The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = (x, y, z) is Kr F(r) = |r| where K is a constant. (See this example.) Find the work done as the particle moves along a straight line from (5, 0, 0) to (5, 4, 5).
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- A force acting on a particle moving in the xy plane is given by F = (2yî + x²ĵ), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.80 m and y = 5.80 m, as shown in the figure below. y (m) (x, y) x (m) (a) Calculate the work done by on the particle as it moves along the purple path (oⒸ). (b) Calculate the work done by F on the particle as it moves along the red path (0 BC) J O conservative (c) Is F conservative or nonconservative? nonconservativeA 7.00-kg particle moves from the origin to position ©, having coordinates x = 6.50 m and y = 6.50 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W = FAr cos 0 = F · Ař), calculate the work done by the gravitational force in going from O to © along the following paths. у (m) B (х, у) x (m) (a) the purple path (o0©) (b) the red path (O®© (c) the blue path (O© (d) Your results should all be identical. Why? This answer has not been graded yet.The force on a particle is described by 2x^3−6 at a point x along the x-axis. Find the work done in moving the particle from the origin to x=7.
- A force F(x) = 3.3 x N acts on a particle as it moves along the positive x-axis. (a) How much work (in J) does the force do on the particle as it moves from x = 2.5 m to x = 5.8 m? J (b) Picking a convenient reference point of the potential energy to be zero at x = 1 m, find the potential energy for this force. (Use the following as necessary: x. Assume U(x) is in joules and x is in meters. Do not include units in your answer.) U(x) =Given: A shopper pushes a grocery cart for a distance 21 m at constant speed on level ground, against a 37.5 N frictional force. He pushes in a direction 22.5° below the horizontal. What is the work done on the cart by friction, in joules? What is the work done on the cart by the gravitational force, in joules? What is the work done on the cart by the shopper, in joules? Find the magnitude of the force, in newtons, that the shopper exerts on the cart. What is the total work done on the cart, in joules?A particle is acted on by the constant force F = (8.00î + 1.00ĵ) N as it moves from position O to C along several different paths shown in the figure below. Determine the work done on the object by the force as the object moves from position O to C along the following paths. (Include the sign of the values in your answers.) (a) path OAC J(b) path OBC J(c) path OC J(d) From the above, we may conclude that the given force is which of the following? not a conservative force There is not enough information to tell. a conservative force
- An object moves in the xy plane in above figure and experiences a friction force with constant magnitude 3.00N, always acting in the direction opposite the objects velocity. Calculate the work that you must do to slide the object at constant speed against the friction force as the object moves along (a) the purple path O to A followed by a return purple path to O, (b) the purple path O to C followed by a return blue path to O, and (c) the blue path O to C followed by a return blue path to O. (d) Each of your three answers should be nonzero. What is the significance of this observation?How much work is done on the book by friction during a displacement of 3.6 m to the left? The book now slides 3.6 m to the right, returning to its starting point. During this second 3.6 m displacement, how much work is done on the book by friction? What is the total work done on the book by friction during the complete round trip? On the basis of your answer to the previous question, would you say that the friction force is conservative or nonconservative?An object moves in the x-y plane while acted on by the force F(x,y) = k1yi + k2xj, where k1 and k2 are constants with units of N/m. The object moves along a straight line path from Cartesian coordinate (x1, y1) to (x2, y2). Write an expression for the work done on the object by this force.