"In Section 1.3, you will consider the gravitational potential, kinetic, and the total mechanical energy of a cart moving down an inclined ramp in a cart-Earth system. (Refer toFigure 6. 2). Define the gravitational potential energy to be zero when the cart is at the bottom of the ramp. Write an expression for the gravitational potential energy of the cart-Earth system in terms of the cart’s mass mm, the cart’s position along the inclined ramp xx, and the angle of the ramp T. "

If it takes a planet 2.8 x 10^8 s to orbit a star with a mass of 6.2 x 10^30 kg what is the average distance between the planet and the star

Gasoline comes from petroleum, which is made from ancient living things. petroleum, therefore, contains a type of energy. a. heat b. nuclear c. biological d. chemical potential

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants