Two objects slide without friction on a circular ring of radius r oriented in a vertical plane. the heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. the fixed end of the spring is attached to a point a horizontal distance 2r from the center of the circle. the lighter object (of mass m) is initially at rest at the bottom of the ring. the heavier object is released from rest at the top of the ring, then collides with and sticks to the lighter object. find the value for m that will allow the combined object (of mass 4m) to just reach the point a on the ring, but go no higher. express your answer in terms of some or all of the quantities k, r and the acceleration of gravity g.

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.

The frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.

How many neutrons does element x if it’s atomic number is 28 and its mass number is 87