a force of 5 N extends a spring of natural length 0.5m by 0.01, what will be the length of the spring when the applied force is 20 N

The 20@kg wheel has a radius of gyration about its center g of kg = 300 mm. when it is subjected to a couple moment of m = 50 n # m, it rolls without slipping. determine the angular velocity of the wheel after its mass center g has traveled through a distance of sg = 20 m, starting from rest.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

A2000 kg car is rounding a curve of radius 200 m on a level road. the maximum frictional force the road can exert on the tires of the car is 4000 n. what is the highest speed at which the car can round the curve?