A rectangular solid made of aluminum has a density p= 2.70 g/cm³. The dimensions of the solid are shown below. The solid is placed on top of a truncated cone whose circular ends have the dimensions shown. The bottom of the rectangular solid presses down on the top surface of the cone. Find the pressure (in N/m²)between those two surfaces. (Ignore air pressure.) (1 kg = 1000 g, 1 m 100 cm)
A rectangular solid made of aluminum has a density p= 2.70 g/cm³. The dimensions of the solid are shown below. The solid is placed on top of a truncated cone whose circular ends have the dimensions shown. The bottom of the rectangular solid presses down on the top surface of the cone. Find the pressure (in N/m²)between those two surfaces. (Ignore air pressure.) (1 kg = 1000 g, 1 m 100 cm)
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
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![**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 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 in m³/s): \[ Q = vA \]
- Continuity Equation: \[ v_1 A_1 = v_2 A_2 \]
**Bernoulli’s Principle:**
\[
P_1 + \rho g h_1 + \frac{1}{2} \rho v_1^2 = P_2 + \rho g h_2 + \frac{1}{2} \rho v_2^2
\]
This educational content covers fundamental physics concepts such as Young’s modulus, density, pressure, buoyancy, fluid flow, and Bernoulli’s principle. These equations are essential for understanding material properties, fluid dynamics, and forces in physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff456c65b-f482-4083-8c37-6fe7d8344e1a%2Fceb0865b-2811-4136-98b9-da0ef3249af8%2Fohhkcvu_processed.png&w=3840&q=75)
Transcribed Image Text:**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 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 in m³/s): \[ Q = vA \]
- Continuity Equation: \[ v_1 A_1 = v_2 A_2 \]
**Bernoulli’s Principle:**
\[
P_1 + \rho g h_1 + \frac{1}{2} \rho v_1^2 = P_2 + \rho g h_2 + \frac{1}{2} \rho v_2^2
\]
This educational content covers fundamental physics concepts such as Young’s modulus, density, pressure, buoyancy, fluid flow, and Bernoulli’s principle. These equations are essential for understanding material properties, fluid dynamics, and forces in physics.
Transcribed Image Text:A rectangular solid made of aluminum has a density \( \rho = 2.70 \, \text{g/cm}^3 \). The dimensions of the solid are shown below. The solid is placed on top of a truncated cone whose circular ends have the dimensions shown. The bottom of the rectangular solid presses down on the top surface of the cone. Find the pressure (in N/m\(^2\)) between those two surfaces. (Ignore air pressure.) \( (1 \, \text{kg} = 1000 \, \text{g}, \, 1 \, \text{m} = 100 \, \text{cm}) \)
**Diagrams:**
1. **Rectangular Solid:**
- Dimensions: 15.0 cm (length) x 10.0 cm (width) x 8.0 cm (height)
2. **Truncated Cone:**
- Top radius (\( r \)): 2.00 cm
- Bottom radius (\( R \)): 6.00 cm
The rectangle is placed with its base of 15 cm x 10 cm on the top surface of the truncated cone, as illustrated by the diagram on the right side. Use these dimensions to determine the force exerted by the rectangular solid and the area it contacts with the truncated cone to calculate the pressure.
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