The gravitational force on a point mass m due to a point mass m at the origin is a gradient field with potential u(r)= (gmm)/r , where g is the gravitational constant and r = (x^2 + y^2 + x^2)^(1/2) is the distance between the masses a. find the components of the gravitational force in the x-, y-, and z-directions, where f(x, y,z) = -gradientu(x, y,z) b. show that the gravitational force points in the radial direction (outward from point mass m) and the radial component is f(r) = (gmm)/(r^2) c. show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of u

What are the theoretical properties of a gas at a temperature of 0 kelvin?

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.

A3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. it takes 6060 nn to loosen the bolt when the force is applied perpendicular to the wrench. how much force would it take if the force was applied at a 3030 degree angle from perpendicular? a 3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. it takes 6060 nn to loosen the bolt when the force is applied perpendicular to the wrench. how much force would it take if the force was applied at a 3030 degree angle from perpendicular?