A 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.)

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?

Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin. Write an expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x2.    If the object starts at a position of x1 = 8.5 m apart, how much work, in joules, is required by an external force to bring it to a position of x2 = 2.5 m apart when a = 19 and b = 11?    If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?

On a horizontal surface, an object slides from point P to point Q along a straight line, then slides back from Q to P along a semicircle. If P and Q are a distance L apart, how much work did the force of kinetic friction do during the entire process? The magnitude of fk is fk.