A particle moves from ^ri = (1 m)ˆi + (5 m)ˆj to a position ^rf = −(2 m)ˆi − (8 m)ˆj due to a force ^F = (6x N)ˆi + (4 N)ˆj where x is in meters. Compute the work done by this force.
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A particle moves from ^ri = (1 m)ˆi + (5 m)ˆj to a position ^rf = −(2 m)ˆi − (8 m)ˆj due to a force ^F = (6x N)ˆi + (4 N)ˆj where x is in meters. Compute the work done by this force.

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- A particle is subject to a force Fx that varies with position as shown. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x = 10.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x = 0 to x = 15.0 m?An object has several forces acting on it. One of these forces is F=αxyî, a force in the x-direction whose magnitude depends on the position of the object, with α=2.50N/m2. Calculate the work done on the object by this force for the following displacements of the object: (a) the object starts at the point (x=0, y=3.00 m) and moves parallel to the x-axis to the point (x=2.00m, y=3.00m). (b) the object starts at the point (x=2.00m, y=0) and moves in the y-direction to the point (x=2.00m, y=3.00m). (c) the object starts at the origin and moves on the line y=1.5x to the point (x=2.00m, y=3.00m).You have two vectors: A = 7.27î + 3ĵ and B = 4î - 0.95ĵ + 12k. If vector A represents a force vector and vector B is a displacement vector, what is the magnitude of work done by this force?
- An object is subject to a nonconstant force F = (5x3 − 4x) such that the force is in newtons when x is in meters. Determine the work done on the object as a result of this force as the object moves from x = 0 to x = 1.30 ✕ 102 m.A single conservative force acts on a 4.70-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 0.96 m to x = 7.50 m, calculate the following. (a) the work done by this force on the particle 81.488 J (b) the change in the potential energy of the system J (c) the kinetic energy the particle has at x = 7.50 m if its speed is 3.00 m/s at x = 0.96 m JA particle is subject to a force F, that varies with position as shown in the following figure. F, (N) 3 1 х (m) 4 6 10 12 14 16 (a) Find the work done by the force on the particle as it moves from x = 0 to x = :3.00 m. (b) Find the work done by the force on the particle as it moves from x = 5.00 m to x = 9.00 m. J (c) Find the work done by the force on the particle as it moves from x = 11.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x = 0 to X = 15.0 m?
- 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 nonconservativeA particle moves along a curved path y(x) = (10 m){1+cos[(0.1 m−1)x]} , from x = 0 to x = 10π m, subject to a tangential force of variable magnitude F(x) = (10 N)sin[(0.1 m−1)x]. How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)The force F(x,y) = [(2.56 N/m)y]i + [(3.14 N/m)x]j acts on a particle. What is the work done, in joules, by the force if the particle moves in a straight line from Cartesian coordinate (0.00 m, 0.00 m) to (4.39 m, 4.39 m)?
- The force required to compress a non-standard spring varies as the spring is compressed, as shown by the plot of force vs displacement. Distances are x1 = 10, x2 = 25 cm, x3 = 55 cm, and x4=75cm, and the forces are F1 = 110 N and F2 = -60N. Calculate the work done in Joules, on the spring as it is compressed from origin to point x4.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.