You release a block from the top of a long, slippery inclined plane of length l that makes an angle θ with the horizontal. the magnitude of the block's acceleration is gsin(θ).1- for an x axis pointing down the incline and having its origin at the release position, derive an expression for the potential energy of the block-earth system as a function of x. suppose that the gravitational potential energy is measured relative to the ground at the bottom of the incline, ug(x=l)=0.express your answer in terms of g and the variables m, l, x, and θ.(u^g=? )2-use the expression you derived in the previous part to determine the speed of the block at the bottom of the incline. (vx, f=? )express your answer in terms of g and the variables m, l, and θ.

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)

Blank liquids and gases exert a buoyant force on objects placed in them

Astudent wears sunglasses to her read a book more easily which wave interaction occurs as light passes from the air into the plastic lenses? a polarization b. refraction c. diffraction d. interference