A solid cone made of unknown material is suspended from a scale. Before submersion, the scale reads 100 Newtons. After submersion in water the scale reads 88.0 N as shown below. (a) What is the force of buoyancy on the cone? (b) What weight of water is displaced by the cone? (c) What mass of water is displaced by the cone (in kg)?

A solid cone made of unknown material is suspended from a scale. Before submersion, the scale reads 100 Newtons. After submersion in water the scale reads 88.0 N as shown below. (a) What is the force of buoyancy on the cone? (b) What weight of water is displaced by the cone? (c) What mass of water is displaced by the cone (in kg)?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

Question

**Young’s Modulus**

\[
\frac{F}{A} = Y \frac{\Delta L}{L_0}
\]

**Density:**

\[
\rho = \frac{M}{V} \quad (\text{kg/m}^3)
\]

**Pressure:**

\[
P = \frac{F}{A} \quad (\text{Pa}) \quad P = P_0 + \rho gh
\]

**Buoyancy Force:**

\[
B = \text{weight in air} - \text{weight in fluid}
\]

**Area of a Circle:**

\[
A = \pi r^2
\]

**Weight:**

\[
\text{weight} = mg, \quad \text{where } g = 9.80 \, \text{m/s}^2
\]

**Pressure (repeated):**

\[
P = \frac{F}{A} \quad (\text{Pa})
\]

**In Liquid:**

\[
P = P_0 + \rho gh
\]

**Buoyancy Force on a Submerged Object:**

\[
B = \rho_{\text{fluid}} V_{\text{object}} g
\]

**Fluid Flow:**

Flow rate \( Q (\text{m}^3/\text{s}) = vA \)

\[
v_1 A_1 = v_2 A_2
\]

**Bernoulli’s Principle:**

\[
P_1 + \rho gh_1 + \frac{1}{2} \rho v_1^2 = P_2 + \rho gh_2 + \frac{1}{2} \rho v_2^2
\]

A solid cone made of unknown material is suspended from a scale. Before submersion, the scale reads 100 Newtons. After submersion in water, the scale reads 88.0 N as shown below.

(a) What is the force of buoyancy on the cone?
(b) What weight of water is displaced by the cone?
(c) What mass of water is displaced by the cone (in kg)?
(d) What volume of water is displaced by the cone (in cubic meters)?
(e) What is the volume of the cone (in m³)?
(f) What is the mass density of the cone (in kg/m³)?
(Density of water, ρ = 1000 kg/m³)

**Diagrams:**

1. **Diagram on the left:**
- Shows a solid cone suspended and weighed in the air with a scale reading of 100 N.

2. **Diagram on the right:**
- Shows the same solid cone submerged in water, resulting in a reduced scale reading of 88.0 N.

**Explanation:**

The scale reading decreases due to the buoyant force exerted by the water, which is equal to the weight of the water displaced by the submerged cone. The problem involves determining various physical properties of the cone and the water it displaces, using the given data and principles of buoyancy and fluid mechanics.

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