1. A flat-bottomed wooden box is 2.5 m long and 1.5 m wide, with sides 1 m high.
ID: 2282008 • Letter: 1
Question
1. A flat-bottomed wooden box is 2.5 m long and 1.5 m wide, with sides 1 m high. The box serves as a boat carrying five people as it floats on a pond. The total mass of the boat and the people is 1400 kg.
a. What is the total weight of the boat and the people in newtons?
b. What is the buoyant force required to keep the boat and its load afloat?
c. What volume of water must be displaced to support the boat and its load? (The density of water is 1000 kg/m3.)
d. How much of the boat is underwater? (What height of the sides must be submerged to produce a volume equal to that of part c?)
Explanation / Answer
a)total weight = (mass of boat + mass of person) g
=(1400)*9.8
=13720N
b) byont force required = weight of boat and people = 13720N
C) weight of water displaced = weight of boat people system
volume of water * density of water*g = 13720
v * 1000 kg/m3 * 9.8= 13720
=> V = 1.4m3 or 1400 Liters
d) let h be the height merge in water
volume = l*b* h = 2.5*1.5*h =1.4
=> h = 0.3733m
this means boat will be merged completely
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