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1answer
40 views

Objects Rolling Downhill - Ratio of Rotational and Translational Kinetic Energies [on hold]

Let's say I roll a uniform disk down a ramp (without slipping), and the disk rolls 10 meters down the ramp which is angled at 30 degrees to the horizontal. At the bottom of the ramp, what is the ratio ...
-1
votes
1answer
61 views

Change in kinetic energy of pendulum [closed]

"An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts from rest and pulled slowly until the string makes an angle $\theta$ with the ...
0
votes
1answer
39 views

Two black holes in rotation - Energy conservation

I was looking at this problem: Let consider two black holes of mass $M$ rotating around a point $O$ (circular montion). The first black hole center is $M_1$, the second $M_2$. Each of them has ...
0
votes
0answers
25 views

Deriving expressions for momentum in relativistic elastic collision

I have the following question from D'Inverno book 'Introducing Einstein's Relativity': A particle of rest mass $m_0$, energy $e_0$, and momentum $p_0$ suffers a head on elastic collision with a ...
1
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0answers
49 views

How to evaluate the period of a particle in a system with potential energy $U=-U_0/\cosh^2(\alpha x)$?

I am working through the textbook "Mechanics", from the series "Course of Theoretical Physics " by Landau and Lifshitz. In Chapter 3, where the authors talk about integrating the equation of motion $E=...
0
votes
1answer
55 views

How to calculate the conserved energy $E$ from the Lagrangian?

I am reading a PhD thesis that considers the Lagrangian $$\mathcal{L}=\partial_\mu\phi\partial^\mu\phi^\star-U(|\phi^2|)$$ where $\phi$ is a complex scalar field and $U(|\phi|^2)$ is an arbitrary ...
1
vote
1answer
45 views

Deriving equation for $\theta$ [closed]

I have that the energy $E$ in a system is $$E = \frac{1}{2}L^2\dot{\theta}^2(m_1+4m_2) - Lg(m_1+2m_2)cos(\theta) + c$$ where $c\in\mathbb{R}$. I have used the conservation of energy over time to ...
0
votes
1answer
34 views

The work due to friction given an influential force

Statement: I am trying to work through Chapter 8, Problem #70 of OpenStax University Physics Volume 1 and I cannot figure out what I'm doing wrong. The problem statement is as follows: A particle of ...
0
votes
1answer
82 views

Not able to clearly understand the text of a problem [closed]

I've not clearly understood what it's meant by the text of this problem. To me, it seems that I have to show why an object travels AB in less time than ACB. However, if an object travels from A to C, ...
-1
votes
6answers
63 views

How is speed affected (or not affected) by acceleration by gravity?

I am a new physics student and I was reading a question posted on here earlier: Which Sphere is Fastest? It posits that three spheres thrown with the same speed at the same point (one thrown ...
12
votes
3answers
1k views

Which sphere is fastest? [closed]

I was doing a physics problem, and it seemed simple at first, but now it doesn't at all, and I need help. Here it is. Three identical spheres are thrown from the same height above the ground. Sphere ...
1
vote
2answers
93 views

Question on energy conservation from the stress tensor of a classical scalar field

I am struggling to answer an old general relativity exam question, which is as follows: "Consider a scalar field $\phi(t,x^i)$ with potential $V(\phi)$ on a general spacetime. Its stress tensor is ...
1
vote
2answers
51 views

Momentum of solar panel after photon is absorbed [closed]

A solar panel installed on a car of mass 1 kg lying on a friction free road. Let the efficiency of the solar panel be 100%.let the momentum of photons be $m_o$ and and the car be at rest before ...
2
votes
2answers
69 views

What is the significance of maximum compression in spring?

A block of mass $m$ sliding on a smooth horizontal surface with a velocity $v$ meets horizontal spring of spring constant $k$ fixed with wall. Find maximum compression of spring. Why is the word ...
0
votes
1answer
39 views

Kinetic Energy Comparison Marble Question

A uniform marble of mass M rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. The bowl is rough enough to ...
6
votes
5answers
4k views

Why do I get negative height?

