The potential energy function for a system is given by:

u(x) = 3x^3 - 2x^2 - 6x

where x is in meters and u is in joules.
a) determine the force fx as a function of x
b) for what values of x is the force equal to zero
c) plot u(x) versus x and fx versus x, and indicate thepoints of stable and unstable equilibrium.
d) if a particle moves from x= 2m to x = 4m, find thechange in its kinetic energy. assume that the only force acting onthe particles is the force found in part (a).

According to the law of conservation of mass, in a chemical reaction the total starting mass of all the reactants equal the total final mass of all the products. true or false?

What is the relationship between atmospheric pressure and the density of gas particles in an area of increasing pressure? (2 points) as air pressure in an area increases, the density of the gas particles in that area decreases. as air pressure in an area increases, the density of the gas particles in that area increases. as air pressure in an area increases, the density of the gas particles in that area remains constant. as air pressure in an area increases, the density of the gas particles in that area increases and decreases in an alternating pattern. 3. which of the following correctly describes a way in which earth's atmosphere interacts with the geosphere? (2 points) it contains gases that living organisms breathe. it contains gases that trap incoming solar radiation. it provides a medium for cycles that provide nutrients to living organisms. it provides a medium for water to move between earth's surface and the air. 4. which of the following is considered a drawback to using wind energy as a source of power? (2 points) wind energy is nonrenewable. wind energy produces large amounts of air pollution. wind turbines can kill birds that fly through the rotors. wind turbines are built too close to major population centers. 5. a meteorologist predicts that the weather in a region will soon change from clear skies to probable thunderstorms. prior to making this prediction, what did the meteorologist most likely observe on a barometer? (2 points) the barometer fell slightly. the barometer fell substantially. the barometer rose slightly. the barometer rose substantially. 6. which of the following do meteorologists not typically use weather balloons to record? (2 points) atmospheric pressure cloud types humidity temperature 7. during which step in the can crush lab did water vapor force air from the can? (2 points) the can was filled nearly to the top with water. the can was placed on the hot stove top burner for several minutes. the can was removed from the hot stove top burner. the can was placed upside-down in the water-filled pan.

What effects result when there is an impact between earth and an asteroid? check all that apply. a.massive flooding. b.extinction of many life forms.c.major earthquakes change in average global temperature.d. giant dust cloud