Classical mechanics Definition and 1000 Threads

I can’t find the chapter list online, does anyone know what topics are covered in John Taylor’s classical mechanics? Would it be similar to what’s covered in Newtonian mechanics, but obviously more advanced. Cheers in advance 👍

Summary: How to calculate the equilibrium angle of a bar that is lifted on its two ends with ropes attached to fixed lifting points? Hello and good day all, First of all I would like to apologize in advance for my english, I am not a native speaker so some grammar errors may be left. My...

Three (many) body problems where three or many bodies (particles) interact are impossible to solve analytically. First one appeared in classical mechanics where equations of motion of planets were tried to be found by applying Newton's 2nd law for system of planets and stars interacting via...

I have drawn a fbd and the logic I think is that at rest the block moves down the wedge but when a force P is applied vertical force becomes zero and the horizontal force ##F_N\sin \beta## = P?

Suppose you have a heavy body placed on a surface. We apply a horizontal force such that it is on the verge of moving (maximum static friction). We measure this force and note it down. Now we cut the body from the top and remove a thin layer and again do the same thing. We apply a force and...

Imagine a solid body big and heavy. It will have friction between it and the surface when tried to move. Somehow the cluster of molecules opposes the push. When free these molecules stick on surface and can be moved by a mere blow of wind but when bonded into a solid body the structure of large...

Water is made up of loose molecules but a body like ice is bonded strongly into a shape. Imagine a ice brick. It will have friction between it and the surface when tried to move. Now it slowly starts melting. The molecules of ice will start sticking on the surface. Somehow the cluster of...

https://www.feynmanlectures.caltech.edu/I_09.html 9-7 "From this figure we see that the horizontal component of the force is related to the complete force in the same manner as the horizontal distance x is to the complete hypotenuse r, because the two triangles are similar. Also, if x is...

https://www.feynmanlectures.caltech.edu/I_10.html https://www.feynmanlectures.caltech.edu/I_09.html Using Mathematical approach we can describe the motion of a falling body whose gravity is 32 m/s^2. Analysis shows that this is simply ##s-s_0=ut+1/2at^2##. Similarly we can describe the motion of...

I came up with these: (especially not sure if second is right)

I have read about several approcahes to bypass some classical restrictions to quantum facts such as the electron being in a torus-like shape to avoid ,the greater than speed of light, rotation paradox . Could you recommend websites , sources or books that give good classical analogy to quantum...

When we take the x-axis parallel to incline surface its clear that the horizontal component of weight is causing the block to come down but when we take the standard orientation its not so clear to me. Is horizontal component of ##F_N## causing the block to come down? <Moderator's note: Use of...

We know the minimum force to move the body in presence of friction will be ##F>\mu F_N## But it’s not right.

https://www.feynmanlectures.caltech.edu/I_09.html “Weight and inertia are proportional, and on the earth’s surface are often taken to be numerically equal, which causes a certain confusion to the student. On Mars, weights would be different but the amount of force needed to overcome inertia...

##T-2mg=2ma_1## (acceleration of heavier mass) ##T-mg=ma_2## (##-a_1=a_2##) On solving the eqns, ##a_1=-g/3=-a_2## ##s=1/2at^2## ##s=-g/6## , distance covered by heavier mass. ##s=g/6## , covered by lighter mass. Edit: ##\Delta U_1=mgh=-2mg^2/6## (decrease in U of heavier mass) ##\Delta...

##W_{ext}=mgh+KE_f+0=-20(5\sin 37)+(1/2)2(10^2)## ##W_{ext}=-60.18+100=39.81J## But it’s not consistent with ##W=F.d=20*5=100J## I can’t figure it out.

a) $$v=u+at$$ $$v=0+(F/m)t$$ $$v=-10$$ Now $$v^2=0+2as$$ $$s=-5$$ $$W=F.d=(-20)(-5)=100J>40$$ b) $$W=-mgh$$ $$W=-20(3)$$ $$W=-60$$

https://futurism.com/why-you-can-never-actually-touch-anything/amp We know the friction happens because of the intermolecular forces between the atoms of the surfaces in contact. When we place something on other there are places where they get come in contact there are bonding formed and due to...

For lower half ,$$Fnet=-\mu F_N+mg\sin \phi$$ For upper half, $$v^2=u^2+2as$$ (s is half of the total slant distance) $$v^2=0+2\frac{mg\sin \phi}ms$$ $$v=\sqrt{2g\sin \phi s}$$ again for lower half, $$v^2=u^2+2as$$ $$0=2g\sin \phi s+2\frac{-\mu F_N+mg\sin \phi}ms$$ $$\mu=\frac{2gm\sin...

As we always say eat food and rest because tomorrow you have to go to work. When we throw a ball up, it gains a max PE at some height. More the height more energy it has which makes it do more work. Is this right to say?

I think on top of the wedge the KE of both the wedge and block will be same but this fact doesn't take me anywhere. The base length of the wedge is not given. Maybe that would have helped.

I think if the two parts move in -x and +y direction, it must be balanced by the resultant of the two vectors but in opposite direction. So ##p\sqrt5## will be the answer. But I don’t think this is the right way to solve this.

##W=-k(y\hat i+ x\hat j)d##. I am not getting the coordinate of particle correctly so that I can find the value of d. Also the force is varying.

d=5m But the force is not mg since there is water so net force must be less. But how much?

The force is -Mg and distance is L/3. So W=-MgL/3. Not right! Maybe it’s done using COM but there is no additional information is given.

