Questions tagged [newtonian-mechanics]

Newtonian mechanics discusses the movement of classical bodies under the influence of forces by applying Newton’s three laws. For more general concepts, use [classical-mechanics]. For Newton’s description of gravity, use [newtonian-gravity].

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Question about a harmonic oscillator

I was solving the following problem on harmonic oscillation and I don't understand a specific part in the proof. I will emphasize (italic) the part which I don't understand. Problem: The following ...
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1 answer
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How can I know which direction the system will move?

Pin A is fixed to link EC, DO is rotating clockwise as shown. How do I know if CE will rotate clockwise/counter clockwise? I fail to imagine the movement in this case. On A, there is a normal force ...
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Why is the work done by an expanding ideal gas $\textbf{P}_{ext}\Delta V$?

Consider an ideal gas in a cubical container as our system (only the gas is the system, not the walls of the container). If I understand correctly, if the gas expands at constant pressure $P_{int}$ ...
2 votes
1 answer
543 views

Confusion regarding torque and calculating linear/angular acceleration of an object when a force is applied a distance from its center of mass?

From what I have read/learned about torque, it appears that it is derived based on the idea that applying a force farther from a point about which an object rotates increases the rotational force ...
12 votes
7 answers
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What happens if a slow train hits you?

It's funny, I used to wonder this at school many years ago. For the purposes of discussion, imagine there is a big (very massive) cube that slides towards you as you're sitting on the floor. It doesn'...
10 votes
2 answers
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Arnold´s Math Methods of Classical Mechs - a question on Newtonian Mechanics

There is the following question/answer on Arnold´s book Mathematical Methods of Classical page 10. Arnold's Question A mechanical system consists of two points. At the initial moment their ...
3 votes
1 answer
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At what $ω$ would the dust particles fly off the tilted rotating disc?

I've been struggling with question below: "A metal disc of radius R can rotate about the vertical axis passing through its centre. The top surface of the disc is uniformly covered with dust ...
1 vote
3 answers
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What is the relativistic Hamiltonian for a charged particle in an EM field, using the magnetic scalar potential?

The Hamiltonian for a relativistic charged particle moving in a static electromagnetic field is the well known: $$H=c\sqrt{\left(\mathbf{P}-q\mathbf{A}\right)^{2}+m^{2}c^{2}}+q\phi$$ where,\begin{...
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3 answers
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What are pre-collisions and post-collisions in forces and momentum?

What are pre-collision and post-collision exactly? I assume it is before collision and after collision. I can not find an answer on google.
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Angle for ruler falling off the table

When you place a ruler on the edge of the table so that one end is hanging off the table, and you apply a force to the hanging end with your hand, at what angle (angle between ruler and table) will ...
1 vote
1 answer
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Why is the normal force of a rope on a pulley, not considered while analyzing the free body diagram of pulley?

Suppose an inextensible massless rope is placed on a pulley surface. Obviously there will be a normal force between the pulley and rope, right? Why is the normal force of rope on the pulley ($N_{...
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2 answers
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Work done by conservative and non-conservative forces

Work done by conservative forces changes one form of mechanical energy into another. Is it correct to assume that work done by non-conservative forces changes one form of energy to another, for e.g., ...
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Directions of Coriolis Force [closed]

I am actually confused about the direction of Coriolis force. Like why the Coriolis force along x axis will have a velocity V and vice versa. Also why the force in y direction is negative? I have also ...
1 vote
2 answers
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What does it mean that the relationship between material mass and weight is constant and proportional?

I hope someone can help me with this apparently very basic doubt, but I feel like a stupid monkey trying to join two sticks to reach bananas and without success. My English is not good, I am Mexican ...
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4 answers
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How do you calculate the energy required to hold a weight against gravity?

What is the energy required to hold a mass in place? To lift 1kg 1m at sea level I must use 9.8 J. but if I simply grab onto a 1 kg mass that is on a table and the table is removed. I am now using ...
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Settle an argument on rotation [closed]

The story of this problem is convluted But basically, an old classmate who loved to brag his precieved intelligence sent me a bunch of problems to idk, show off I guess. Today, I remembered that and ...
1 vote
1 answer
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If three forces act on an object in equilibrium, they must pass through a common point. How does this generalise?

