Questions tagged [newtonian-mechanics]

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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Numerical integration for simulation of rigid body using euler parameters

I am trying to numerically integrate the following equation of motion and solve for $\boldsymbol\omega $ vector(3x1) : $$\textbf{M} = [I]\dot{\boldsymbol\omega} + \tilde{\boldsymbol\omega}[I]\...
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“Inverse” $(N+M)$-body problem

This question is a logical continuation of the question about "Inverse" $N$-body problem. Let's consider the following extension of that problem: Assume that there are $(N+M)$ particles in ...
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Solving for minimum frequency in a circular motion problem [closed]

A 200g mass is tied on the end of a 1.6 m long string and whirled around in a circle that describes a vertical plane. What is the minimum frequency of rotation required to keep the mass moving in a ...
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How can a bicycle keep its momentum while changing direction?

I was riding my bicycle downhill. When the street leveled I realized I had forgotten something so I started turning around without pedaling, pretty much using the momentum I had acquired. Soon I was ...
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1answer
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“Inverse” $N$-body problem [closed]

There is a well-known $N$-body problem in classical mechanics: Given an initial positions and velocities of $N$ particles in some space, describe their dynamics over some time interval. I'm interested ...
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Help on understanding Bernoulli's equation for unsteady flows

My questions are on the definitions of each of the terms in Bernoulli's equation for unsteady flows - which is the following equation (and which holds throughout the entire fluid): $p+\frac{1}{2}\rho|\...
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How do I go about calculating a force vector? [closed]

A asteroid of mass 2000 kg is traveling at 100 m/s, and a probe of mass 500kg is moving perpendicularly toward it with a speed of 400 m/s. Unfortunately, the landing gear does not work right, so the ...
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2answers
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Why are the tension force and the gravitational forces not equal and opposite? [closed]

Solving a complex system with two masses: In the picture below, we see an Atwood machine. In this apparatus, m1 starts out from rest 1.5m above the ground. The mass of m1 is 3kg and m2 is 2kg. m2 is ...
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Can we stop asteroids from hitting the earth using a laser? [closed]

This new video from Veritasium talks about the probabilities of an asteroid hitting the earth and the destructions it can cause. At last they talk about how can we prevent an asteroid from colliding ...
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Two-body central force mechanics problem [closed]

Problem: A particle of mass $m$ is in an attractive central force field given by $f(r)=-km/r^4$, where $k$ is a positive constant and $r$ is the distance from the particle to the centre of force. ...
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Question about a spring [closed]

An object of mass $0.9Kg$ is attached to a spring on a horizontal smooth surface. The object is put into motion. One side of the spring is attached to a wall and another side of the spring is attached ...
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Problem to understand the internal potential energy

I am reading Goldstein, at the page eleven, he is deriving what he called later the internal potential energy of a body. He made so three equality: Let ${\bf r}_i$ be the position of $i$ particle Let $...
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In block wedge system why horizontal component of normal doesn't affect the momentum of the system?

Diag. For ques: In that L shaped wedge of 4kg a block of 1kg is released from top... We give the reason of not conserving momentum in $y$ direction that a vertical component of normal due to the ...
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3answers
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Proof/Derivation that a normal force applied to a rigid body object causes a torque? [closed]

I saw this answer here but didn't understand it. If someone could provide a simpler proof starting from newton's second law F = ma and only using his 3 laws that would be helpful (only because I don't ...
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2answers
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How can a mass $m_1$ lift a heavier mass $m_2=2m_1$? [closed]

In below diagram, in what angle $\theta$ should we drop $m_1$ so that, right at the moment of dropping, $m_2$ would lift upwards? Assume $m_2=2m_1$. This is in my homework and I don't even understand ...
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Mass attached to spring on frictionless slider [closed]

Write down the kinetic and potential energies of the mechanism in terms of the generalised coordinate x; the horizontal component of the mass m.
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Mechanics problem involving a rope on a rod [closed]

I've been given this question. It's in the chapter dealing with linear differential equations, so I'm assuming the solution will have something to do with it. "A rope of length 20 meters is ...
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1answer
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Velocity of different sized balls rolling down the same rail [duplicate]

During mechanics lab we conducted an experiment in which we rolled two balls (glass and steel) down an eliptic heightened rail and measured the impact point. The lines of the rail were 0.76~cm. The ...
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Why did the apple explode when spun very fast?

