We can use an atomic force microscope (afm) to measure forces exerted on a molecule attached to a surface (and hence to measure the spring-like force of the molecule pulling back on the afm tip) as a function of molecular length. however, when we measure forces at the microscopic scale, one problem is that you have to attach the molecules of interest using stretchy bonds of some sort. let? s model that and solve for a result.

instead of an afm tip pulling on the springy-molecule, let? s use a mass applying a weight to a spring. let? s replace the bond attaching the molecule to the surface with a different spring in between the first spring and the ceiling. let? s compute what happens and see what lessons emerge.

a) we have two springs suspended as shown at the right. the top spring (spring constant 3k) is attached to the ceiling and the bottom spring (spring constant k) is attached to a mass, m. assume the entire system is at rest. draw the free body diagram for each spring and the mass.

image for we can use an atomic force microscope (afm) to measure forces exerted on a molecule attached to a surface (and
b) find the extension of each spring in terms of m, k and g.

c) comment on why this result is relevant to our experimental problem, and, based on your result from part b), what properties you? d like the bond attaching the molecule to the afm tip and surface to have.

Imagine you had to physically add electrons, one at a time, to a previously neutral conductor. you add one electron very easily, but the second electron requires more work. in your initial post to the discussion, explain why this is. also, what happens to the work needed to add the third, fourth, fifth, and subsequent electrons

19. explain why a magnet from your refrigerator could not be used to lift something as heavy as a car. (chapter 7 – pages 202-203) 20. can a magnet ever have a single pole? explain your answer. (chapter 7 – page 208) 21. what happens to the wavelength of a wave if the frequency is increased? (chapter 9 – pages 280-281) 22. an ocean wave has a wavelength of 10 m and a frequency of 4.0 hz. what is the velocity of the wave? show the appropriate equation from your book and show your work with units. (chapter 9 – page 282) 23. as you sit outside, the sound of a siren becomes lower in pitch. is the emergency vehicle moving away from or towards you? explain how you know. (chapter 10 – page 315-316) 24. why are two astronauts in space unable to hear one another? (chapter 10 – page 307) 25. explain in at least 3 sentences how electromagnetic waves form. (chapter 11 – page 338-339) 26. using the chart on page 345 in your textbook, what are the three types of electromagnetic wave with wavelengths shorter than those of visible light. give an example of each. (chapter 11 – pages 345-351) 27. explain why a leaf usually appears to be green, but a rose typically appears red. (chapter 12 – page 373) 28. what is the difference in light that is refracted compared to light that is reflected? think in terms of speed of light as well as what happens to light waves when they interact with a medium. (chapter 12 – pages 369-370) 29. how are concave and convex lenses different? (chapter 13 – page 408-410) 30. what type of mirror is used in rearview mirrors in cars? why is it important that these mirrors have the warning, “objects in mirror are closer than they appear.”? (chapter 13 – page 405)

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.