Homework Answers
(5)
Force is given by,
F = -dU / dx + (-dU / dy)
F = d(3x3y - 7x) / dx - d(3x3y) / dy
F = (9x2y - 7) i - (3x3) j
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5. A potential energy fumction for a two-dimensional force is of the fornV-3y-7t FPind the force...
6. The 200 g particle (Fig. 4) is released from point A at rest. The radus...
6. The 200 g particle (Fig. 4) is released from point A at rest. The radus is 30 cm. The speed of the particle at point B is 1.5 m/s. (a) What is its kinetic energy at B? (b) How much energy is lost as a result of friction as the particle goes from A to B? (c) Is it possible to determine μ from these results in any simple manner? Explain. Figure 4
A potential energy function for a two- dimensional force is of the form U= a ry+br,...
A potential energy function for a two- dimensional force is of the form U= a ry+br, where a = 2.56 J/m' and b = -5 J/m. Find the magnitude of the force that acts at the point (x, y) for x = 69 m, y = 16 m. Answer in units of N.
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,...
5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well...
5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well created by a one-dimensional force where a and b are known positive constants. Assume the particle is trapped in the well on the positive side of the y-axis. a) Find and expression for the potential energy U(x) for this force. (10 points) NOTE: There will be one undetermined constant. b) Set Umin, the minimum value for this potential energy function, equal to zero. Solve...
(a) Sketch a potential energy function as a function of position (one-dimensional) that has two stable...
(a) Sketch a potential energy function as a function of position (one-dimensional) that has two stable equilibriums and one unstable equilibrium. (b) For three different locations (none of which should be a point of equilibrium), indicate the direction of the force a particle at these locations would experience.
A particle of mass 5 kg is subject to a conservative force whose potential energy (in...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
A -1mC, 2mg particle is released from rest at point ID. A. a. What is its kinetic energy at point B? b. What is its kinetic energy if it is later observed at point C Draw a field line going throug...
A -1mC, 2mg particle is released from rest at point ID. A. a. What is its kinetic energy at point B? b. What is its kinetic energy if it is later observed at point C Draw a field line going through D c. Contour line values in volts
A -1mC, 2mg particle is released from rest at point ID. A. a. What is its kinetic energy at point B? b. What is its kinetic energy if it is later observed...
Problem 2 A particle with charge +7.60 nC is inside a uniform electric field directed to...
Problem 2 A particle with charge +7.60 nC is inside a uniform electric field directed to the left. Another force, in addition to the electric force, acts on the particle so that when it is released from rest, it moves to the right. After it has moved 8.00 cm, the additional force has done 6.50-10-4 J of work and the particle has 4.35-10-5 J of kinetic energy. (a) What work was done by the electric force? (b) What is the...
1a. 1b. 1c. A single conservative force = (AX - B) N, where x is in...
1a.
1b. 1c.
A single conservative force = (AX - B) N, where x is in meters, and A and B are positive constants, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 0 at x = 0. (a) Write an expression for the potential energy associated with this force. (b) What is the maximum positive value of the potential energy? In the figure, a block of...
Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of...
Learning Goal: To be able to interpret potential energy diagrams
and predict the corresponding motion of a particle. Potential
energy diagrams for a particle are useful in predicting the motion
of that particle. These diagrams allow one to determine the
direction of the force acting on the particle at any point, the
points of stable and unstable equilibrium, the particle's kinetic
energy, etc. Consider the potential energy diagram shown. (Figure
1) The curve represents the value of potential energy U...
6. The 200 g particle (Fig. 4) is released from point A at rest. The radus is 30 cm. The speed of the particle at point B is 1.5 m/s. (a) What is its kinetic energy at B? (b) How much energy is lost as a result of friction as the particle goes from A to B? (c) Is it possible to determine μ from these results in any simple manner? Explain. Figure 4
A potential energy function for a two- dimensional force is of the form U= a ry+br, where a = 2.56 J/m' and b = -5 J/m. Find the magnitude of the force that acts at the point (x, y) for x = 69 m, y = 16 m. Answer in units of N.
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,...
5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well created by a one-dimensional force where a and b are known positive constants. Assume the particle is trapped in the well on the positive side of the y-axis. a) Find and expression for the potential energy U(x) for this force. (10 points) NOTE: There will be one undetermined constant. b) Set Umin, the minimum value for this potential energy function, equal to zero. Solve...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
A -1mC, 2mg particle is released from rest at point ID. A. a. What is its kinetic energy at point B? b. What is its kinetic energy if it is later observed at point C Draw a field line going through D c. Contour line values in volts
A -1mC, 2mg particle is released from rest at point ID. A. a. What is its kinetic energy at point B? b. What is its kinetic energy if it is later observed...
Problem 2 A particle with charge +7.60 nC is inside a uniform electric field directed to the left. Another force, in addition to the electric force, acts on the particle so that when it is released from rest, it moves to the right. After it has moved 8.00 cm, the additional force has done 6.50-10-4 J of work and the particle has 4.35-10-5 J of kinetic energy. (a) What work was done by the electric force? (b) What is the...
1a.
1b. 1c.
A single conservative force = (AX - B) N, where x is in meters, and A and B are positive constants, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 0 at x = 0. (a) Write an expression for the potential energy associated with this force. (b) What is the maximum positive value of the potential energy? In the figure, a block of...
Learning Goal: To be able to interpret potential energy diagrams
and predict the corresponding motion of a particle. Potential
energy diagrams for a particle are useful in predicting the motion
of that particle. These diagrams allow one to determine the
direction of the force acting on the particle at any point, the
points of stable and unstable equilibrium, the particle's kinetic
energy, etc. Consider the potential energy diagram shown. (Figure
1) The curve represents the value of potential energy U...
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