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Question regarding kinetic energy of a body

You stop doing work on the block as soon as you stop applying a force on it. The rest of the work is done by friction.
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Question regarding kinetic energy of a body

The work done is $F$ times the distance that it moved during the short time you were pushing. The distance it moved later is not relevent.
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Effect of object mass in coeficient of restitution

The masses affect the magnitude of impulse in a collision. Consider two bodies of mass $m_1$ and $m_2$ about to collide with relative velocity $v_{\rm rel} = v_2 - v_1$. Considering the coefficient of ...
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Will the puck rotate without slipping in this situation?

The problem here is the assumption that $V_P=V_{CM}$ Your first thought that the motion of the centres of mass will be identical for the same total amplitude and direction of external force is correct,...
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Why does Newton's second law involve mass?

Mass requires input of energy to accelerate...Newton's second law is a description of the changes that a force can produce on the motion of a body, not what the body adheres to on the substantive ...
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1 vote

Helicopter hover flight question

For this kind of problem, I find it easier to think about momentum than about mass and acceleration. Remember that momentum is mass times velocity, $$ \vec p = m\vec v $$ and so Newton's second law ...
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Why does Newton's second law involve mass?

Newton's second law states that the force experienced by a body is vectorially equal to the rate of change of its momentum which is defined as mv. For a fixed mass, this rate reduces to the familiar ...
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Angular Momentum and Coefficient of Restitution

No the coefficient of restitution does not apply to with rotational velocity. In fact conservation of momentum will not apply either because the bodies are pinned and can transfer momentum to the ...
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Helicopter hover flight question

When analysing a fan, propeller or engine which isn't moving, the air which is being sucked through the rotor starts far away and not moving. Air is drawn in from all around, so the area far away is ...
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2 votes

Helicopter hover flight question

accelerates from 0 to +9.8m/s A mistake is here. The speed 9.8m/s isn't anything. The acceleration of Earth gravity is $9.81\text{m/s}^2$. Thats a column of 30 meter of air above the rotor. I don't ...
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Gear Ratio And Torque Relationship

The angular acceleration of the smaller one must be 10 times its coupling pair. It is what happens when a car moves from the rest. The motor's RPM grows faster than the wheels' RPM. On the other hand, ...
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Proof of principle of stationary action when the Lagrangian is not $L=T-V$

I will first give some general remarks about Hamilton's stationary action, and then I will write specifically about the case you are asking about: a force that is a function of velocity. The ...
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Angular Momentum and Coefficient of Restitution

The problem is that angular momentum is not conserved in this scenario. In order to define angular momentum in a system, there needs to be an origin. If we put the origin at the center of the first ...
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3 votes

Proof of principle of stationary action when the Lagrangian is not $L=T-V$

Often the principle of stationary action is taken as a first principle/axiom, i.e. it has no proof. However OP is apparently only considering the class of systems in Newtonian mechanics$^1$ that ...
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Can someone explain why this would not create an infinitely rotating disk (perpetual motion)

The simple answer is that the accepted laws of physics don't allow this to happen. Energy cannot be created or destroyed so your system could not get kinetic energy from nothing. Finding 'exactly' ...
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2 votes
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Why $\omega=vR$ can not be applied in this question?

It's $v = R\omega$, not $\omega = Rv$.
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Simulating Torsion Springs

The differential equation for this model should be something like \begin{align} \frac{d}{dt} \left(\,\sin^2(\alpha) \frac{d\alpha}{dt}\,\right) \,=\, \sin(\alpha)\cos(\alpha)\left(\frac{d\alpha}{dt}\...
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Will the puck rotate without slipping in this situation?

There is no contradiction. $v_Q$ (the instantaneous horizontal peripherical speed) and $v_P$ (the horizontal speed of the string) are the same when $Q$ is at the top. But around every turn $v_Q$ ...
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10 votes

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

I'll start from the premise that a helium-filled party balloon has risen through the atmosphere to the point of buoyant equilibrium without otherwise changing significantly, and we then let the gas ...
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Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

How I would do it. Have a decent nuclear heater onboard, somewhat like a dirigible. After max hydrostatic altitude is reached, use gas for thrust. If you could heat it up to a few thousand degrees, ...
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5 votes

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

A fundamental challenge you will run into is that bouyancy and rocket propulsion want to opposing things. For bouyant lift, you want low densities. This means relatively low pressures. However, for ...
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6 votes
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Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

After reaching this height, can the helium balloon be used as a propellant, the same way if you release a balloon, it will fly through the room? Sure. There's pressure built up in the balloon ...
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Why is angular momentum equal to mass times radius times velocity?

Rotational distance from the center effects momentum because it effects the velocity. A mass rotating 100RPMs with radius x will have more energy if the radius is 2x because it changes the ...
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Angle-free two-dimensional inelastic collision formula?

The direction of the velocities (in a center of mass system) after a collision in two (or three) dimensions will depend on the shape and size of the colliding objects (and their elastic properties). ...
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Why is angular momentum equal to mass times radius times velocity?

The linear momentum of a system is conserved in the absence of a net external force. The angular momentum of a rotating object is conserve in the absence of a net external torque. That is reflected ...
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1 vote

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

TL;DR It is almost certainly impossible, and even if achieved it would be utterly useless. If we assume that the balloon is made out of an indestructible plastic substance, like with a real balloon, ...
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1 vote

Can someone please explain energy of electrons in Bohr's model?

