Suppose the potential energy of an object is given by:
U = ar^2 + br^4
where a = 5 J/m2 and b = 9.6 J/m4. What is the force on the object when it is at r = 2.9 m?
A block of mass 2 kg is kept at rest as it compresses a horizontal massless spring (k = 120 N/m) by 8.52 cm. As the block is released, it travels 0.611 m on a rough horizontal surface before stopping. The acceleration of gravity is 9.8 m/s2 . Calculate the coe?cient of kinetic friction between surface and block.
A box of mass 8 kg sits on a horizontal tabletop. An unstretched spring of force constant 420 N/m runs between the box and a wall. The coe?cient of friction between box and table is 0.5. Another box of mass 10 kg is hung from a string of negligible mass tied to the front of box 1, and allowed to fall from rest. By what amount has the spring has been stretched when the acceleration of the boxes has magnitude 1 m/s^2?