The gravitational forces exerted by the Sun on the planets are always directed toward the Sun and depend only on the distance r. This type of field is called a central force field. Find the potential energy at a distance r from a center of attraction when the force varies as 1/r. Set the potential energy equal to zero at infinity.
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- ASSIGNMENT: (0,1,1) Problem 1 Given the force field F= 2yi + 2x) + 2zk, (-1,0,0) find a scalar potential o such that F= Vo; () use the potential p to find the work W done by force F in moving from point (-1,0,0) to (0,1,1).Any solution ?Compute the work performed in moving a particle al ong the path r(t) = (r*,te,2-t) for 0St54 by the force field F = {cos z,yz,(x+y)*}. Include a plot of the path and the force field on the same axis.
- The gravitational field of a spherical object at any distance from it points back to the center of the object. That is, in the field simulator it has arrows toward the center of the sphere. Put a test mass in this field and it will fall toward the center with increasing speed following the line of force. Locally, the field is the acceleration of gravity at that point. Now, how would you move a small mass so that you would not have to do work on it during the move? That work would be the change its energy. You would move it radially toward the center. You would move it radially away from the center. You would move it perpendicularly to the line of force, that is, move it in a local plane that is perpendicular to the radius at that point. There is no way to do this. Any displacement direction will take work.162) Consider the following potential U = x³ -4x. a) Find the equilibrium point/points. b) Find the work done by the force if the particles move from x = 0 to x =4m. c) What is the force applied to the particle at x = 4m. IF NEEDS G *Take gravitational constant g =10 m/s?.
- A particle moves in the xy plane (see the figure below) from the origin to a point having coordinates x = 7.00 m and y = 4.00 m under the influence of a force given by 7 = -2y²1 - 3x1. y (m) 2 (7.00, 4.00) x (m) (a) What is the work done on the particle by the force F if it moves along path 1 (shown in red)? -84 (b) What is the work done on the particle by the force F if it moves along path 2 (shown in blue)? -224 (c) What is the work done on the particle by the force F if it moves along path 3 (shown in green)? -32.7 X Your response differs from the correct answer by more than 10%. Double check your calculations. J (d) Is the force conservative or nonconservative? conservative nonconservativeIn the figure, a small block of mass m = 0.029 kg can slide along the frictionless loop-the-loop, with loop radius R = 16 cm. The block is released from rest at point P, at height h = 5R above the bottom of the loop. How much work does the gravitational force do on the block as the block travels from point P to (a) point Q and (b) the top of the loop? If the gravitational potential energy of the block-Earth system is taken to be zero at the bottom of the loop, what is that potential energy when the block is (c) at point P, (d) at point Q, and (e) at the top of the loop? (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i Units (e) Number i Units R eTWhat is the work done by the force field F(x,y,z)=(2xy,x2,3z) to move a particle from the point (0,0,0) to other point (2,2,8) along the curve given by the intersection of the surfaces z=x2+y2 and x=y.
- Calculate the work done by the force field F(x,y,z)=(2xy,x2,3z) to move a particle from the point (0,0,0) to point (2,2,8) along the curve given by the intersection of the surfaces z=x2+y2 and x=y.Find the work done by the force field F = (y cos x + 2°)i + (2y sin x – 4)j+ (3xz² + 2)k 1 sin t, y = 1 – 2t, z = 3t – 1 ( in moving a particle along the curve x = 0The potential energy of a system is given by: U(x,y,z)=5(J/m^2) x^2 + 7(J/m^3) xy^2 + 8(J/m^2) zy Find: The force acting on the system. Write the forces as the sum of its components. The magnitude of the force when x=1, y=0, z=2SEE MORE QUESTIONS