(c) Find the generalized potential. (d) Find the equation of motion for the path x(t) of the syst em (Don't try to solve this nonlinear equation.) (e) Find the total energy of the system (f) Show that energy is conserved in this system. t) Q2 stationary moving
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11.9. As shown in the figure, an object of charge Q, and mass m moves near a stationary object wi...
A charged particle with mass M and charge q moves in the x – y plane....
A charged particle with mass M and charge q moves in the x – y plane. There is a magnetic field of magnitude B in the z-direction and an electric field E in the x-direction. (a) Find the Lagrangian in a form where there is an ignorable coordinate. (b) Find the energy function. Is it energy? Is it conserved? Explain why. (c) Find and solve the equations of motion.
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
A point charge of mass m = 9x10 ^ -31 kg and load + q =...
A point charge of mass m = 9x10 ^ -31 kg and load + q = 1.62 × 10 ^ -19C is released from rest in an electric field E generated by two plates, separated by a distance of 20 mm a) Draw the electric field lines b) Find the v (t) of the load + q c) Find the kinetic energy of + q d) Find the same result of the number c) using the work and energy theorem...
Consider a system of three charges shown in (Figure 1). An object with charge q4 =...
Consider a system of three charges shown in (Figure 1). An
object with charge q4 = +7.0×10−9C is moved to position C
from infinity (not shown in the figure). q1 = q2
= q3 = +10.0×10−8C.
A) Determine the initial electric potential energy of the system
consisting of all four charges. B) Determine the final electric
potential energy of the system consisting of all four charges. C)
Determine the work done on the system by moving the charge
q4 from...
An object of mass m = 4.9 g and charge Q = 40 ?Cis attached to...
An object of mass m = 4.9 g and charge Q = 40
?Cis attached to a string and placed in a uniform electric
field that is inclined at an angle of 30.0 ? with the horizontal
(see the figure). The object is in static equilibrium when the
string is horizontal.
Find the magnitude of the electric field.
Find the tension in the string.
Consider a system of three charges shown in (Figure 1).An object with charge q4 = +6.0×10−9C...
Consider a system of three charges shown in (Figure 1).An object
with charge q4 = +6.0×10−9C is moved to position C from infinity
(not shown in the figure). q1 = q2 = q3 = +10.0×10−8C. a.
Determine the initial electric potential energy of the system
consisting of all four charges. b.
Determine the final electric potential energy of the system
consisting of all four charges.
c. Determine the work done on the system by moving the charge q4
from infinity...
+A A d Gambarajah 3/Figure 3 Question 3 Two very long wires, carrying free charge, of...
+A A d Gambarajah 3/Figure 3 Question 3 Two very long wires, carrying free charge, of equal but opposite charge densities, 2. of +0.4 nC/m, are placed parallel to each other (Figure 3). Each wire has a diameter of 2 mm and they are separated by a distance d, of 1.0 cm. The distance d is measured from the centre point of each wire. You may assume the charge distributions on the wires are the same as if they were...
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin as s...
Please help, I am
struggling!
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin as shown in the figure below. There is a uniform electric field = Eo? and a uniform magnetic field B = BoZ The path of the charged sketched below is a cycloid whose radius of curvature at the top points is twice the y-coordinate at that level. This path is exactly the same as the path of...
2) In figure, a top view of a solid conducting cylinder with radius a - 1 em, whose center is at ...
2) In figure, a top view of a solid conducting cylinder with radius a - 1 em, whose center is at the origin of the coordinate system and +z axis is towards out of page. It is concentric with a hollow cylindrical conductor of inner radius b 3 cm and outer radius c 5 cm. Both cylinders have L-5 m lengths which can be assumed to be infinitely long since L > c. The solid cylinder has total net charge...
A charge, q=91.0000 microCoulombs on a particle with mass m=1.00000 milli- grams, moves through a pipe...
A charge, q=91.0000 microCoulombs on a particle with mass m=1.00000 milli- grams, moves through a pipe from the origin to a point at coordinate x=1.40000m and y=1.8000m. All space is filled with a uniform electric field E=1,900.00000N/C and pointing parallel to the x axis. What is the change in electric potential as the mass moves from initial to final positions (in VOLTS) An object is placed 50.0cm in front of a lens. The image forms on the same side of...
A charged particle with mass M and charge q moves in the x – y plane. There is a magnetic field of magnitude B in the z-direction and an electric field E in the x-direction. (a) Find the Lagrangian in a form where there is an ignorable coordinate. (b) Find the energy function. Is it energy? Is it conserved? Explain why. (c) Find and solve the equations of motion.
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
Consider a system of three charges shown in (Figure 1). An
object with charge q4 = +7.0×10−9C is moved to position C
from infinity (not shown in the figure). q1 = q2
= q3 = +10.0×10−8C.
A) Determine the initial electric potential energy of the system
consisting of all four charges. B) Determine the final electric
potential energy of the system consisting of all four charges. C)
Determine the work done on the system by moving the charge
q4 from...
An object of mass m = 4.9 g and charge Q = 40
?Cis attached to a string and placed in a uniform electric
field that is inclined at an angle of 30.0 ? with the horizontal
(see the figure). The object is in static equilibrium when the
string is horizontal.
Find the magnitude of the electric field.
Find the tension in the string.
Consider a system of three charges shown in (Figure 1).An object
with charge q4 = +6.0×10−9C is moved to position C from infinity
(not shown in the figure). q1 = q2 = q3 = +10.0×10−8C. a.
Determine the initial electric potential energy of the system
consisting of all four charges. b.
Determine the final electric potential energy of the system
consisting of all four charges.
c. Determine the work done on the system by moving the charge q4
from infinity...
+A A d Gambarajah 3/Figure 3 Question 3 Two very long wires, carrying free charge, of equal but opposite charge densities, 2. of +0.4 nC/m, are placed parallel to each other (Figure 3). Each wire has a diameter of 2 mm and they are separated by a distance d, of 1.0 cm. The distance d is measured from the centre point of each wire. You may assume the charge distributions on the wires are the same as if they were...
Please help, I am
struggling!
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin as shown in the figure below. There is a uniform electric field = Eo? and a uniform magnetic field B = BoZ The path of the charged sketched below is a cycloid whose radius of curvature at the top points is twice the y-coordinate at that level. This path is exactly the same as the path of...
2) In figure, a top view of a solid conducting cylinder with radius a - 1 em, whose center is at the origin of the coordinate system and +z axis is towards out of page. It is concentric with a hollow cylindrical conductor of inner radius b 3 cm and outer radius c 5 cm. Both cylinders have L-5 m lengths which can be assumed to be infinitely long since L > c. The solid cylinder has total net charge...
A charge, q=91.0000 microCoulombs on a particle with mass m=1.00000 milli- grams, moves through a pipe from the origin to a point at coordinate x=1.40000m and y=1.8000m. All space is filled with a uniform electric field E=1,900.00000N/C and pointing parallel to the x axis. What is the change in electric potential as the mass moves from initial to final positions (in VOLTS) An object is placed 50.0cm in front of a lens. The image forms on the same side of...
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