Suppose you have 4 stars with given initial conditions (positions and momenta). the net force on each star is the vector sum of 3 forces exerted by the other 3 stars, for a total of 12 forces that must be evaluated in each iterative step. in each step, how many forces would you have to calculate fully, and how many forces could you calculate simply by reversing vectors already calculated?

The bubbles in a carbonated soft drink are produced when carbonic acid decomposes to form carbon dioxide and water. in a closed system, this equilibrium exists as why does a carbonated soft drink lose carbonation when the container is left open? a. water evaporates, which favors the formation of h2co3. b. pressure decreases, which favors the formation of h2co3. c. the open container warms up, which causes more gas to escape. d. co2is removed, which favors the formation of h2co3.

Aswimmer is determined to cross a river that flows due south with a strong current. initially, the swimmer is on the west bank desiring to reach a camp directly across the river on the opposite bank. in which direction shoud the swimmer head? a. the swimmer should swim southeast. b. the swimmer should swim south. c. the swimmer shuold swim northeast. d. the swimmer should swim due north. e. the swimmer should swim due east.

How many milliliters of water at 23 °c with a density of 1.00 g/ml must be mixed with 180 ml (about 6 oz) of coffee at 95 °c so that the resulting combination will have a temperature of 60 °c? assume that coffee and water have the same density and the same specific heat. how much will the temperature of a cup (180 g) of coffee at 95 °c be reduced when a 45 g silver spoon (specific heat 0.24 j/g °c) at 25 °c is placed in the coffee and the two are allowed to reach the same temperature? assume that the coffee has the same density and specific heat as water. a 45-g aluminum spoon (specific heat 0.88 j/g °c) at 24 °c is placed in 180 ml (180 g) of coffee at 85 °c and the temperature of the two become equal. (a) what is the final temperature when the two become equal? assume that coffee has the same specific heat as water. (b) the first time a student solved this problem she got an answer of 88 °c. explain why this is clearly an incorrect answer.