What is Newton mechanics: Definition and 55 Discussions
In classical mechanics, Newton's laws of motion are three laws that describe the relationship between the motion of an object and the forces acting on it. The first law states that an object either remains at rest or continues to move at a constant velocity, unless it is acted upon by an external force. The second law states that the rate of change of momentum of an object is directly proportional to the force applied, or, for an object with constant mass, that the net force on an object is equal to the mass of that object multiplied by the acceleration. The third law states that when one object exerts a force on a second object, that second object exerts a force that is equal in magnitude and opposite in direction on the first object.
The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems, which laid the foundation for Newtonian mechanics.
I've already solved this problem using another resource (just get the coordinate of the range of the center of mass and from there, get it for the larger mass ##R_{2}=(3v_{0}^{2})/(4g))##:
Range CM: $$R_{(CM)} = \frac{v_{0}^2 sin{2\theta}}{2g}=\frac{v_{0}^{2}}{2}$$
then:
$$ R_{(CM)}=...
Hi, in the Hamiltonian formulation of classical mechanics, the phase space is a symplectic manifold. Namely there is a closed non-degenerate 2-form ##\omega## that assign a symplectic structure to the ##2m## even dimensional manifold (the phase space).
As explained here Darboux's theorem since...
Does it exist an invariant way to define acceleration in Newton physics like the proper acceleration in GR ?
In Newton physics if an accelerometer attached to an object reads 0 it does not mean it is actually not accelerating (since gravity is a force).
To define inertial motion the concept of...
Hi, Penrose in his book "The Road to Reality" claims that Newton/Galilean spacetime has actually a structure of fiber bundle. The base is one-dimensional Euclidean space (time) and each fiber is a copy of ##\mathbb E^3##. The projection on the base space is the "universal time mapping" that...
I'm trying to make a 2D game on Unity similar to Universe Sandbox 2. I currently am working with a star and planet, both with roughly the masses of the sun and earth respectively for comparison and at a distance of 31,000,000km.
My current model uses Newton's formula for gravitational force (F...
The thing with this exercise is that I don't think that the question makes sense at all (or, at least, is incomplete).
First of all, we don't know if the mass moves with any of those tensions, therefore I cannot know which coefficient apply. Second of all, even if we suppose that the mass is...
TL;DR Summary: I don't know if my procedure is correct in this excercise
I've tried to solve this problem but I find my solution unintuitive and I think I might be wrong.
First of all, applying Newton's Laws I calculated the value for ##T_1## like this:
$$
\begin{align}
\sum F_{x} &=0\\...
Hi,
I was reading the interesting lecture of Feynman about Characteristics of Force -- https://www.feynmanlectures.caltech.edu/I_12.html
He basically says that nominal definitions like mathematical definitions of "abstract" objects have actually no physical meaning. For instance take the...
Hi,
I was thinking about a simple scenario in the framework of Newton (classic) mechanics.
Take a spring scale/balance fixed at one end (wall) with a body attached to the other end's hook. From an analysis point of view we can consider as "system" the spring scale + the wall + the body. Then...
Usually, I like to take a physical approach to phenomena that occur in everyday life. But I feel difficult to solve problems because I don't have higher education
My question stems from this question (What's the difference between running up a hill and running up an inclined treadmill?), which...
I used m1=m2=15,0kg
System:
FBD:
Note: I believe I have solved a) correctly and am more confused about b).
a) I started with drawing the FBD. Knowing that the net sum has to be zero for the system to be at rest I used the left mass to find the tension on the rope: S1 = G1 = 15kg*9,81m/s2 =...
The question is solved in a single step by taking the blocks as a system and using conservation of linear momentum in the horizontal direction as there is no net force acting in the horizontal direction.
Conserving the momentum we get,
m x v + M x 0 = (m+M)v',
so,,v' = mv/(m +M).where v' is the...
We know that if we take two particles and assume no external force is applied then by Newtons third law total momentum gets conserved after collision. If we take three particles and there is collision between them and no external force then the momentum is again conserved for each pair like in...
