Q. A potential difference of 75 mV exists between the inner and outer surfaces of a cell's membrane. The inner surface is negative relative to the outer surface. How much work is required to eject a positive sodium ion (Na+) from the interior of the cell?

Q. 1) Suppose a pendulum bob is suspended from a pivot by massless string of length l, measured to the center of the bob.

a)show that if I draw the pendulum back by an angle θ, the center of the bob is elevated by the distance

Δh=l(1-cos(θ))=2l(sin(θ/2))^2

b) using the results of part a, show that the speed of the pendulum bob at the bottom of its travel should be

v=2√(gl)*sin(θ/2)

2) suppose the height of the ramp is h1=0.3 m, and the foot of the ramp is horizontal, and is h2=1.00 m above the floor. what will be the horizontal distancec traveled by the following four objects before they hit the floor? Assume that R=12.7 mm in each case; assume that the density of steel is 7.8 g/cm^3; and assume that the density of aluminum is 2.7 g/cm^3.

a) A solid steel sphere sliding down the ramp without friction.

b)a solid steel sphere rolling down the ramp without slipping.

c) A spherical steel shell with shell thickness 10 mm rolling down the ramp without slipping.

d) A solid aluminum sphere rolling down the ramp without slipping.