A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assume that the total energy of the ball-Earth system remains constant.
(a) What is the tension in the string at the bottom? (Use the following as necessary: m for the mass of the ball, g for gravitational acceleration, vb for the velocity at the bottom, and R for the radius of the circle.)
(b) What is the tension in the string at the top? (Use the following as necessary: m, g, vt for the velocity at the top, and R.)
(c) How much greater is the tension at the bottom? (Use the following as necessary: m, g.)

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Amira pulls a 3 pound wagon 4 feet. how much work has she done?

Arailroad car collides with and sticks to an identical railroad car that is initially at rest. after the collision, the total kinetic energy of the two cars is a) the same as before. b) half as much as before. c) one third as much as before. d) one fourth as much as before. e) twice as much as before.