I know we can prove that a Galilean transformation sends one inertial frame to another inertial frame, by proving ##\frac{d^2 f(\vec{r})}{d(f(t))^2} = \frac{d^2 \vec{r}}{dt^2}##, but can we prove the reverse? Can we prove that if the acceleration seen in two frames are the same, then the...
Hi,
I've a doubt about the application of the principle of relativity as follows.
Assume as principle of relativity the following statement: It is impossible by any experiment performed inside a "closed" laboratory to say whether we are moving at constant velocity or staying at rest.
Consider...
I solve the following problem, there is a particle of mass ## m_p ## and velocity ## \vec{v}_p ## which collide with sail installed on rail car with mass ## m_c ## resting in the frame of reference associated with it before the collision. The cart is fixed on straight rails for which the vector...
I'm really struggling with this problem. I can't understand which are the forces that i need to calculate work. Probabily when the sand falls the force of which i need to calculate work is weight force, but which is the force that carries the sand at the top of the roller?
If a closed system has kinetic and potential energy such as the total energy (the sum of the two) equals zero for all times, what does that mean? In other words, what does it physically mean that the total energy is always zero for a closed system?
I think I have a small misunderstanding of the...
Let F_ki be the force applied by a point mass i on a point mass k. This force depends on the variables x_k and x_i which are the position vectors of respectively k and i (to simplify let´'s consider this in 1 dimension). Suppose this force is conservative. Then, according to my course and...
Hello,
1) Suppose I throw a ball with a force ##F=ma##, the instant it leaves my hand, does it have the same acceleration ##a## added to it accelerations due to "ambient" forces (air resistance, gravity..)?
2) If I am right about 1), doesn't my hand already carry the acceleration/deceleration...
Homework Statement
A mass of 3kg is acted upon by three forces of 4.0 N, 6.0N, and 9.0N and is in equilibrium. The 9N force is suddenly removed. Determine the acceleration of the mass.
Homework Equations
F=ma.
The Attempt at a Solution
My main problem with this question is that I cannot think...
I studied the vector analysis in Arfken and Weber's textbook : Mathematical Methods for Physicists 5th edition.
In this book they give the definition of vectors in N dimensions as the following:
The set of ##N## quantities ##V_{j}## is said to be the components of an N-dimensional vector ##V##...
in case of rolling without slipping of a solid sphere having uniform mass density the condition is
Vcm (velocity of center of mass ) = Rω or [a][/cm] = Rα ,which comes from the fact that if an object that rolls without slipping the geometric center of the body travels 1 circumference along...
Homework Statement
A mass m is initially at rest. A constant force $F$ (directed to the right) acts
on it over a distance d. The increase in kinetic energy is therefore $Fd$.
Consider the situation from the point of view of someone moving to the left
at speed $V$ . Show explicitly that this...
Homework Statement
Homework EquationsThe Attempt at a Solution
what's the Fa and Fb?
my logic is
Fa = Wa - N = mg - ##\frac{N}{\cos \theta}##
so is Fb...
so the ratio is 1. But I know it's wrong. What will make the difference between Fa and Fb?
can anyone give a clue please?
Homework Statement
Consider a billiard table with balls of radius r. How high should be the edge of the table to not allow undesirable pressures (and thus slips of the ball)? I.e. if there was no gravity, the billiard ball would still bounce off parallelly to the table plane.
However I do not...
Homework Statement
The given system is released from rest. Assuming no friction, mass-less pulleys and ideal strings; calculate the accelerations of the pulleys.
Homework Equations
Constraint equations.
F=ma
The Attempt at a Solution
Taking the above assumptions;
And applying constraints...
Homework Statement
Given a plank is moved with uniform velocity v. To which a mass is connected by a spring of force constant k. What is work done by the external agent on the maximum compression of the spring
Homework Equations
Work done by spring=0.5*k*x2
Work-energy theorem: total work...
If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz.
However, in this case, I had to calculate the work done by the spring force as a function of y
Over here, I assumed the spring force, which is a function of its elongation x (F =...
