The inertial mass of a particle is, by definition, the mass that appears in Newton's second law. Consider free fall of a particle with gravitational mass mo and inertial mass m' near the surface of a homogeneous planet having gravitational mass MC and radius R. Express the gravitational acceleration a of the particle in terms of these quantities. (Neglect any frictional forces.)
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: Determine the height habove the surface of a planet of radius R and mass M at which the…
A: The gravitational field will be 60% on its surface, gh=g×60100=35g Then, weight of a mass on the…
Q: If the Earth had twice the radius but the same density (assume constant density), then the…
A:
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: A ring of radius 7 m lies in the x-y plane, centered on the origin. The portions of the ring in the…
A:
Q: gravitation with the Earth as m2 and the radius of the Earth for the distance F = GmME RE2. Now…
A:
Q: you are asked to verify Kepler's Laws of Planetary Motion. For these exercises, assume that each…
A: Solution:
Q: Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of…
A: The expression to solve for the velocity of the star is as follows: v=2πRTR=vT2π…
Q: Suppose you’re a physicist in 1859, and you are measuring the gravitational pull of the Sun to…
A:
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: Determine the exact gravity force on B due to P. (
A:
Q: You have been assigned to a team charged with developing a plan to explore a new planetary body…
A: Given g=2.8 m/s2 specific gravity of oil=0.93 weight of oil=4 lbf
Q: Your response differs from the correct answer by more than 10%. Double check your calculations. m…
A:
Q: A ring of radius 6.5 m lies in the x-y plane, centered on the origin. The portions of the ring in…
A:
Q: Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of…
A:
Q: Don't use chatgpt will upvote
A:
Q: A satellite of mass 175 kg is launched from a site on Earth's equator into an orbit at 180 km above…
A: As you have asked only solution of the part (c) so that I have solved only part (c). The answer of…
Q: Quite apart from effects due to Earth’s rotational and orbital motions, a laboratory reference frame…
A: Given:- L = 20cm = 0.2m v = 0.992c = 0.992 x 3 x 108 m/s = 2.976 x 108 m/s
Q: (a) Consider a particle of mass m projected upward with a velocity vo from the ground (taken to be…
A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…
Q: A projectile is fired at a velocity of 100 m s-¹ at an angle of 36° to the horizontal as shown…
A:
Q: The star Sirus A has a mass of 2.06 MO and a radius of 1.71 RO, where M0 is the mass of the Sun…
A:
Q: At what altitude h above the north pole is the weight of an object reduced to 27% of its…
A:
Q: A particle of mass m is projected in a uniform gravitational field. The initial conditions at time t…
A:
Q: A ring of radius 6.5 m lies in the x-y plane, centered on the origin. The portions of the ring in…
A: Given data: Radius of the ring, R=6.5 m Mass density of first and third quadrant of the ring, ρ1=3.6…
Q: Two particles move about each other in circular orbits under the influence of gravitational forces,…
A: The gravitational force between two particles is directly proportional to the product of their…
Q: An asteroid, headed directly toward Earth, has a speed of 12 km/s relative to the planet when the…
A: Solution
Q: 20. Determine the force of gravitational attraction on a particle of mass m located in P(0, 0, b)…
A: You must integrate the gravitational force contributions (dF) over the whole mass distribution of…
Q: The answer key to this problem is stated as follows: x(t) = (4.0 cm)cos[(2π/8.0 s)t - π/3.0] Did…
A: On the 2nd page of answer there was a mistake. cos-1ϕ=12thus ϕ can have values of 600 or -600i.e.…
Q: A drill bit is able to reach 2000 rpm in 0.50 s. Assuming a constant angular acceleration, how many…
A: Given: The final angular speed of the drill is dω=2000 rpm= 2000×2π60 s=209.44 rads. Time required…
Q: At a given time, satellite are: inert position and velocity ectors in a geocentric equatorial frame…
A:
Q: NOTE: Your answer suggests that you have assumed constant gravitational
A: Explained as, F=-GMMR+y2
Q: On the surface of the earth, the gravitational field (with z as vertical coordinate measured in…
A: (A). The potential function for given F is fx,y,z=-gz
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
- Consider an astronaut Alice space station orbiting the earth at a radius R = 4R⊕ from the center, where R⊕ = 6.4 × 10^6 m is the earth’s radius and M⊕ = 5.972 x 10^24 kg. Assume the orbit is circular. Consider a second astronaut Julie who’s far away outside the earth’s gravitational field and is at rest with respect to the earth. 1. Considering only special relativity, how much time does Alice age if Julie ages 1 year? 2. Considering only gravity (not special relativity), how much time does Alice age if Julie ages 1 year? 3. Now considering both of these effects (gravity and special relativity) , how much time does Alice age if Julie ages 1 year?A particle of mass m is placed at a distance r away from the center of a thin circular hoop of mass M and radius R. The particle is in the plane of the hoop, and r < R. M. Find the gravitational force on the particle. Does your answer make sense in the limit r + 0? r + R? 2.A planet of mass 5 ⨯ 1024 kg is at location <4 ⨯ 1011, −4 ⨯ 1011, 0> m. A star of mass 4 ⨯ 1030 kg is at location <−6 ⨯ 1011, 4 ⨯ 1011, 0> m. (a) What is the relative position vector pointing from the planet to the star? (b) What is the distance between the planet and the star? (c) What is the unit vector in the direction of r? (d) What is the magnitude of the force exerted on the planet by the star?(e) What is the magnitude of the force exerted on the star by the planet? (f) What is the force (vector) exerted on the planet by the star? (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.)
