Homework Answers
Here I have simply used conservation of total energy of an isolated particle. And total energy which is kinetic energy + potential energy remains same everywhere .
If you still have any confusion regarding solution or any step then please let me know in the comments section.
Thank you.
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4. A particle of mass m 2 kg moves under the potential energy function U(x.y.z)- (kx...
A particle of mass m moves in one dimension. Its potential energy is given by U(x)...
A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function...
2. Consider a point particle of mass m undergoing a one-dimensional motion under the action of...
2. Consider a point particle of mass m undergoing a one-dimensional motion under the action of a force F(x) =-kx + az where k and ? are positive constants. Follow Example 3 in the lecture notes on Differential equations and discover an integral of motion I(x,v) - const for this mechanical system. Plot the integral curves (x, v) in phase space, by using the ContourPlot command in Mathematica to plot the lines of constant I(x,v). Set significance. (6 points)
A particle of mass m is in a potential energy field described by, V(x, y) =...
A particle of mass m is in a potential energy field described by, V(x, y) = 18kx² +8ky? where k is a positive constant. Initially the particle is resting at the origin (0,0). At time t = 0 the particle receives a kick that imparts to it an initial velocity (vo, 2vo). (a) Find the position of the particle as a function of time, x(t) and y(t). (b) Plot the trajectory for this motion (Lissajous figure) using Vo = 1,...
from O. 8 A particle of mass 2 kg moves in a straight line. At time...
from O. 8 A particle of mass 2 kg moves in a straight line. At time t, its displacement from a fixed origin is x metres and its velocity is v ms-t. If the resultant force (in newtons) acting on the particle is: (a) 6 cost, and v=2 and x = 0 when t= 0, then find x in terms of t (b) 2 + 4x, and v= 2 when x = 0, then find v when x = 2...
24&25 please The figure below shows the potential energy function U (r)for a particle moving along...
24&25 please
The figure below shows the potential energy function U (r)for a particle moving along an axis labeled by the coordinate r. Values for energy and distance are in joules (j) millimeters (mm), respectively. The total energy of this particle is E = -4 J. Initially, the particle is at r = 1 mm and moving to the right (direction of increasing r) Which of the following statements best describes the subsequent motion of this particle? a. The particle...
#1 A particle of mass, m, moves in a field whose potential energy in spherical coordinates...
#1 A particle of mass, m, moves in a field whose potential energy in spherical coordinates has a 2 , where r and are the standard variables of spherical coordinates and k is a positive constant. Find Hamiltonian and Hamilton's equations of motion for this particle. form of V --k cose
A particle of a mass 1.2 x 10-11 kg and negative charge – 1.0 °C moves...
A particle of a mass 1.2 x 10-11 kg and negative charge – 1.0 °C moves to the right with a speed of 3.0 x 103 m/s. It enters a uniform electric field region where the field is known to be parallel to particle's direction of motion. If the particle is to be brought to rest in the space of 4.0 cm, (a) What potential difference does it have to go through to stop this way? (b) what is the...
A particle of a mass 1.2 x 10-11 kg and negative charge – 1.0 uC moves...
A particle of a mass 1.2 x 10-11 kg and negative charge – 1.0 uC moves to the right with a speed of 3.0 x 103 m/s. It enters a uniforn.lectric field region where the field is known to be parallel to particle's direction of motion. If the particle is to be brought to rest in the space of 4.0 cm, (a) What potential difference does it have to go through to stop this way? (b) what is the strength...
Interpret and model using appropriate Mathem 5) Suppose a particle of mass m in a gravitational...
Interpret and model using appropriate Mathem 5) Suppose a particle of mass m in a gravitational feld g is atached to a horizontal spring whose stifes is k and suppose the particle is allowed to slide on a horizontal surface such that pu is the kinetic coefficient of friction between the surface and the mass as it slides (a) Write a differential equation describing the motion of the mass on the surface when it is subject to only the spring's...
4. Determine approximately the law of motion of a particle of mass m in the field...
4. Determine approximately the law of motion of a particle of mass m in the field Ucx) in the vicinity of turning point of motion E-Ua) where E is total energy. Proceed by expanding U(x) in a Taylor series about x-a. Consider the cases when (a) U(a)#0 and 5. Find the law according to which the period of motion T for a particle of mass nm moving in the field sketched below approaches infinity as ε=um-E goes to zero. The...
A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function...
2. Consider a point particle of mass m undergoing a one-dimensional motion under the action of a force F(x) =-kx + az where k and ? are positive constants. Follow Example 3 in the lecture notes on Differential equations and discover an integral of motion I(x,v) - const for this mechanical system. Plot the integral curves (x, v) in phase space, by using the ContourPlot command in Mathematica to plot the lines of constant I(x,v). Set significance. (6 points)
A particle of mass m is in a potential energy field described by, V(x, y) = 18kx² +8ky? where k is a positive constant. Initially the particle is resting at the origin (0,0). At time t = 0 the particle receives a kick that imparts to it an initial velocity (vo, 2vo). (a) Find the position of the particle as a function of time, x(t) and y(t). (b) Plot the trajectory for this motion (Lissajous figure) using Vo = 1,...
from O. 8 A particle of mass 2 kg moves in a straight line. At time t, its displacement from a fixed origin is x metres and its velocity is v ms-t. If the resultant force (in newtons) acting on the particle is: (a) 6 cost, and v=2 and x = 0 when t= 0, then find x in terms of t (b) 2 + 4x, and v= 2 when x = 0, then find v when x = 2...
24&25 please
The figure below shows the potential energy function U (r)for a particle moving along an axis labeled by the coordinate r. Values for energy and distance are in joules (j) millimeters (mm), respectively. The total energy of this particle is E = -4 J. Initially, the particle is at r = 1 mm and moving to the right (direction of increasing r) Which of the following statements best describes the subsequent motion of this particle? a. The particle...
#1 A particle of mass, m, moves in a field whose potential energy in spherical coordinates has a 2 , where r and are the standard variables of spherical coordinates and k is a positive constant. Find Hamiltonian and Hamilton's equations of motion for this particle. form of V --k cose
A particle of a mass 1.2 x 10-11 kg and negative charge – 1.0 °C moves to the right with a speed of 3.0 x 103 m/s. It enters a uniform electric field region where the field is known to be parallel to particle's direction of motion. If the particle is to be brought to rest in the space of 4.0 cm, (a) What potential difference does it have to go through to stop this way? (b) what is the...
A particle of a mass 1.2 x 10-11 kg and negative charge – 1.0 uC moves to the right with a speed of 3.0 x 103 m/s. It enters a uniforn.lectric field region where the field is known to be parallel to particle's direction of motion. If the particle is to be brought to rest in the space of 4.0 cm, (a) What potential difference does it have to go through to stop this way? (b) what is the strength...
Interpret and model using appropriate Mathem 5) Suppose a particle of mass m in a gravitational feld g is atached to a horizontal spring whose stifes is k and suppose the particle is allowed to slide on a horizontal surface such that pu is the kinetic coefficient of friction between the surface and the mass as it slides (a) Write a differential equation describing the motion of the mass on the surface when it is subject to only the spring's...
4. Determine approximately the law of motion of a particle of mass m in the field Ucx) in the vicinity of turning point of motion E-Ua) where E is total energy. Proceed by expanding U(x) in a Taylor series about x-a. Consider the cases when (a) U(a)#0 and 5. Find the law according to which the period of motion T for a particle of mass nm moving in the field sketched below approaches infinity as ε=um-E goes to zero. The...
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