If three forces act on an object in rotational equilibrium, the line of action of each force must pass through a common point (parallel forces satisfy this as they go through a common point at ...
2 votes
1 answer
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How to find particular solution to this system of two masses connected by a spring with constant applied forces? Does an analytic solution exist?

This question comes from review I'm doing on my own, so it's not any homework question. I thought this question would be easy to solve, but I seem to be stuck and I am having second thoughts, so I'm ...
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3 answers
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Work done on a frictionless surface

Imagine that we apply a force $F$ on a frictionless surface to move a body by a distance $d$. (The body starts at rest and is stopped after moving a distance $d$.) Is the work done $F d$? But from ...
1 vote
2 answers
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What if we used extensible string in pulley?

While I was solving questions,I saw that in most the questions, it's written that the used string in pulley is non-extensible, Why? What would happen if we used extensible string having elasticity?
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1 answer
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Are there only 2 types of motion -- Translational & Rotational?

When searching up the different types of motion, results show circular motion, translational motion, oscillatory motion, rotational motion, periodic motion, etc. But just to clear things up in my head,...
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1 answer
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How can the Joule be the unit of both work and energy?

Say a person applies 1 N to a box with a mass of 1 kg, displacing 1 m. This is one Joule of work (1 N for 1 m). Now say the person applies 1 N to a box with double the mass, displacing 1 m as well. ...
2 votes
1 answer
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Extensible string on a pulley

Suppose we have an extensible massless string satisfying Hooke's Law, tied to a wall at one end and going over a 'frictional pulley'. Now if we tie the other end with a mass $M$, the total length of ...
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1 answer
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How was the reference system taken here?

in this Atwood machine digram y1 is the amount that m1 gets displaced and y2 is the amount that m2 gets displaced the lecturer then wrote $y1=-y2$ , I am trying to understand what did he do to get ...
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1 answer
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Work done to raise an object in two sample cases

I know that gravity does a work of an amount equal to $MGH$ because a more formal definition of work $W$ done by a net force $F$ is $$\int_a^bF(x)dx$$ where $F(x)$ is the net force acting on a ...
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Force Distribution and Torque [closed]

They say that torque helps us when we switch from linear force to rotational force. If there had never been such a thing as torque defined, what would it be like if I tried to figure it out with force ...
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4 answers
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Centre of mass frame

I was just looking at the equation: $$v2-v1=-e(u2-u1).$$ This equation is to describe the collision between two masses, where $v$ is the final velocity and $u$ is the initial velocity, $e$ is the ...
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Why is $R$ not the Radius of Curvature, here?

Consider this question, Two masses A and B are connected by a massless string. A rest in equilibrium on a rough horizontal table and limiting friction is acting on it. B hang vertically at a distance ...
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Where am i going wrong in this circular motion problem? [closed]

What am i doing wrong? Bob of a pendulum is taken to horizontal position and left. Find the angle of string with vertical when the vertical component of velocity is maximum. The vertical component of ...
1 vote
2 answers
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Bike leaning angle computed in stationary frame

In the problem of computing leaning angle ($\theta$) of a turning bike, the traditional approach is to move to the accelerating reference frame and compute the balanced torques with respect to the ...
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Does a spring exert no force while in a slack condition?

Consider a block of mass $m$ hunged by a spring of spring constant $k$. Let it be in equilibrium position where $mg=kx$. Now it is given a sudden impulse in upward direction so that it starts moving ...
1 vote
3 answers
309 views

How much more fuel to double the speed?

Suppose it requires a certain amount of fuel to accelerate a car (or a spaceship) from 0 to a speed $v_1$ (in some initial frame of reference). Let's ignore all friction forces, and only consider ...
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2 answers
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Where does a body get its energy to heat up when falling from height $h$?