Homework Statement
Find the total tension acting on a rod rotating about its end with an angular velocity of w as a function of its length x(length)
Homework Equations
F = ma[/B]
The Attempt at a Solution
Let the function be T(x) where x is the length of the rod.
Considering an interval...
Homework Statement
Hi,
Infinitely far away from a mass-->gravitational potential is zero.
As get closer-->becomes negative.
At surface-->it is the smallest value of r, i.e. the radius of the mass, hence the most negative value for gravitational potential.
But as you go below surface of Earth...
Can anyone help me? I have a question with 3 part answers on my Mechanical Principles assignment. I believe I have answered question part 'a' and 'b' but I have been stuck on question part 'c' for days!
So the question is:
Q5. The simply supported beam shown in FIG 4 is 5meters long with a...
I could've peeked at the solution manual and end with it at that. However, I'm trying to change this nasty habit and solve this problem myself. I might be too ambitious. Here goes.
Homework Statement
Consider the infinite Atwood's machine shown. A string passes over each pulley, with one end...
In the image above, a centroid with radius 1 is depicted. F1 is pointing directly at point A (which is the center of the circle), and F2 is pointing directly at point B. The radius for finding the torque would be the perpendicular between the center of the object and the force vector, so r1...
Homework Statement
[/B]
Question :- Find the acceleration of block of mass ##M##. The coefficient of friction between blocks is ##\mu_1## and between block and ground is ##\mu_2##.
free body diagram at the end.
Variables :-
##f_1## - friction between blocks.
##f_2## - friction between block...
Question :-
A car has to move on a path, that is a arc of a circle of radius (##R##). The length of the path is (##L##). Suppose it starts on the highest point of the path, find the highest uniform speed for which, it does not lose contact with the path on any point ?
My attempt :-
I made a...
Homework Statement
A solid sphere of density ##ρ## and radius ##R## is centered at the origin. It has a spherical cavity in it that is of radius ##R/4## and which is centered at ##(R/2, 0, 0)##, i.e. a small sphere of material has been removed from the large sphere. What is the the center of...
Standing within a field, should the force required to move an object in the opposite direction of the field without acceleration be equal to the force exerted by the field on it or a little more than that?
Homework Statement
A bead of mass m kept at the top of a smooth hemispherical wedge of mass M and radius R is gently pushed towards right.As a result,the wedge slides due left.Find the magnitude of velocity of bead relative to the wedge.
Homework Equations
$$MV=m(v\cos(\theta)-V)$$
and...
I know that gravitational potential due to uniform sherical shell at a point outside the shell is equivalent to the potential due to particle of same mass situated at the centre and got proof here http://m.sparknotes.com/physics/gravitation/potential/section3.rhtml. But I was looking for more...
Homework Statement
A person would like to pull a car out of a ditch. This person ties one end of a chain to the car's bumper and wraps the other end around a tree so that the chain is taut. The person then pulls on the chain perpendicular to its length. If the distance between the car and tree...
In the above cases I want to find the acceleration a for m1. I can do it by considering m1 and m2 to be a system, which would give me a = F/(m1+m2). How can I use a free-body diagram instead to calculate the acceleration? Using a free-body diagram, m2 only affects the vertical motion by exerting...
I have been asked by someone if it is true that in general, for a constantly accelerating reference frame, i.e. a non-inertial reference frame, the acceleration of a particle (as observed in this frame) due to the corresponding fictitious force is independent of its mass.
My response was yes...
Homework Statement
Block 1 (mass 2 kg) is moving rightward at 10 m/s and block 2 (mass 5kg kg) is moving rightward at 3 m/s. The surface is frictionless, and a spring with spring constant of 1120 N/m is fixed on the left side on block 2. When the blocks collide, the compression of the spring is...
let's look at force at the atomic level to understand the Newtons third law of motion. I'll use Helium atoms as an example.
Now imagine we start with one atom HE2 stationary, and throw another atom HE1 at it.It is the velocity of HE1 that affects the motion of HE2 , because the system of these...
in shm,if minimum potential energy of an shm is not zero,does that mean that in mean position ,spring is stretched.
eg mass attached to a vertical spring.