The gravitational force and potential energy at the surface of a planet with radius $r$ are $f_1$ and $u_1$, respectively. what are the gravitational force and gravitational potential energy, $f_2$ and $u_2$, respectively, at the surface of a planet with radius $2r$ that has the same mass density?

Apatient has a history of poor nutrition. he has skin rashes, bleeding gums, and a cut that hasn’t healed in a long time. what vitamin deficiency most likely caused this symptom?

Abag of potato chips contains 2.00 l of air when it is sealed at sea level at a pressure of 1.00 atm and a temperature of 20.0 deg c. what will be the volume of the air in the bag if you take it with you, still sealed, to the mountains where the temperature is 7.00 deg c and atmospheric pressure is 70.0 kpa? assume that the bag behaves like a balloon and that the air in the bag is in thermal equilibrium with the outside air.

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.