Suppose we have a single particle moving in one dimension whose potential energy as a function of x x is u ( x ) u(x). show (using the chain rule and the relationship f ( x ) = − u ′ ( x ) f(x)=−u′(x)) equation (4) (4), conservation of energy, for this system.

Heena wants to measure the volume of a ball that is 24 cm across. how should she set up her equation?

A2-kg bowling ball is 2.5 meters off the ground on a post when it falls. just before it reaches the ground, it is traveling 7 m/s. assuming that there is no air resistance, which statement is true?

The astronauts on the space shuttle flights experienced an acceleration of 29 m/s2 (about 3 "g's") during lift-off. what upward force must the astronaut's seat apply to the astronaut in order to cause this acceleration? assume the astronaut's mass is 70 kg, and compute this force when the acceleration is near the earth's surface so their weight equals latex: mg m g .