This new video from the slow-mo guys captures the explosion of an apple when it is rotated really fast (roughly $109$ rotations per second). But can someone explain me why did it explode? Can we ...
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Plot functions of: path of a point, velocity-time, $v(t)$ & acceleration-time $a(t)$ [closed]

I'm confusing about the 2nd part questions (Challenge), I already did the 2 first questions, you will find them in the image. [
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1answer
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Hitting bottom of an axe to seat the axe head

I have been thinking about a certain step in hafting an axe which I can't seem to explain physically. As a reference, I've found a forestry manual which explains the process, in case my explanation is ...
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1answer
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Errors in conservation of energy equation of a falling stick

I have been trying to write out a conservation of energy equation of a falling stick (at an angle $\theta$ to the horizontal) at the instant of its bounce. Firstly, I write out the equation that ...
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1answer
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What is the gravity/inertia question?

Is the discussion about how gravity and inertia are the same, about the idea that when you hit a ball, it doesn't come back but when you throw a ball up, it does come back?
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Circular motion speed of object [closed]

When I apply the formula for it $v^2/r=(mg+m)/m$ I found the result $\sqrt{220}$. But the answer is $20\ {\rm m/s}$.
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Frictional force on an inclined plane, with 2 different planes [closed]

So the question is as follows: The speed of the 8.0 $kg$ mass in position A in the figure is 6.0 $ms^{-1}$. By the time it gets to B the speed is measured to be 12.0 $ms^{-1}$. What is the frictional ...
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Is there a limitation for the acceleration in this problem? [closed]

Starting from rest a car takes at least ‘t’ second to travel through a distance s on a flat concrete road. Find the minimum time that will be needed for it to climb through a distance ‘s’ on an ...
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How come the formula $W=Fd$ doesn't apply for energy stored in springs?

I always thought that work is like the energy transferred and it is given by $W=Fd$, but this concept gets problematic for springs. If the force $F$ is applied to a spring which compresses it by a ...
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1answer
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How could we use varying environmental temperature to measure the time taken in Newton’s law of cooling [closed]

I am a high school student that is interested on how changes in environnemental temperature could affect the measurements on the time taken of death. I found a website that used both examples, using ...
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Can we use sine and cosine graphs for varying temperatures? [closed]

I have been researching for a while looking for what to include more than just deriving the equation of Newton’s law of cooling and a website gave me inspiration by stating what if the temperature of ...
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2answers
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Deriving mechanical energy balance law from assumed pairwise potential

I'm currently working through a book on continuum mechanics that derives mechanical balance laws by considering the particles that compose the continuum. One of the balance laws, pertaining to the ...
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1answer
39 views

How to calculate conservation of Angular momentum with several rotations/axis in a system?

Imagine a turn-table in space, therefore there are no external forces on the system. This turntable has two motors, turning various masses at different radius. Imagine one motor is at the edge of the ...
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What is the relationship between balloon's volume and distance travelled?

A balloon has been blown, hung with a thread with the help of a straw, and then taken the measurements to test Newton's laws of motion. Newton's Third Law and Aircraft Propulsion The above link ...
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Why do internal forces not affect the conservation of momentum?

