2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian L= ml² -(0² + osin²0) +mglcos 0. 2
Q: Einstein concluded that gravity is the warping of the geometry of space-time based on the presence…
A: Yes, according to Einstein's theory of general relativity, the gravitational field of massive…
Q: If the Earth had twice the radius but the same density (assume constant density), then the…
A:
Q: A = (2, -4) and B = (-3,3). Determine the distance between points A and B and find their polar…
A: Two points given in the xy plane A = (2, -4) and B = (-3,3) Find: Distance between the A and B…
Q: The mass of an electron is 9.109 381 88 × 103'kg. Find (a) y and (b) ß for an electron with kinetic…
A: Given: The mass of the electron is 9.10938188×10-31 kg. The kinetic energy of the electron is…
Q: In a certain binary-star system, each star has the a mass of 1.08 x 1030 kg, and they revolve about…
A:
Q: The Schwarzschild radius RBH for an object of mass M is defined as RBH = 2GM c² where c is the speed…
A:
Q: For the graph of vx versus t shown, estimate the following: i) What is the slope of the tangent line…
A: The above problem can be solved in two different ways. The first method using the two-point formula…
Q: Prove that the total gravitational potential energy can be written as W = .5 ∫d3xρ(x)Φ(x). ρ(x) and…
A: To derive the expression for the total gravitational potential energy, we start with the definition…
Q: A planet with a mass of 3.0 x 1023kg orbits 6.0 x 1010m from a star with a period of 2.2 x…
A: The mass of the planet is, m=3×1023 kg. The distance between the planet and the star is, r=6×1010 m.…
Q: 1. In this problem you will prove that the shortest distance between two points is a line using the…
A:
Q: Plaskett's binary (also known as HD 47129) in the constellation Monoceros is a star system of two…
A: Given: Orbital speed of the stars = 250 km/sec = 250,000 m/s Period of the star = 14.4 days Suppose…
Q: A huge cannon is assembled on an almost airless planet. The planet has a radius of 5 x 10^6 m and a…
A: Given information: The Radius of the planet (R) = 5 x 106 m The mass of the planet (M) = 2.6 x 1024…
Q: A spring of force constant k is compressed by a distance x from its equilibrium length. (a) Does…
A: Given: A spring of Force constant k is compressed by a distance x from it's equilibrium position.…
Q: The rest energy E of an object with rest mass m is given by Einstein's famous equation E = mc²,…
A:
Q: Two asteroids head straight for Earth from the same direction. Their speeds relative to Earth are…
A:
Q: star in the Andromeda galaxy is found to have a planet orbiting it at an average radius of…
A: Given radius(r)=3.38 x 1010 m Orbital period(T)=5.46 x 104 s
Q: c. Below are data on the length and weight for the Blue Marlin [2]. Length (m) Weight (kg) Length…
A: The below is the MATLAB code for the given problem data.1clear; close all; clc; 2 3% Load data…
Q: 1. The dimensions of gravitational constant are: (a) [M*£T*] (b) [M*LT=] [M'Er*] «d) [M*¢r*] (e)…
A: Solution:
Q: Two students of opposite sex with masses 70.0kg and 52.0kg respectively are sitting 1.50m apart…
A:
Q: A rogue black hole with a mass 39 times the mass of the sun drifts into the solar system on a…
A: A rogue black hole with a mass times the mass of the sun drifts into the solar system on a…
Q: A number of gas giant planets orbiting other stars at distances less than 1 A.U. have been…
A: Hey there, since you have asked multiple questions we have solved the first three for you. Please…
Q: Consider an astronaut Alice space station orbiting the earth at a radius R = 4R⊕ from the center,…
A:
Q: The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that…
A: Given, Rh = 2GM/c2 a. Gravitational acceleration is given byag=Gmr2dag=2Gmr3drSince, h<<48…
Q: A particle of mass m is placed at a distance r away from the center of a thin circular hoop of mass…
A: Given, mass as, m1=Mm2 =m radius=R, distance=r.
Q: A simple pendulum consists of a pendulum bob of mass M at the end of a "mass-less" string of length…
A: Given: The free-body diagram of the given system is:
Q: Three uniform spheres of masses m1 = 2.50 kg, m2 = 4.00 kg, and m3 = 7.50 kg are placed at the…
A: Given Datam1 = 2.5 kgm2 = 4 kgm3 = 7.5 kgDistance between m1 and m2, r12 = 3 mDistance between m3…
Q: A.) i. Define the plane polar unit vectors ŕ and 0 and show that they are orthonormal. Determine dr…
A: Step 1: Step 2: Step 3: Step 4:
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
- Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle. Part A Find the gravitational force of one star on the other. Express your answer in terms of G, M, R. Πν ΑΣφ ? F = Part B Find the orbital speed of each star. Express your answer in terms of G, M, R. να ΑΣΦ7 ? Part CThe class I'm taking is physics for scientists and engineers! I am completely stuck. Need help. I have attached the problem. Please view both attachments before answering. Please write step-by-step solution so I can fully understand.Uranium-238 decays via the alpha decay process. Part (a) Calculate the energy released in units of megaelectron volts when a uranium-238 nucleus undergoes alpha decay. Part (b) What fraction of the mass of a single uranium-238 nucleus is destroyed in the decay? Part (c) Why is difficult to observe the change in mass for a macroscopic sample of uranium-238?
- 16. Given vectors Ã= 2â, + 4ây + 10â, and B = -5âp + âo – 3âz, find (a) Ã+ B at P(0, –2,5) , with o = 90° (b) ÷Ē (c) Ã× B (d) The angle between A and B at P (e) The scalar component of A along B at Pdx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.
- An astronomer is measuring the light emitted by a binary star system. One of the stars appears to be much more massive than the other. The astronomer notices that the smaller star orbits the larger one in a nearly circular orbit at fr = 845 ×10º| a distance of r = 845 x 106 km. Through careful observation, she measures the smaller star's orbital speed to be v 12.0 km/s. Using Keppler's Laws she calculates the mass of the larger star. What is it? Use G = 6.67 x 10-¹1 N-m²/kg². - M = 30 x1030 kg (± 0.05 × 10³0 kg)After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0 cm. The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 145 s. What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per secondgPlanet=(?)m/s^2The energy to mové a rocket (mass m) nfinitely far from the Earth (Radius R and mass M) E = jGMma 1 E = x? 2 is What escape velocity at liftoff gives an energy that equals E. R
- You are an alien on an alien planet orbiting the planet's sun in a circular orbit. You want to find the mass of your sun. You determine the center-to-center distance between your planet and sun to be 6.75E+10 meters. The period of motion of your planet (the length of your year) is 1.21E+7 seconds. You know G=6.67*10^−11Nm2kg2 . What is the mass of your sun?QB1c. Write down an expression for the height has a function of time for an object, initially at rest, falling from the height H on Earth. Take g to be the gravitational field strength. Please use appropriate algebraic symbols for multiplication (* for a x b), division (/ for a/b), exponents (a^b for a"), square root (sqrt(a*b/c) for Vax blc) etc. Please use the "Display response" button to check you entered the answer you expect. h(t)=A rocket is traveling through space and its Lorentz factor (y) is 3.9. Determine the rocket's speed (in terms of c) and the ratio of its kinetic energy to its total energy. V= ? X c KE/E= ?