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 rho = 890 kg/m^3 , the scale reads 1.00 N . A sphere of density rhob = 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 for the acceleration due to gravity. 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. 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. 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

Explanation / Answer

The weight of the cylinder is rho*g*V
= 5000 kg/m^3 * 9.8 m/s^2 * 0.00006 m^3

= 0.3 kg * 9.8 m/s^2

= 2.94 N

Because the cylinder is being held up mostly by the rod,
the fluid pressure on the bottom of the cylinder is just the same as before.
The scale does not "know" the ball is there at all.
That's why it still reads 1N.

The buoyant force of the fluid on the cylinder is equal to the weight of
the displaced fluid, namely,
890 kg/m^3 * 9.8 m/s^2 * 0.00006 m^3 = 0.52 N
So the force needed for the rod to hold up the ball is

2.94 N - 0.52 N = 2.42 N

Now the scale "feels" the weight of the cylinder,
so the scale reads the weight of the cylinder
PLUS the weight of the original fluid
MINUS the weight of the fluid that was displaced
= 2.94 N + 1.00 N - 0.52 N = 3.42 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.