How is momentum conserved? I know that the condition is that no external resultant force should act on the interacting objects. But how is the momentum conserved if the objects surfaces touch and ...
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How to solve this question from an inertial frame of reference? [closed]

This was the original question in Volume 1 , Concepts of Physics by HC Verma , page 116: A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in ...
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1answer
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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 ...
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Understanding Feynman's screw jack visually

Excerpt from Chapter 4.2: Let us now illustrate the energy principle with a more complicated problem, the screw jack shown in Fig. 4–5. A handle 20 inches long is used to turn the screw, which has 10 ...
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Unbalancing weights on an inclined plane with pulleys

Richard Feynman uses the following figure in Chapter 4.2 of his lectures: Then he goes on to explain why $W$ must weigh 3/5 of a pound for the system to be in balance. There are two explanations and ...
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Force versus time and force versus angular displacement graph - simple pendulum

How to graph Force versus time and force versus angular displacement graph in simple harmonic motion of a pendulum system (Force= net force directed towards equilibrium) It seems to me that force ...
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4answers
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Can the Sun orbit the Earth?

You know how the earth orbits the sun because of gravity?...well if the sun were the right distance from the earth and it had the perfect tangential velocity...could it orbit the earth? In other words....
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Applying the unsteady Bernoulli equation to a U tube with two vertical tubes of different cross sectional areas

So we have incompressible, inviscid fluid in the U tube which is oscillating on both the LHS tube and the RHS tube vertically but eventually reaches equilibrium height $h$ above the bottom of both ...
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1answer
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Confusion about rotation of a beam due to a couple moment and Newton's 2nd Law

I'm struggling with the following concept. If we have a uniform beam with a single pivot at its centre, and we apply two forces in opposite directions on opposite ends creating a couple moment, then ...
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1answer
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What is $\dfrac{\partial x}{\partial t}$ in a progressive wave?

I actually divided the velocity of a particle in a progressive wave $\dfrac{\partial y}{\partial t}$ to $\dfrac{\partial y}{\partial x}$ and got $\dfrac{\partial x}{\partial t}$. Which is equal to $\...
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5answers
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Do pseudoforces arise due to inertia?

Wikipedia says The fictitious force is due to an object's inertia when the reference frame does not move inertially, and thus begins to accelerate relative to the free object. The fictitious force ...
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4answers
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Normal force and the assumption of motion of an object in an inclined plane

I was watching a video of object's motion on an inclined plane on Khan Academy. https://youtu.be/Mz2nDXElcoM The video describes the motion of an ice block on an inclined ice plane (meaning that the ...
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1answer
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Calculating angular velocity from 3D coordinates [closed]

I have been given 3D coordinates with timestamps(from $t=0$ to $t=50$) for the desired trajectory of a quadcopter. I need to find the angular velocity of the quadcopter with respect to the inertial ...
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Apsidal precession

There is the formula: $$ \Delta\theta=-2\frac{\partial}{\partial p_{\theta}}\left[\int_{r_{min}}^{r_{max}}\sqrt{2\mu\left(E-V_{eff}\right)}dr\right] $$ That indicates the change in angle for the ...
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1answer
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Elliptical orbits: Where have I made a mistake? [closed]

Sorry for not using latex, I am new. Assuming conservation of angular momentum and mechanical energy in an elliptical orbit, the sum of velocities at any two arbitrary points in orbit is constant? I ...
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3answers
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Why is the time period of a pendulum with a spring of force constant $k$ and a bob of significant mass $m$ the same on the Moon as on the Earth?

A question I came across in class today: How will the time period of a loaded spring change when it is taken to the Moon? What I've been told: The formula for the time period of a loaded spring $$ ...
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1answer
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I don't understand how these complex pulleys work [closed]

The pulley system above requires a person to pull on the rope with a minimum force $F$ in order to lift the block of mass $m$. An inclined plane of angle $θ$ requires that same force to push the block ...
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1answer
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How are Taylor and Maclaurin series applied in Newton’s law of cooling?

I am a high school student that’s having a hard time figuring out what to carry out in his report. As we know that Newton’s law of cooling shows an exponential curve in other words. This question ...