Find the potential energy U(x) of the particle. Also graph quantitatively F(x) and U(x) vs. x.

the mass of the object is m=0.2kg the spring is compressed at a distance of X=4cm when the mass is released it slides up to the height of 10cm. and then it turns around and slides back down. find the spring constant, K of the spring? WwwM A note: that the equation for spring potential energy is (1/2*k*x2). and gravitational potential energy is m*g*h. also, the conservation of mechanical energy is MEi=MEf.

A shopper in a supermarket pushes a cart with a force of 33.0 N directed at an angle of 25.0° below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed. Find the work done by the shopper on the cart as she moves down a 54.2-m-long aisle. The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the work done by frictional forces doesn't change, would the shopper's applied force be larger, smaller, or the same? What about the work done on the cart by the shopper? Is the work larger in part a, or is the work larger in part b; or is the work the same in both parts?

Find 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)

A block of mass 3 kg compresses spring 1 with a force constant, k1=7000 N/m, by 6 cm. It is released and slides for a total of 50 cm on a surface with μk=0.2, at which point it compresses another spring 2, k2=1000 N/m, and momentarily comes to rest. Remember that Us is the potential energy of the spring. Find the following values:What is the Initial spring potential energy of spring 1? How much energy is dissipated by heat? This is the amount of work done by friction × -1. How much Potential Energy does spring 2 have when the block has compressed spring 2 and is momentarily stopped? By how much does spring 2 compress?

A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)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.  b)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).  c)What is the child's final speed, vf in m/s?

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?

The graph shows the xx component of a force that acts on an object that moves on the x axis. The vertical spacing between adjacent grid lines is 4.93N, while the horizontal spacing between adjacent grid lines is 1.0m.  What is the work, in joules, done by the force as the object moves from x=4m to x=5m?

A force = (8x + 7y ) N acts on an object as if moves in the x direction from the origin to x = 7.00 m. Find the work done on the object by the force.

A certain spring found not to obey Hooke’s law exerts a restoring force Fx(x) = -ax - bx2 if it is stretched or compressed, where a = 60.0 N/m and b = 18.0 N/m2. The mass of the spring is negligible. (a) Calculate the potential-energy function U1x2 for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?