Modern Physics

5. What is the force (magnitude and direction on the 4 nC charge? -6 nC 4 nC 5 cm 5 cm 35° 35° 1 nC O2 nC 5 cm

distances. por = - magnificaron ma Solve for u 3 Used as a magnifying glass, the image of an object 4 cm from a converging lens is five times the object length. What is the focal length of the lens? Lens forme 4 A slide of dimensions 2. cm by 2 cm produces a clear image of area 6400 cm² on a

This is an extra credit assignment and completely optional. In order to receive full credit, you must show all work. Complete as many parts as you want and hand in work during class on Monday 10/17/22. You can earn a maximum of 20 points.

1) [Sedimentation Rate and Centrifuge] Proteins and other macromolecules can be separated by size using centrifugation. The idea is to spin a sample of proteins to produce a centripetal acceleration go that is much higher than gravitational acceleration g. We assume that a protein in the sample can be approximated as a ball of radius R. (a) Start from Newton 2nd law, prove that the terminal speed of the protein follows Vt 2(Pprotein - Psolvent)9cR² 9η where pprotein and psolvent are the densities of the protein and the solvent, n is the solvent viscosity. (b) We would like to separate two similar proteins, having the same density of 1.35g/cm³ but different diameters of 4nm and 5nm, respectively. The two protein species start out mixed together in a thin layer at the top of a 1cm long centrifuge tube. How large should the centripetal acceleration be so that the two proteins are separated before they drift to the end of the tube within about 20s? Assume the solvent as water where density is 1000kgm³ and viscosity is 10-³Nsm-². (Hint: Initially, the proteins are all on the same height, with both centers on the surface level, separation is achieved when their radii no longer overlaps)

2) [Electric Force] Three point charges are located at the corners of an equilateral triangle as in figure below. Find the magnitude and direction of the net electric force on the 2.00μC charge. 00

3) [Capacitance] A model of a red blood cell portrays the cell as a spherical capacitor, positively charged liquid sphere of surface area A separated from the surrounding negatively charged fluid by a membrane of thickness, t. Tiny electrodes introduced into the interior of the cell show a potential difference of 100mV across the membrane. The membrane's thickness is estimated to be 100 nm and has a dielectric constant of 5.00. (a) If an average red blood cell has a mass of 1.00x10-¹2kg, estimate the volume of the cell and thus find its surface area. The density of blood is 1,100kg/m³. (b) Estimate the capacitance of the cell by assuming the membrane surfaces act as parallel plates. (c) Calculate the charge on the surface of the membrane. How many electronic charges (number of electrons) does the surface charge represent? Take electronic charge to be 1.6 x 10-1°C.

3. A group of hikers hears an echo 4.50 s after shouting. How far away is the mountain that reflected the sound wave? (Assume the speed of sound is 347 m/s.)

2. On a hot summer day, the temperature of air in Arizona reaches 123°F. What is the speed of sound in air at this temperature? (The speed of sound at 0°C is 331 m/s. Use the conversion 0°C = 273 K as necessary.)

6. A light ray is incident on the surface of a block of diamond at an angle of 25.0° with respect to the normal (a line perpendicular to the surface at the spot where the ray hits the block). A fraction of the light is reflected and the rest refracted. What is the angle (in degrees) between the reflected and refracted rays?

4. Find the sound level in dB of 8.27 x 10^-2 W/m² ultrasound used in medical diagnostics.