When a body falls from a height $h$ it loses some energy to the surroundings, is it the energy that is lost to the surroundings that increases its temperature on the remaining energy that is stored in ...
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Lami's Theorem Problem

Lami's Theorem states that the magnitude of each force in an equilibrium state consisting of three coplanar, concurrent forces acting at a point is directly proportional to the sine of the angle ...
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Accelerating car under the influence of rolling friction

Consider the following textbook problem: An electric car of mass $m = 3500 kg$ has stored $E = 100 kWh$ in its battery. The rolling resistance coefficient is $\mu_R = 0.8$. How far can the car travel ...
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What is the moment acceleration of the center of mass for a rigid body under an external force

As shown in the following, a rigid body experiences an external force $\overrightarrow{F}$ away from its center of mass C: The rigid body is assumed to be free in space, experiencing no other force. ...
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1 answer
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Extension of Orbit by Reflection about Apsidal Vectors

I am self-studying the 3rd edition of Goldstein's Classical Mechanics and I'm having trouble making sense of a certain figure, namely, Figure 3.12 (p. 88), reproduced below. The figure follows an ...
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Is this how friction is a centripetal force when a car is making a turn? [closed]

I've been wondering why frictional force acts as a centripetal force when a car is turning; my intuition would not lead me to believe it would act perpendicular to velocity, but I think I have at ...
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2 answers
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Momentum conservation laws and explanation

I understand that momentum can be conserved along a certain axis while not along another. If there are forces that are affecting our system in the axis we are interested in that means the momentum ...
54 votes
5 answers
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What allows a pull-back toy car to drive further than it was pushed?

Imagine you have a pull back toy car. Its back part is on $x_0$. You push it down and move it in the back direction to the point $y$ (not marked): Then you leave the car to move away: Then you mark ...
4 votes
2 answers
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Why is $mg$ split into components instead of the tension in vertical uniform circular motion?

I am a beginner physics student. I am trying to prove that the magnitude of the tension varies sinusoidally as an object P travels around the circle or something of that sort. Thus, I am evaluating ...
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Why isn't momentum conserved in this situation?

This is a homework problem, however I am not looking for the solution but trying to know why I got the correct solution and why other methods don't work. Consider the attached diagram. We have two ...
3 votes
2 answers
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Can we have pressure with zero net force on a 2d plane?

From Wikipedia: Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Suppose we apply 2 equal and opposite forces on a 2d plane ...
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Difference between working at a constant rate and exerting a constant force [closed]

Let's assume that two trains of equal masses are moving along parallel paths. The engine of train 1 exerts a constant force, and the engine of train 2 works at a constant rate. If in time $t$ they ...
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Different results for torque in inertial and non-inertial frames of reference

I have a right handed coordinate system with origin O. On the plane yz there's a triangular-shaped plate with sides lying on the axes, both of length a. The plate rotates around the z axis (vertical ...
2 votes
1 answer
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Why applying the second law of motion gives me the wrong value of tangential acceleration in vertical circular motion?

Let's take two small masses from the rod, $dm$ each. One from the point $A$ and another from the point $B$. Now both the masses would have two forces acting on it i.e. tension and $(dm)g$. From ...
1 vote
2 answers
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Force and torque provided by a string on pulley

Suppose there is a pulley of mass m and two blocks are suspended on both sides of the pulley. Now what are the forces that the string applies on the pulley? I can visualise the normal force acting ...
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Skating off an edge with torque ambiguity

Problem In this particular case of a dynamic skating motion combining translation and rotation, I consider the question of determining the appropriate torques and applying the correct rotational ...
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When not pedaling, the friction force on the wheels of the bicycle is directed backwards, but doesn't this give the tires angular velocity?

The bicycle in the figure gained speed and then the feet were pulled back from the pedals. Since no torque is applied to the pedals, the friction force on the rear wheel is directed backwards. However,...
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Would a giant ball on earth roll towards the poles?

The radius of the earth is higher at the equator than at the pole. Would it mean then, that if I put a giant ball at the equator, it would roll up towards the pole? Why, why not?

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