A baseball is thrown from the roof $50.1^\circ$ above the horizontal. The initial velocity is $11.5\ \mathrm{m/s}$. I'm trying to find how high the ball goes. I choose positive direction upwards. $$...
1
vote
3answers
248 views

Rotational KE vs Translational KE [closed]

Q. Horizontal electric field E = mg/q exists as shown in the figure and a mass m is attached at the end of a light rod. if mass m is released from the position as shown in the figure. find the angular ...
0
votes
1answer
31 views

Rolling on a track in vertical plane

A sphere of mass m and radius r is released from rest at point A on a track in vertical plane. The track is rough enough to support rolling between A and B and from B onwards it is smooth. My ...
0
votes
2answers
98 views

Mechanics Question - Bullet fired into Block

I am studying for the GRE and came across this question (Question 93 from Sample Exam 2 in Kahn and Anderson's Conquering the GRE): A bullet of mass 5 g is fired at a block of wood of mass 1 kg, ...
0
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2answers
62 views

What happens to the energy of an absorbed photon?

Photons are electromagnetic wave fields that travel at the speed of light. When they are absorbed by an object, their momentum and energy is transferred to the absorbing object. What is that ...
-1
votes
1answer
49 views

Can this sum be done without integrating?

As by using conservation of mechanical energy, we can just be concerned about the final and initial position and the velocity could be found out. Am I not right? But I am not getting the correct ...
2
votes
4answers
68 views

Conceptual question regarding velocity in projectile motion vs. up a ramp

I have a question regarding conservation of energy in regards to two different scenarios: In the first case I was told that a ball with an initial velocity, V, was launched at an angle, $\theta$ and ...
18
votes
5answers
878 views

Applying energy and momentum conservation to the problem of pulling a bent carpet at a constant speed

Consider this system. A long, thin, pliable carpet is laid on a floor. One end of the carpet is bent back and then pulled backwards with constant speed $v$, just above the part of the carpet ...
1
vote
2answers
75 views

Acceleration downhill, fastest trajectory for a ball

Given 3 ways of going downhill, like in this image: Would a ball behave like that in real life? Intuitively, it makes no sense. The shortest path here is not the fastest. Any hints to the math ...
1
vote
1answer
49 views

Pion decaying energy

The question is: A pion decays into a muon and a neutrino (which is almost massless, so we’ll take it to have a mass of zero). If the pion is initially at rest, find the energy of the outgoing ...
1
vote
1answer
70 views

Two black holes colliding (classical mechanics)

I had this question come up in my exam where two identical black holes are in orbit around each other. There is a loss of energy via gravitational waves : $$\frac{d E}{d t} = kr^4\omega^6$$ where $k$ ...
2
votes
0answers
31 views

Max velocity before toppling risk

I want to find out the maximum velocity a machine can travel before there is a risk of toppling. Say, worst case, is that the castors hit a dead stop and the machine is brought to rest '...
0
votes
1answer
39 views

Mass and energy in special relativity [conservation of energy problem] [closed]

A certain quantity of ice at $0$ celsius melts into water at $0$ celsius and in doing so gains $1.00$ kg of mass. What was its initial mass? Now the problem with my solution is that it of course ...
2
votes
2answers
137 views

The time component of the geodesic equation for Newtonian gravity

I am working on a simple and popular GR textbook exercise. In Dodelson's Modern Cosmology (p. 54), it is stated thus: The metric for a particle traveling in the presence of a gravitational field ...
0
votes
1answer
34 views

The horizontal velocity $v$ that must be given to the mass $m$ to rotate the pendulum $90$ degrees

A compound pendulum consists of a uniform rod of length $L$ of negligible mass. A body of mass $m$ is fixed at the lower end and a body of mass $2m$ is fixed exactly in the middle of the rod. The ...
0
votes
1answer
106 views

Conservation of kinetic energy in two dimensional elastic collisions

I have a question where two particles collide with each other in a non central way. Mass of particle 1 ($m_1$) is $1\text{kg}$ and its velocity $v_1$ is $5\text{m/s}$ (moving along the x-axis) ...
0
votes
4answers
196 views

Can you derive the acceleration of a cylinder rolling down an inclined plane by ONLY using conservation laws?

I want to solve the standard problem of a cylinder rolling down an inclined plane by only using conservation laws. In particular I want to use the equation: $$E_{pot}=\frac{1}{2}mv^2+\frac{1}{2}I\...
-1
votes
1answer
66 views

Conservation of Momentum vs. Energy [closed]

If a mass $m$ travelling at velocity $v$ collides ideally with a massless shaft mounted on a massless bearing with an identical mass on the other end of the shaft: Conservation of momentum requires ...
1
vote
2answers
114 views

Proof of total energy is constant in a central force field

I saw many proofs of total energy is constant in a central force field. But all the proofs end up showing this formula $$m[{\dot r}^2 + r ^2{\dot \theta}^2 ]+ \int f(r)dr = E$$ is constant. But ...
-1
votes
4answers
213 views

