Question

Three children weighing 400 N together make a raft with logs of 0.30 m in diameter and 1.60 m in length. How many logs are needed to keep them floating in fresh water? Suppose the specific mass of wood is 900 kg / m³ and the specific mass of freshwater is 1000 kg / m³. Consider the acceleration of gravity equal to 10 m / s².

Três crianças, pesam juntas 400 N, fazem uma jangada com toras de madeira de 0,30 m de diâmetro e 1,60 m de comprimento. Quantas toras são necessárias para mantê-las flutuando em água doce? Suponha que a massa especifica da madeira é 900 kg/m3 e a massa específica da água doce seja 1000 kg/m2. Considere a aceleração da gravidade igual a 10 m/s2 a. 8 b. 4 C. 7 d. 6 e. 5 OOO OO

Answer 1

We have given weight of three children together. = 400N Diameter of wooden log = 0.30m length of wooden raft = 1. Gom Specific mass of wood = gookg/m3 Specific mass of freshwater - 1000 kg/m3 object is equal we need to determine g=10m/s² the no. of logs are needed to keep the floating the fresh water. An object will float if its weight is equal to the buoyant force on the object. and from Archimedes Principle that bonyant force on an object is equal to weight of fluid displaced by the object Consider we have used N logs so I weight of 3 children & weight of N logs) = (Swater Varsplaced og V displaced water = Verg or weight of 3 children + weight of a logs] = (Swata Neog g [400+ N(Ming g)] = (Sivation Vitog) g meog = flog Veog 1400 + N( Slog Veog) g = (I water Ndog) g 400+ N(Slog Veog) g = Suatey NNog g 400 = Swater N Veog g - N Ilog Virag g NVlog (SW-Sugg

IN Veog ( Sirates - Ilag) g = 400) 0 Veog= r²h (assuming that the logs are cylindrical) - tuding) hing = 3:14 (0:30) 8x1.60 m3 2 m x 1.60 = 0.113 m3 N (013) (1000-900) 10 = 400) = 400 400 103 7 N= [0.113 (1000-900) 102 23.54 N=3.54 ñ Approximately 4 logs. they needed to keep them floated in Option (6) may be correct fresh water.
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