You write E = kinetic energy + negative of potential energy. (eq-1) and then as the electron goes from lower orbital to higher […] the potential energy should increase and the total energy should ...
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Why is angular momentum equal to mass times radius times velocity?

When momentum is mass times velocity, why is angular momentum mass times radius times velocity? High-school summary We are interested in both angular momentum and linear momentum because they are ...
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Why is angular momentum equal to mass times radius times velocity?

In the simplest way possible, they are two different quantities. Linear momentum is not the same as angular momentum. They have similar names because they’re both conserved quantities, and angular ...
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22 votes

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

I think some people are misunderstanding your question: you're asking if a helium balloon can be used as propellant, the same way if you release a balloon it will fly through the room. The answer is ...
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11 votes

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

No This is essentially analogous to asking if an inflatable boat can fly. A helium balloon will ascend until it reaches the atmospheric "surface", and then it will stop and float. In much ...
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3 votes
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Would it be correct to state that the damping force and the spring force are equal in the case of critical damping?

Would it be correct to state that the damping force and the spring force are equal in the case of critical damping? No. Regardless of whether a damped harmonic oscillator is underdamped, critically ...
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Free fall and contact force

When we are talking about contact forces here, we have to think about Normal reaction and friction. Normal reaction is applied by a rigid surface on a body to prevent it's motion into the surface. ...
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1 vote

How do I find the constraint relation in this question?

The speed of the connecting belt must be twice the downward speed of the center of the lower pulley. This means that $α_1 = 2 α_2$. Then: $mg – T – t = ma = mr α_2$ where, $T$, is the connecting ...
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6 votes

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

Helium is used in balloons because it is lighter than air, which is the reason why such a balloon rises. That’s why it only works up to a certain altitude. Once you’re high up enough, air becomes so ...
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37 votes

Can a balloon start from Earth and fly to the Moon, using Helium for lift to the top of the atmosphere and then as propellant?

With the helium tightly sealed inside? No. Once the density of the atmosphere is as thin as the density of the helium gas, the buoyant net upward force is gone and the balloon stops going further up. ...
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Why is it incorrect to find the period of a physical pendulum by considering forces on the centre of mass?

For a simple pendulum there is only one particle, because all the mass is concentrated in a point. For that particle it is possible to apply the Newton's second law. If we make the dot product with ...
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On the defining properties of hydrostatic center of pressure

For the torque about a given point produced by a force, the force can be applied to an object at any point along the line of action of the force.
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2 votes

Why is it incorrect to find the period of a physical pendulum by considering forces on the centre of mass?

A simple pendulum is generally analyzed as a point mass. A physical pendulum has extended mass which must rotate about the center of mass. This requires the existence of an additional dedicated torque ...
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2 votes
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Why do we use moment of inertia about centre of mass to calculate rotational KE in rolling without slipping?

The rotation/translation decomposition depends on the axis of rotation that you choose. If you consider the cylinder to be rotating about $A$ as it translates, $$\text{KE}_\text{translational}^A = \...
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Newton's third law cancelling

I'd really appreciate if someone could give a more descriptive answer on why Newtons Third Law does not cancel out. The effect of the forces each object exerts upon the other depends on the ...
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Newton's third law cancelling

Let me describe a setup that makes friction effect way smaller than exerted force: There is a demonstration apparatus called 'air table' It consists of a plate with small holes in it, spaced closely ...
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Newton's third law cancelling

You accelerate less than the ball does partly because of the frictional force (as you noted) but also partly because (in most cases) your mass is greater than the ball's, so the same force produces ...
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Newton's third law cancelling

All Newton's 3rd law is really saying is that every force is two sided. Forces don't act like this $\longrightarrow$ they act like this $\longleftrightarrow$ Or this $\longrightarrow \longleftarrow$ ...
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How do I find the constraint relation in this question?

I believe the first equation should be $\alpha_2r + 2a = \alpha_1r$ In the diagram you have shown, the top pulley (pulley 1) is fixed and can only rotate, while the bottom one (pulley 2) can move. Now,...
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Angle-free two-dimensional inelastic collision formula?

you can use those equations \begin{align*} &m_1\,(\mathbf v_1-\mathbf u_1)=-\lambda\,\mathbf n\\ &m_2\,(\mathbf v_2-\mathbf u_2)=\lambda\,\mathbf n\\ &\left[(\mathbf v_2-\mathbf{v}_1)+...
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-1 votes

Why forces exerted by fluids, inside or outside, are always perpendicular?

Answers are different for liquids and gases. In liquids, there are forces parallel to surface. This happens when liquid flows alongside a surface. This force is called viscous force (or sometimes ...
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Kepler's laws for circular orbits

My question is, should we swap out "semi-major axis" and replace it with "radius"... We can always do that. As you noted, circle is a special case of ellipse. The second law ...
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4 votes

Why forces exerted by fluids, inside or outside, are always perpendicular?

Why all fluids exert only perpendicular force. Why not parallel? Fluids certainly can and do exert parallel forces. Such forces are called shear, and the defining feature of a fluid is that it ...
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Null conserved angular momentum

First of all, the angular momentum is defined only with respect to a point. If we treat that point as the origin, and the position of the particle is $P(t)$, then angular momentum is $mP(t)\times P'(t)...
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