I recently solved a problem where a tenis ball is kept on a basketball and basket ball is at some height from the ground [closed]

. When the system is released the tennis bounces back to a larger height than it was before. what is the reason for this? I mean the problem assumes elastic collisions. How can the tennis ball rise ...
2
votes
0answers
117 views

Simple Harmonic Motion of a Pendulum Derivation Questions [closed]

A simple pendulum with mass m on a string of length l is released from rest at an angle of $\theta_0$ to the vertical. (i) Assuming that the pendulum undergoes simple harmonic motion, find an ...
-1
votes
2answers
47 views

Use of conservation of energy [closed]

A ball starts rolling down a slope as shown in the figure below. All units shown are in meters. The floor has very little friction. Which of the following is true after a long time? options A. ...
5
votes
5answers
3k views

Why isn't energy conserved in this collision problem? [closed]

I am stuck in a question where energy conservation is failing and momentum conservation is correct. I think I might be doing something wrong, that's why I'm asking this question. The problem is as ...
0
votes
1answer
43 views

Conversion of Kinetic energy to electric potential energy [closed]

Two deuterium nuclei, separated by a large distance with same initial speed are travelling towards each other; the radius of the nucleus is given. How can I find the minimum speed of the nucleus? I ...
1
vote
1answer
112 views

Get relation from definition of stress-energy tensor and the conservation of energy

Starting from the following definition of stress-energy tensor for a perfect fluid in special relativity : $${\displaystyle T^{\mu \nu }=\left(\rho+{\frac {p}{c^{2}}}\right)\,v^{\mu }v^{\nu }-p\,\eta ...
1
vote
2answers
80 views

Can't understand energy conservation in simple thermodynamics example

SITUATION Consider a very big cylinder with a mobile piston in the middle separating two sections (A and B) filled with gas. Both the cylinder walls and the piston are adiabatic, so there is no ...
-2
votes
1answer
39 views

What is the largest radius that the circular track can have such that the car remains in contact with the track? [closed]

A car is travelling at $u$ as it enters a vertical loop of radius $r$. What is the largest value of $r$ that the track can have such that the car goes up and around the track whilst remaining in ...
-2
votes
2answers
70 views

How to identify if the law of conservation of energy is violated in a nuclear reaction? [closed]

I have encountered many textbook questions that ask for what laws of conservation is violated in a given nuclear reaction, and I can't seem to figure out how to identify if a nuclear reaction violates ...
0
votes
1answer
51 views

How do I show that $E\equiv \frac12 m \dot{x}^2 + U(x)$ is constant for a classical particle moving under the action of $F(x) = -dU/dx$? [closed]

A mass $m$ moves in one dimension $x$ under the action of a (net) force $F(x)$. The force can be derived from a function $U(x)$ according to the formula $$ F(x) = -dU/dx. $$ Show that the quantity ...
0
votes
1answer
44 views

Decreasing energy but at expanse of what

question : A hollow spherical shell with radius R has charge Q uniformly distributed over it. (i) show that the energy stored in this system is $\dfrac{Q^2}{8\pi \epsilon_{0}R}.$ (ii) Now imagine ...
-1
votes
1answer
135 views

Spring-Block system [closed]

Here is a multiple spring and a block system. I need to find the maximum elongation of the spring. I tried to take $mg-(k_1+k_2)x=0$, and find $x$ from there. The answer is coming wrong. It should ...
-1
votes
2answers
113 views

why work done by spring is negative eventhough KE increases? [closed]

Suppose a block is attached to a compressed spring, it is released so moves under spring force of magnitude $kx$, let it moves from $-a$ (negative since displacement is negative for a compressed ...
0
votes
4answers
98 views

How does $W=0$ for the following equation and question on conservative forces?

We have $W = fd\cos(\theta)$ = Kinetic Energy + Potential Energy. Our example is a $10$kg ball is falling from a height of $10$m. I can see why Kinetic Energy and Potential Energy cancel out to become ...
0
votes
1answer
290 views

Problem based on Gravitation [closed]

A rocket is launched vertically from the surface of the earth with an initial velocity of 10 km/s. How far above the surface of the earth would it go? Radius of the earth = 6400 km; g=9.8 m/s^2. ...
2
votes
1answer
98 views

Potential energy and conservation law

I'm preparing for my masters entrance exam on pure mathematics (thought some problems are devoted to classical/lagrangian mechanics). I would be grateful to clarify some basics regarding the ...