- ) Several planets possess nearly circular surrounding rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ringlike structures. Consider a homogeneous ring of mass M and radius R. a) What gravitational attraction does it exert on a particle of mass m located a distance x from the center of the ring along its axis? b) Suppose the particle falls from rest as a result of the attraction of the ring of matter. Find an expression for the speed with which it passes through the center of the ring. (a: see notes from class, b: Use the definition of potential energy.)A Block-Spring System A block of mass 1.0 kg is attached to horizontal spring that has a force constant of 2,000 N/m as shown in figure (a). The spring is compressed 3.0 cm and then released from rest as in figure (b). (a) A block attached to a spring is pushed inward from an initial position x -0 by an external agent. (b) At position x, the block is released from rest and the spring pushes it to the right. x = 0 (For the following, when entering a mathematical expression, do not substitute numerical values; use variables only.) (a) Calculate the speed of the block as it passes through the equilibrium positio x = 0 if the surface is frictionle SOLUTION Conceptualize This situation has been discussed before, and it is easy to visualize the block being pushed to the right by the spring and moving with some speed at x = 0. Categorize We identify the system as the block and model the block as [--Select-- Vsystem. Analyze In this situation, the block starts with v, = 0 at x, = -3.0 cm, and…Problem 1 Consider two celestial bodies of masses m₁ and m2. The bodies only interact gravitationally and can be considered pointlike for the purpose of this problem. (a) List the conserved quantities of the system. (b) For each conserved quantity, state the Noether symmetry responsible for its conservation.
- I whirl John (mass 0.27 kg) over my head in a circle. There is a spring scale between my hand and the string, so I can measure the force of tension in the string, which I find to be 2.12 N. I measure the length of the string (the radius of the circle) and find it to be 1.34 m. Assuming that John's speed is not changing, how fast is he going?When the Moon is directly overhead at sunset, the force by Earth on the Moon, FEM, is essentially at 90° to the force by the Sun on the Moon, FSM, as shown below. FEM=1.98×10^20N and FSM=4.36×10^20N, all other forces on the Moon are negligible, and the mass of the Moon is 7.35×10^22kg. 1. Write an expression for the magnitude of the acceleration of the Moon. 2. What is the acceleration of the Moon in m/s^2?Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is V = 240 km/s and the orbital period of each is 12.1 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses XCM M
- An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 74.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 19.4 years as measured in a rest frame. Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) yr (b) How far is the probe from Earth when its batteries fail as measured by mission control? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) ly (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? ly (d) For what total time…Consider the observation that the acceleration due to the gravitational force acting on a mass around a host planet decreases with the square of the separation between the objects. We can ask ourselves: why is it still accurate to consider a gravitational acceleration value of 9.8\frac{m}{s^2}9.8s2m for all of our projectile motion problems and all of our gravitational potential energy from prior modules? Let's analyze a situation and justify this analysis method: consider an object being launched from ground level to an altitude of 10,000 meters, roughly the cruising altitude of most jet liners, and far above our everyday experiences on Earth's surface. Compare the gravitational acceleration of the object at Earth's surface (the radius of Earth is about r_E=6.37\times10^6mrE=6.37×106m) to the acceleration value at the 10,000 meter altitude by determining the following ratio: g10,000m/gsurfaceWe will use differential equations to model the orbits and locations of Earth, Mars, and the spacecraft using Newton’s two laws mentioned above. Newton’s second law of motion in vector form is: F^→=ma^→ (1) where F^→ is the force vector in N (Newtons), and a^→ is the acceleration vector in m/s^2,and m is the mass in kg. Newton’s law of gravitation in vector form is: F^→=GMm/lr^→l*r^→/lr^→l where G=6.67x10^-11 m^3/s^2*kg is the universal gravitational constant, M is the mass of the larger object (the Sun), and is 2x10^30 kg, and m is the mass the smaller one (the planets or the spacecraft). The vector r^→ is the vector connecting the Sun to the orbiting objects. Step one ) The motion force in Equation(1), and the gravitational force in Equation(2) are equal. Equate the right hand sides of equations (1) and (2), and cancel the common factor on the left and right sides. Answer: f^→=ma^→ f=Gmm/lr^→l^2 a^→=Gmm/lr^→l^2 x r^→/lr^→l r^→=r^→/lr^→l * Gmm Could you please…