(a) Suppose that a glass tank has the shape of a cone with circular cross section as shown in Figure 3.2.10. As in part (a) of 33, assume that h(0) = 2 ft corresponds to water filled to the top of the tank, a hole in the bottom is circular with radius in., g = 32 ft/s2, and c = 0.6. Use the differential equation in to find the height h(t) of the water.(b) Can this water clock measure 12 time intervals of length equal to 1 hour? Explain using sound mathematics. (reference problem 33)Time Drips By The clepsydra, or water clock, was a device that the ancient Egyptians, Greeks, Romans, and Chinese used to measure the passage of time by observing the change in the height of water that was permitted to flow out of a small hole in the bottom of a container or tank.(a) Suppose a tank is made of glass and has the shape of a right-circular cylinder of radius 1 ft. Assume that h(0) = 2 ft corresponds to water filled to the top of the tank, a hole in the bottom is circular with radius in., g = 32 ft/s2, and c = 0.6. Use the differential equation in to find the height h(t) of the water.(b) For the tank in part (a), how far up from its bottom should a mark be made on its side, as shown in Figure 3.2.9, that corresponds to the passage of one hour? Next determine where to place the marks corresponding to the passage of 2 hr, 3 hr, . . . , 12 hr. Explain why these marks are not evenly spaced.
Chapter 8: Photosynthesis A Closer Look at the “Light Reactions” o ATP synthase works when hydrogen ions move through it from the thylakoid space (more hydrogen ions in thylakoid space) to the stroma (less hydrogen ions in stroma) down their concentration gradients using passive transport (facilitated diffusion) o Products are oxygen, NADPH, and ATP o In mitochondria, ATP synthase is found in the inner mitochondria membrane o In chloroplasts, ATP synthase is found in the thylakoid membrane o In bacteria, ATP synthase is on the plasma membrane Calvin Cycle Makes Sugars o Calvin Cycle is endergonic because it uses ATP o First phase is carbon fixation Carbon dioxide reacts with a 5C RuBP it is catalyzed by enzyme rubisco This 6 carbon compound is unstable and splits into 3phosphoglycerate (3C) (PGA or 3PG) Rubisco is associated with Calvin Cycle and only found in plants and it is found in the stroma In organic carbon in the form of carbon dioxide is fixed or incorporated into organic compound PGA Because PGA consists of 3 carbons Calvin Cycle is also known as C 3 Pathway or C 3Photosynthesis o Plants are divided into 3 types of plants C , C , and CAM plants all of them carry out C pathway in addition to 3 4 3 lightdependent reactions Majority are C3 plants Combine 6 molecules of carbon dioxide with 6 RuBP to produce 12 PGA Calvin Cycle must turn 6 times each time Use ATP and NADPH from the Light Reactions o Second Stage: Reduction o 12 ATP are used o 12 PGA are reduced to 12 G3P 10 G3P continue the Calvin cycle 2 G3P are released from the cycle and used to make glucose and other sugars + 12 NADPH are oxidized to 12 NADP The Last Phase of Calvin Cycle o Third Stage: Regeneration of RuBP o 10 G3P are used to regenerate 6 RuBP o 6 ATP are used o Overall Calvin cycle uses 18 ATP and 12 NADPH to eventually make 1 molecule of glucose endergonic Why Hot, Dry Weather is a Problem for Some Plants o By keeping their stomata closed it prevents water leaving and carbon dioxide to come in o Keep their stomata closed to prevent water loss they prevent oxygen from leaving and carbon dioxide from entering Oxygen increases and rubisco binds oxygen to RuBP Photorespiration o Photorespiration Requires sunlight Like aerobic respiration it uses oxygen to produce carbon dioxide and water Unlike aerobic respiration which produces ATP, photorespiration USES ATP (anabolic and endergonic) Wasteful process One Solution to Photorespiration…C Pla4ts o Ex. Corn and Sugar cane o C p4thway = when inorganic carbon in the form of carbon dioxide is fixed into 4 C compound called oxaloacetate o C pathway = bundle sheath cells of C plants have a low concentration of oxygen 3 4 and rubisco allowing rubisco to find oxygen to RuBP o C p4ants overcome photorespiration by separating C pathw4y from C pathway3 (Calvin Cycle) by using 2 different types of cells such as mesophyll and bundle sheath cells o C plants have rubisco in the mesophyll 3 o C p4thway, although it overcomes the problems of photorespiration, does have a cost o To produce a single glucose requires 12 additional ATP compared with the Calvin Cycle alone o C p4otosynthesis is advantageous in hot dry climates where photorespiration would remove more than half of the carbon fixed by the usual C path3ay alone o Overall C p4ants use 30 ATP (12 + 18) to make 1 molecule of glucose Another Solution to Photorespiration…CAM plants (Pineapples and Cacti) o CAM plants overcome photorespiration by performing C and C p3thways 4n the mesophyll cells at different times of the day C 3occurs during the day C 4occurs at night CAM plants probably use the same amount of ATP to make 1 glucose as C 4plants