The rate of diffusion of ions through the membrane of a nerve cell is proportional to the surface area of the membrane. Nerve cells are basically cylindrical in shape. If the rate of diffusion through the membrane of a cell with diameter dis R, the rate through the membrane of a cell of the same length but with diameter 2d will be

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

Ametal ring 4.20 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. these magnets produce an initial uniform field of 1.12 t between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.240 t/s . (a) what is the magnitude of the electric field induced in the ring? (b) in which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?

Astone is dropped from the upper observation deck of a tower, 250 m above the ground. (assume g = 9.8 m/s2.) (a) find the distance (in meters) of the stone above ground level at time t. h(t) = (b) how long does it take the stone to reach the ground? (round your answer to two decimal places.) s (c) with what velocity does it strike the ground? (round your answer to one decimal place.) m/s (d) if the stone is thrown downward with a speed of 2 m/s, how long does it take to reach the ground? (round your answer to two decimal places.) s