A professor has to haul a cart down a ramp. The ramp has an angle of about 10 degrees and is about 5 meters long. His initial speed at the top of the ramp is 5.4 m/s, and the cart has a mass of about 100 kg. How hard does he have to pull on the cart so that at the bottom of the ramp, its speed does not exceed 6.4 m/s

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