I have a question understanding the reasoning in the book. The book says in one dimension F=-dU/dr(p.185). From this, the system is stable at distance a when U'(a)=0 and U''(a)>0 where U is differentiated with respect to r.(p.217) My question arises from the instance of a pendulum where a...

W=-mgd=2*10*1.5=30J. I don’t think this is right.

We know that the force of gravitation is F=GMm/r^2. The acceleration of the body of any mass m is a=GM/r^2 which we call g. So same acceleration regardless of any weight(ignoring air resistance). But when we solve laws of motion problems we take a downward force of -mg. So force depend on mass...

I think because both are launched with same speed so both have same KE. Since one is Thrown downwards it’s KE will increase but not that much as the body which is thrown upwards. Because it covers more distance so it gains more energy(the body thrown up). So 3rd option must be right.

We know that the centripetal force and the tangential velocity is responsible for the motion of Earth around sun. Newton’s second law says F=ma. If we all get together(whole population) in one place like parallel to the tangent to orbit and jump can we displace Earth from its orbit?

When a tomato is thrown up with a velocity ##v_0## it’s kinetic energy is 1/2mv_0^2. It will stop at the top and then again comes back to the launch point where it’s kinetic energy will be same as before, 1/2mv_0^2. How is this possible? Also when we throw the tomato up how can you be so sure...

Its Good to be Back! From Resnik, Fundamentals of physics: Consider a particle of mass m, moving along an x-axis and acted on by a net force F(x) that is directed along that axis. The work done on the particle by this force as the particle moves from position ##x_i## to position ##x_f## is given...

Sometimes there are forces which act for very small time known as impulsive forces. We cannot measure such large forces acting in a very short time but we can ##\Delta p##. ##\Delta p=F\Delta t##.This quantity is defined as Impulse. Why do we keep introducing new quantities? When is a new...

Previously I have posted two threads on Thread 'Monkey climbing up the rope' https://www.physicsforums.com/threads/monkey-climbing-up-the-rope.1012065/ and Thread 'Car's maximum acceleration on a road is proportional to what?'...

What is going on when the ball is thrown up in the sky. It is pushed by a force F for some distance d. Then the object travels a distance s up in the sky before finally coming to a stop. So what is going on here? Is the force doing work for distance d or distance s (s>d)? I think change in...

1. From resnik, Halliday “Kinetic energy K is energy associated with the state of motion of an object. The faster the object moves , the greater is the kinetic energy” If I am right this means that greater the kinetic energy, greater is its speed. 2. Force transfers energy to the body due to...

Net force acting downwards is ##5g-g=4g## in downward direction. Net force on pulley is ##2T-4g##. Weight measured by balance?

##Net force=50-T2+T2-T1+T1-20=10a## ##a=3 m/s^2## I want to ask when we do this way rather than taking individual masses we can’t decide the direction of the system as we can when they are taken individually. So is it correct to just leave ##a## as it is and solve ?

I have gathered everything from post “Monkey climbing up the rope” about tension. Tension is basically a force that the rope applies back when it is under stress. It is an inward force. Tension T's direction at end points of rope where its attached to the body and ceiling is inwards. Tension is...

“Momentum is clearly a vector quantity. The following common experiences indicate the importance of this quantity for considering the effect of force on motion. 1. Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle (say a loaded truck) are parked on a horizontal road. We...

https://www.feynmanlectures.caltech.edu/I_08.html Page 9-3. It says “In these terms, we see that Newton’s second law, in saying that the force is in same direction as the acceleration,is really three laws, in the sense that the components of force in the x, y,z directions is equal to the mass...

This problem is similar to what I have done before here. I think since the system is in equilibrium, that is both bodies are at rest, net force on each should be zero. So to balance the forces in all directions we need only friction forces on each in upward direction. So the force on B due to A...

Since no body accelerates so net force is zero. Force on each mass is zero. T1 and T2 both are 60N. Edit: since there is a force applied so there is acceleration on friction less surface.

The answer should be no change but we know ##F=ma##. In this eqn when acceleration increases mass decreases for same force. So why not here? If normal is doubled ##\mu## should be halved.

If I draw the fbd then some force will accelerate the car in horizontal direction which I think does not effect the string in vertical direction. So same tension regardless of acceleration. But we know it will increase. So what will be the correct physics behind it?

I think the tension in the rope will be equal to its weight , mg. I want to ask what if the monkey accelerates up with acceleration a, then what will be the tension in the rope?

1. ##-f_k\cos\theta-T\cos\theta+F_n\cos\alpha=m_2a_x## 2. ##f_k\sin\theta+T\sin\theta+F_n\sin\alpha-m_2g=-m_2a_y## 3. ##T-m_1g=m_1a_y## I am unable to get anywhere. There are accelerations in x , y directions. I need the value of acceleration. Then I can simply use ##s=ut+\frac12at^2##

We can differentiate twice the y displacement with respect to time t and get the acceleration of block B. $$a_B= \frac12 m/s^2$$. But I don’t think it’s that simple.

Since the car starts from rest it’s accelerating. So, $$F_a-f_k=ma$$ $$F_a-\mu mg=ma$$ $$\frac{F_a-\mu mg}m=a$$ Now from second eqn, ##s=ut+\frac12at^2## $$s=\frac12\frac{F_a-\mu mg}mt^2$$ $$\frac{2sm}{F_a-\mu mg}=t^2$$ $$\sqrt{\frac{2sm}{F_a-\mu mg}}=t$$ I don’t think I am getting any where!

I don’t know what is contact force. Are friction and normal forces called contact forces? And we have to take the resultant of the two to get the net contact force?