A cylindrically shaped container, open at the top, rests on a scale. Its height

Question

A cylindrically shaped container, open at the top, rests on a scale. Its height is 0.100 m and its weight can be neglected. When it is filled to the top with a fluid whose density is = 890 kg/m3 , the scale reads 1.00 N .(Figure 1)

A sphere of density b = 5000 kg/m3 and volume V = 60.0 cm3 is then submerged in the fluid, so that some fluid spills over the container's side. The sphere is held in place by a stiff rod whose volume and weight can be neglected. In this problem, use g = 9.81 m/s2  for the acceleration due to gravity.

A) Determine the scale reading W2 when the sphere is held submerged this way. None of the fluid that spills over stays on the scale.

Calculate your answer from the quantities given in the problem and express it numerically in newtons.

B) Determine the force Fr exterted by the rod on the sphere. Take upward forces to be positive (e.g., if the force on the sphere is downward, your answer should be negative).

Express your answer numerically in newtons.

C)The rod is now affixed to the bottom of the container. Again the container is filled with the fluid, the sphere is submerged and attached to the rod, and none of the fluid that spills over remains on the scale.

Determine the weight W3 now shown on the scale.

Express your answer numerically in newtons.

Explanation / Answer

Mw = 1/9.8 = 0.102 kg
Vw = Mw/890 = 1.146*10^-4 m^3
A) scale reading = weight of water left + weight of sphere + buyoant force
Buoyant force = Vs*(rho-fluid)g = 0.523 N
Weight of sphere = 2.94 N
Weight of left fluid = 0.47 N
Scale = 3.933 N
B) Fr = Buoyant force = -0.523N
C) New scale reading = 2.94 + 0.47 = 3.41N

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