A single conservative force F = (7.0x - 11)§ N, where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 27 J at x = 0. (a) What is the maximum positive potential energy? At what (b) negative value and (c) positive value of x is the potential energy equal to zero?

A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop).  What is the child's final speed, vf in m/s?

A spring with a spring constant of 18.0 N/cm has a cage attached to its free end. (a) How much work does the spring force do on the cage when the spring is stretched from its relaxed length by 7.60 mm? (b) How much additional work is done by the spring force when the spring is stretched by an additional 7.60 mm?

A horizontal force of magnitude 44.1 N pushes a block of mass 4.47 kg across a floor where the coefficient of kinetic friction is 0.576. (a) How much work is done by that applied force on the block-floor system when the block slides through a displacement of 3.31 m across the floor? (b) During that displacement, the thermal energy of the block increases by 38.0 J. What is the increase in thermal energy of the floor? (c) What is the increase in the kinetic energy of the block? (a) Number i Units (b) Number Units (c) Number i Units

A box of unknown mass is sliding with an initial speed vi = 4.40 m/s across a horizontal frictionless warehouse floor when it encounters a rough section of flooring d = 3.30 m long. The coefficient of kinetic friction between the rough section of flooring and the box is 0.100. Using energy considerations, determine the final speed of the box (in m/s) after sliding across the rough section of flooring.

The force required to compress a non-standard spring as a function of displacement is given by the equationF(x) = -Asin(bx) + kx,where A = 11 N, b = 11 rad/m, and k = 78 N/m. Part (b)  Calculate the work done in joules as the spring is compressed from x = 0 to x1 = 32 cm.  Part (c)  Calculate the work done in joules as the spring is compressed from x1 = 32 cm to x2 = 69 cm

An object with a 2.00 kg mass moving along the positive x axis in the +x direction has a speed of v = 2.50 m/s at the position x = 0.500 m and a potential energy of U(x) = (−4.00 J · m)/x. Determine the following. (a) an expression for the x component of the force acting on the object at any position along the x axis (Use the following as necessary: x. Do not enter units in your expression.) Fx =    (b) work done on the object by this force acting on the object from x = 1.00 m to x = 1.94 m J(c) change in potential energy of the object as it travels from  x = 1.00 m to x = 1.94 m  J(d) total energy of the object at any point along the x axis J(e) maximum distance the object can travel from the origin in the +x direction m

A 13 N force with a fixed orientation does work on a particle as the particle moves through displacement à = (3î − 5ĵ + 3k) What is the angle between the force and the displacement if the change in the particle's kinetic energy is (a) +17.0 J and (b)-17.0 J? (a) Number i (b) Number i eTextbook and Media Units Units m.

A 0.500-kg particle has a speed of 2.10 m/s at point and kinetic energy of 7.90 J at point B. (a) What is its kinetic energy at ? J (b) What is its speed at Ⓡ? m/s (c) What is the net work done on the particle by external forces as it moves from A to Ⓡ?