(b) Write Newton\'s second law for the system in one dimension, using B for buoy
ID: 1976847 • Letter: #
Question
(b) Write Newton's second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Use any variable or symbol stated above as necessary.)Fy =
(c) Calculate the numeric value for the buoyancy, B. (Seawater has density 1025 kg/m3.)
= N
(d) Using the value of B and the weight w of the survivor, calculate the weight wr of the Styrofoam.
= N
(e) What is the density of the Styrofoam?
= kg/m3
(f) What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface?
= N
(g) What total mass of survivors can the raft support?
= kg
Explanation / Answer
Mass of the survivor m = 62 kg Styrofoam volume V = 2.0 m * 2.0 m* 0.06 m = 0.24 m3 Volume of the submerged V' = 2.0 m * 2.0 m* 0.026 m = 0.104 m3 (b) By applying Newton's laws, the net force Fnet = Fb - w - wr = 0 Buoyant force Fb = w + wr (c) The buoyance force is equal to the weight of the volume submerged Fb = w + wr = V'g = (0.104 m3)(1025 kg/m3) (9.8 m/s2) = 1044.68 N (d) The weight of the Styrofoam is wr= Fb - w = 1044.68 N - (62 kg)(9.8 m/s2) = 437.08 N (e) Density of Styrofoam = m/V = (437.08 N)/(9.8 m/s2) /0.24 m3 = 185.8 kg/m3 (f) The maximum buoyant force F = Vg = (0.24 m3)(1025 kg/m3) (9.8 m/s2) = 2410.8 N (g) Again from Newton's laws Fb = w + wr w = Fb - wr = 2410.8 N-437.08 N = 1973.72 N Therefore the mass m = 201.4 kg w = Fb - wr = 2410.8 N-437.08 N = 1973.72 N Therefore the mass m = 201.4 kg = 2410.8 N-437.08 N = 1973.72 N Therefore the mass m = 201.4 kgRelated Questions
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