Sir Dudley the Dextrous is loading cannons on top of the castle's tallest towers in preparation for an expected attack. He slips, and a cannonball of mass 6.00 kg rolls to the edge of the tower, which has a perfectly horizontal surface, and falls to the ground below. It takes the cannonball 1.65 s to fall to the ground, and air resistance is negligible. How much work is done by gravity on the falling cannonball?

Aforce of 200 n is applied to an input piston of cross-sectional area 2 sq. cm pushing it downward 2.8 cm. how far does the output piston of cross-sectional area 12 sq. cm move upward? show all work.

Acharge of 8.4x10^-4 c moves at an angle of 35 degrees to a magnetic field that has a field strength of 6.7x10^-3 t. if the magnetic force is 3.5 x10 ^-2 n, how fast is the charge moving?

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