A single conservative force acts on a 5.0-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 = 1.00 m to x = 5.00 m, calculate (a) the work done by this force on the particle, (b) the change in the potential energy of the system, and (c) the kinetic energy the particle has at x = 5.00 m if its speed is 3.00 m/s at x = 1.00 m.

A particle is subject to a force F, that varies with position as shown in the following figure. F, (N) 3 1 x (m) 2 4 6 8 10 12 14 16' (a) Find the work done by the force on the particle as it moves from x = 0 to x = 2.00 m. (b) Find the work done by the force on the particle as it moves from x = 5.00 m to x = 7.00 m. (c) Find the work done by the force on the particle as it moves 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?

A block of mass m = 2.50 kg is pushed d = 2.60 m along a frictionless horizontal table by a constant applied force of magnitude F = 11.0 N directed at an angle ? = 25.0° below the horizontal as shown in the figure below. (a) Determine the work done by the applied force.J=?(b) Determine the work done by the normal force exerted by the table.J=?(c) Determine the work done by the force of gravity.J=?(d) Determine the work done by the net force on the block.J=?

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? nonconservative

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) =

A force between F (vector) = (4î-5ĵ) N acts on a particle that undergoes a displacement  Δr (vector) = (2î+ĵ) m. Find the work done by the force on the particle. What is the angle between F (vector) and Δr (vector)?

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.

The figure gives the acceleration of a 5.0 kg particle as an applied force moves it from rest along an x axis from x-0 tox-9.0 m. The scale of the figure's vertical axis is set by a,- 6.0 m/s². How much work has the force done on the particle when the particle reaches (a) x-4.0 m, (b)x - 7.0 m, and (c) x-9.0 m? What is the particle's speed and direction (give positive answer if the particle moves along x axis in positive direction and negative otherwise) of travel when it reaches (d) x - 4.0 m, (e) x - 7.0 m, and (f)x - 9.0 m? (a) Number i (b) Number i (c) Number i (d) Number i (e) Number i (f) Number i (₂8/) v Units Units Units Units Units Units 2 x (m) < <