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81 Proof of Kepler's Second Law. In this section we force pointing toward the origin 0 in R3. con...
Multivariable Calculus help with the magnitude of angular momentum: My questions is exercise 4 but I have attached exercise 1 and other notes that I was provided 4 Exercise 4. In any mechanics proble...
Multivariable Calculus help with the magnitude of angular
momentum: My questions is exercise 4 but I have attached exercise 1
and other notes that I was provided
4 Exercise 4. In any mechanics problem where the mass m is constant, the position vector F sweeps out equal areas in equal times the magnitude of the angular momentum ILI is conserved (Note: be sure to prove "if and only if") (Note: don't try to use Exercise 2 in the proof of...
Please explain clearly. I need to know each steps reasons. 5) (Kepler's Problem) Suppose that a...
Please explain clearly. I need to know each steps
reasons.
5) (Kepler's Problem) Suppose that a particle is moving in three dimensions under the influence of the force k F=- where k is a positive constant. (a) Find the torque acting on the particle with respect to the origin. Is angular momentum conserved? Show that the magnitude of the angular momentum is given by l = mr2ė. (b) Using Newton's second law, show that the momentum of the particle is...
A) Using Newton's second law, write equations for ax and ay, where a⃗ =axi^+ayj^ is the...
A) Using Newton's second law, write equations for ax
and ay, where a⃗ =axi^+ayj^ is the acceleration of the
particle. Express your answer in terms of the variables q,
B, vx, vy, and m. Enter your answers
separated by a comma.
B) Differentiate the second of these equations with respect to
time. Then substitute your expression for
ax=dvx/dt to determine an equation for
dv2y/dt2 in terms of
vy. Express your answer in terms of the
variables q, B, vy, and...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force pr...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
could you please solve a and b? Chapier 2i. Note: you needn't derive Kepler's laws-but do...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
just 18.3 In other words, the center of mass moves as a free particle (no external...
just 18.3
In other words, the center of mass moves as a free particle (no external force) of mass m. The solution for R corre- sponds to uniform straight-line motion, and eliminates three of the six independent variables in the original equations of motion (three components each of, and r. Let us take, as the remaining three independent variables, the three components of r -. To ma- nipulate the original dynamical equations into a single vector equation for r. divide...
I need help with B, C, D. These are Calc 3 problems 32. Suppose a particle...
I need help with B, C, D. These are Calc 3 problems
32. Suppose a particle of mass m has position given by r(0) =< 1,0,0 >, and velocity given by v(0)0,1,-1 > at time t = 0. Also, assume that for every time t 20 the particle experiences only the force given by the vector function F(t) = m < -cos(t), 0, sin(t) >. Disregard units in this problem a) Use Newton's Second Law, F(t) = ma(t) (where a(t)...
6. (10 points Extra Credit) Electrodynamics is not the only subject that utilizes Gauss' Law. We can also use it to study Newtonian gravity. The acceleration due to gravity (9can be written as, w...
6. (10 points Extra Credit) Electrodynamics is not the only subject that utilizes Gauss' Law. We can also use it to study Newtonian gravity. The acceleration due to gravity (9can be written as, where G is Newton's gravitational constant and ρ is the m ass density. This leads us to the usual formulation of Newton's universal law of gravity,或刃--GM(f/r, as expected (if we assume V xğ-0). This "irrotational" condition allows us write (in analogy to the electric field), --Vo and...
<Chapter 27 Problem 27.74 9 of 9 > A Review | Constants Part C A particle...
<Chapter 27 Problem 27.74 9 of 9 > A Review | Constants Part C A particle with charge q and mass m is dropped at time t = 0 from rest at its origin in a region of constant magnetic field B that points horizontally. What happens? To answer, construct a Cartesian coordinate system with the y-axis pointing downward and the z-axis pointing in the direction of the magnetic field. At time t o the particle has velocity v =...
Multivariable Calculus help with the magnitude of angular
momentum: My questions is exercise 4 but I have attached exercise 1
and other notes that I was provided
4 Exercise 4. In any mechanics problem where the mass m is constant, the position vector F sweeps out equal areas in equal times the magnitude of the angular momentum ILI is conserved (Note: be sure to prove "if and only if") (Note: don't try to use Exercise 2 in the proof of...
Please explain clearly. I need to know each steps
reasons.
5) (Kepler's Problem) Suppose that a particle is moving in three dimensions under the influence of the force k F=- where k is a positive constant. (a) Find the torque acting on the particle with respect to the origin. Is angular momentum conserved? Show that the magnitude of the angular momentum is given by l = mr2ė. (b) Using Newton's second law, show that the momentum of the particle is...
A) Using Newton's second law, write equations for ax
and ay, where a⃗ =axi^+ayj^ is the acceleration of the
particle. Express your answer in terms of the variables q,
B, vx, vy, and m. Enter your answers
separated by a comma.
B) Differentiate the second of these equations with respect to
time. Then substitute your expression for
ax=dvx/dt to determine an equation for
dv2y/dt2 in terms of
vy. Express your answer in terms of the
variables q, B, vy, and...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
just 18.3
In other words, the center of mass moves as a free particle (no external force) of mass m. The solution for R corre- sponds to uniform straight-line motion, and eliminates three of the six independent variables in the original equations of motion (three components each of, and r. Let us take, as the remaining three independent variables, the three components of r -. To ma- nipulate the original dynamical equations into a single vector equation for r. divide...
I need help with B, C, D. These are Calc 3 problems
32. Suppose a particle of mass m has position given by r(0) =< 1,0,0 >, and velocity given by v(0)0,1,-1 > at time t = 0. Also, assume that for every time t 20 the particle experiences only the force given by the vector function F(t) = m < -cos(t), 0, sin(t) >. Disregard units in this problem a) Use Newton's Second Law, F(t) = ma(t) (where a(t)...
6. (10 points Extra Credit) Electrodynamics is not the only subject that utilizes Gauss' Law. We can also use it to study Newtonian gravity. The acceleration due to gravity (9can be written as, where G is Newton's gravitational constant and ρ is the m ass density. This leads us to the usual formulation of Newton's universal law of gravity,或刃--GM(f/r, as expected (if we assume V xğ-0). This "irrotational" condition allows us write (in analogy to the electric field), --Vo and...
<Chapter 27 Problem 27.74 9 of 9 > A Review | Constants Part C A particle with charge q and mass m is dropped at time t = 0 from rest at its origin in a region of constant magnetic field B that points horizontally. What happens? To answer, construct a Cartesian coordinate system with the y-axis pointing downward and the z-axis pointing in the direction of the magnetic field. At time t o the particle has velocity v =...
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