A force field is given by F = Fo (x°i + ryj+ z°k), find the work perform by this force on a circle of radius R centered at (0,0,1) on the plane z = 1. Repeat the calculation along a circle with radius R on the ry-plane with z = 0. Is this a conservative force field?
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- (a) A particle of mass 100 g has an acceleration along the 2-axis given by a = 10 - t. Find expressions for the velocity, v, and the location, r as functions of time (take v = 10 m s-¹ and = 0 at t = 0). (b) What is the furthest (positive) distance from the starting point that the particle attains? (e) What is the work done on the particle between the starting point and the point of furthest distance? (d) What is the power being exerted on the particle at the point (t > 0) when it again passes through x = 0?The work done by the force on paths a, b, and c respectively isFind the work (in J) done by the force F (6 N/m)yî + (27 N/m)xĵ between the points A = (0, 0) and B = (2 m, 2 m) over a circular arc of radius 2 m, centered at (0, 2 m). Evaluate the path integr %3D using Cartesian coordinates. (Hint: You will probably need to consult a table of integrals.) y(m)4 (2, 2) F(x, y) (0, 0) x(m)
- need help on attatched questionA skateboarder is at the top of a frictionless ramp defined by the function y = z². The top of the ramp is located at (-5m, 25m), and the skateboarder skates to the bottom of the ramp, (0m, 0m). (a) What nonconservative forces are in this problem? (b) What is the total nonconservative work done? (c) Is mechanical energy conserved? (d) What is the skateboarder's speed at the bottom of the ramp?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.
- An object of mass 6 kg is at a certain height above the ground. If the potential energy of the the object is 280 J, find the height at which the object is with respect to the ground. Given,g 10 m/s-2.When a truck of mass m is dragged a distance d along a surface with a coefficient of kinetic friction µk and dragged back along the same path to its initial position, the work done by the friction force isA spring with k = 15 N/m with equilibrium length 30 cm is attached vertically to a surface and then allowed to come to equilibrium, after which a weight with mass 0.2 kg is attached to the top side of the spring. → How much work does the Earth do on the weight via gravity between its initial position and the new equilibrium height? Explicitly compute the work with an integral.
- A 9.00-kg particle moves from the origin to position ©, having coordinates x = 4.50 m and y = 4.50 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 e = F . Ař), calculate the work done by the gravitational force in going from O to © along the following paths. у (m) C) (x, y) х (m) (a) the purple path (o0© (b) the red path (OB© (c) the blue path (O© (d) Your results should all be identical. Why?Calculate the force F that we must pull with and the work A that we do to move it to its final height. Take the mass of the body, the final height, the inclination of the plane and the acceleration due to gravity (m,h,alpha,g) as known. Friction and energy losses to the surroundings can be neglectedA 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 nonconservative