Determine the scale reading W_2 when the sphere is held submerged this way. None

Question

Determine the scale reading W_2 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. Determine the force F_I 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. 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 rhow = 890 kg/m^3. the scale reads 1.00 N A sphere of density p_h = 5000 kg/m^3 and volume V = 60.0 cm^3 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/s^2 for the acceleration due to gravity.

Explanation / Answer

Here,

weight of liquid , Wl = 1 N

pb = 5000 Kg/m^3

V = 60 *10^-6 m^3

part A)

scale reading W2 = Wl + p * V * g

scale reading W2 = 1 + 890 * 30 *10^-6 * 9.8

scale reading W2 = 1.262 N

the scale reading W2 is 1.262 N

part C)

Using second law of motion ,

as the rod is not accelerating

net force on the sphere = 0

890 * 30 *10^-6 * 9.8 + Fr = 5000 * 30 *10^-6 * 9.8

Fr = 1.208 N

the force exerted by the rod on the sphere is 1.208 N

part C)

Now , for the scale

W3 = W2 + Fr

W3 = 1.208 + 1.262 N

W3 = 2.47 N

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