. My first answer addressed what I considered to be the more realistic case of non-infinitely rigid connections. This answer specifically addresses the ...
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Why don't we use rocket engines in cars?
From one of your comments:
So is it true that a car uses 100X as much fuel to go 100km/h => 101km/h as 0km/h => 1km/h? And rockets do not have this constraint?
No, rockets have the same ...
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Why don't we use rocket engines in cars?
These answerers are all really dumb.
A unit of fuel produces a unit of v^2 in BOTH examples. The question is wrong.
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Is there a principle that determines the tension in this system?
The way to approach friction problems is to consider all the sliding contacts as sticking first and finding the friction force required to enforce the sticking.
Assume all bodies have zero ...
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Is there a principle that determines the tension in this system?
The problem is poorly worded. "Pulled on a rough surface" could be interpreted to mean the blocks are in motion, in which case the coefficients would be for kinetic friction. But that would ...
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Is there a principle that determines the tension in this system?
For convenience I will label the blocks as $m_1, m_2, m_3$ from right to left to be consistent with the labeling of the tensions in you diagrams.
For simplicity consider a single block of mass $m$ ...
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Difference between torque about point and torque about axis
Difference between torque about point and torque about axis
One difference is the net torque about an axis produces angular acceleration about that axis. The net torque about a point produces angular ...
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Is there a principle that determines the tension in this system?
You are essentially asking about the distribution of static friction when an extended body at rest on a rough surface is pulled from one end. The answer is that it is indeterminate without more ...
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How to determine if there is frictional force?
Ignoring creep, the left board does not provide friction if it suddenly becomes rough. (If you find the sudden emergence of mechanical friction far-fetched, replace it with an adhesive bond that sets.)...
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How to determine if there is frictional force?
When you way "coefficient of friction," that leads me to assume you are talking about Columb friction, where we model friction as a force that opposes motion which can be up to some constant ...
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Limits of the integral for the calculation of work
This response is specifically to this section of your question:
I know that for potential energy the above statement is correct, one can choose the reference (zero) value as one wishes. But, for ...
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How to derive the formula of the buoyant force?
First, let's derive the basic buoyancy equation.
The rectangle on the left represents a vertical cylinder of water of height $H$. The pressure ($P_H$) exerted at depth $H$ is equal to the weight of ...
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Is the efficiency of a balanced lever 100 percent?
The values of $F_R$ and $F_E$ you plugged in for the AMA are the same values that determine the IMA for the given lever arms, so you have proved nothing.
The AMA must account for friction. When there ...
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Is the efficiency of a balanced lever 100 percent?
And that means my actual mechanical advantage would be 2.5, (the ratio
of forces) which means my efficiency would be 100%. That seems wrong to me,
and I wanted to check the conceptual gap I was ...
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Forces between two like charges and Newton's third law
No, it doesn't work this way.
N3L states that interaction forces always come in pairs. Such that if object $1$ applies force $\vec{F}_{12}$ on $2$, then $2$ applies a force $\vec{F}_{21}$ on $1$ that ...
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Clarification of Ehrenfest theorem
The Newton's equation of motion in potential $V(x)$ are:
$$
\dot{x}=\frac{p}{m},\dot{p}=-\frac{dV(x)}{dx}
$$
or simply
$$m\ddot{x}=-\frac{dV(x)}{dx}=F(x),$$
where $F(x)= -\frac{dV(x)}{dx}$ is called (...
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Change of coordinates in a potential energy
Why can I just not write [...] $V(x)=\alpha mgx^2$ and use from there Newton's law of motion to derive [...] the position of the mass $m\ddot{r⃗}=−∇⃗ V$
One simple answer is that the force from the ...
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Difference in answer using relative motion and that without (Newtonian Mechanics)
A better way, for me, to solve the question: consider the equation of the position of each body:
S1 = -V1t + a1t²/2
S2 = v2t - a2t²/2
Therefore, the distance that separates them will be given by the ...
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Why is friction required to rotate a non-ideal pulley-string system?
Friction between the rope and the pulley results in a torque, causing the pulley to start rotating from rest. Without friction, there is no torque, and no rotation - in this scenario, the rope simply ...
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Why is friction required to rotate a non-ideal pulley-string system?
Without friction, the rope would simply slide over the roll with no rotating motion.
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Apple falling from boat mast
However it seems to me that those 2 examples are not the same. On a train, the compartment is closed, so the air is trapped and also moves with the train. With the boat case, there is no close ...
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Apple falling from boat mast
Assuming a 20m mast, I think it takes roughly 2s for the apple to reach the boat, and I'd say that in 2s, the air has ample time to slow the apple enough so that it doesn't fall on the bottom of the ...
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What is the base of defining eccentricity like this?
The equation you are considering represents a conic in polar coordinates, and in that form, the coefficient of $\cos \theta$ is the eccentricity. Of course, such an identification is consistent with ...
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Height of a mass swinging on a rope
If I understood correctly, the problem is to find out why, if the masses have the same angular velocity $\omega$, they also must be always at the same height $h$ from the ceiling.
Given a mass ...
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Pivoting rod analyzed about a rotating axis
So, I will show you the solution using the concept of Conservation of Energy.
So, When the rod is released, it's centre of mass travels a vertical distance of "h" which leads to the loss in ...
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Doubt with Heat and Potential Energy. (Warning: Many Assumptions)
I assume the question is meant to be solved this way: Temperature corresponds to the mean kinetic energy of particles in a substance. So if the water at the bottom of the fall has more kinetic energy (...
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