Question
A crown weighed in an is found to have the same weight as a 5 1 kg mass while the same crown under water seems to weigh only as much as a 4 5 kg mass Assume that the crown is suspended by a string scale Draw a free body diagram showing all the forces on the crown when the crown is suspended under water Write Newton' s 2^nd Law for the forces in the vertical direction. Which of these forces does the scale read? What is the buoyant force acting on the crown in kilograms? What is the volume of water displaced? Calculate the density of the metal with which the crown is made.
Explanation / Answer
(b)
Fnet = 0
T + Fb - W = 0
T = W - Fb
(c)
Tension force
(d)
Fb = W - T
Fb = (5.1-4.5)*9.8
Fb = 5.88 N
(e)
Fb = rho*V*g
5.88 = 1000*V*9.8
volume V = 0.0006 m^3
f)
density D = m/v = 5.1/0.0006 = 8500 kg/m^3