Turn Up The Heat
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The document summarizes the heat output of a hair straightener over time. It is described by three functions between 0-3.2 minutes, 3.2-8 minutes, and 8-12 minutes. The total heat output over the full 12 minutes is found to be 3224.98 hundred degree units by calculating the integrals of each function. The interval with the greatest increase in heat is found to be from 0-3.2 minutes, with a maximum increase of 218.0 degrees F per minute at 0 minutes. The heat decrease at 9.2 minutes is calculated to be 145.24 degrees F per minute by substituting into the third function.
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4) Without the heat sink, the maximum power would be much lower at only 2.60W due to the higher thermal resistance of natural convection alone. The heat sink significantly increases the chip's cooling ability.
Solutions fox
This document contains 20 problems related to fluid mechanics and thermodynamics. Problem 1.20 provides data on measuring the height of a building using horizontal distance and angle measurements, and asks the reader to calculate height, uncertainty, and optimal measurement angle to minimize uncertainty. An Excel file shows calculations and plots uncertainty versus angle. The optimal angle is 31.4 degrees, which minimizes the height uncertainty of 0.95%.
Developing Expert Voices
The student reflects on completing a math project for their calculus course as a way to study for an upcoming exam. They acknowledge that they procrastinated significantly but were able to cover a broad range of calculus concepts through multi-step word problems selected from different units. While the assignment did not dramatically increase their knowledge, it helped reinforce some details and connections between topics. The student resolves to select deadlines more wisely and stop procrastinating for future projects.
trapezoidal rule.pptx
This document discusses various numerical integration techniques including the Trapezoidal rule, Simpson's 1/3 rule, and Simpson's 3/8 rule. These rules allow approximating the definite integral of a function from a set of tabulated values of the integrand. Examples are provided to demonstrate applying each rule to calculate the area under curves and integrals of specific functions over given intervals in 1-3 sentences.
Solution manual 1 3
The document provides solutions to example problems in a chapter on metal forming mechanics and metallurgy. It determines principal stresses for a given stress state. It then solves additional examples involving determining stresses in rods, tubes, and sheets under various loading conditions. The solutions make use of stress-strain relationships and failure criteria like Tresca and von Mises to determine stresses and strains.
numerical.ppt
This document summarizes the finite difference method for numerically solving heat transfer problems. The method involves establishing a nodal network to discretize the domain, deriving finite difference approximations of the governing heat equation at each node, developing a system of simultaneous algebraic equations relating all nodal temperatures, and solving the system of equations using numerical techniques like matrix inversion or iterative methods. Examples are provided to illustrate the finite difference approximations, formation of the algebraic system, and solution via the Jacobi and Gauss-Seidel iteration methods.
Btech admission in india
This document discusses partial differential equations and heat transfer problems. It provides an example of modeling heat flow through a straight bar using principles of physics. This leads to the derivation of the one-dimensional heat equation. Boundary and initial conditions are also discussed. Solutions are found using the method of separation of variables. The document also briefly discusses the wave equation and Fourier series, providing examples of their applications to problems of heat transfer and vibrating strings.
Dynamic response of oscillators to general excitations
This document discusses the response of vibrating systems to arbitrary excitations. It begins by introducing the impulse response function, which describes the response of a system to a brief impulse force. The response to any force input can then be obtained by expressing the force as a sum of impulses and convolving it with the impulse response function. As examples, it shows how to calculate the response to step inputs and multiple impulse inputs using this convolution approach. It also discusses how to handle non-zero initial conditions and multiple inputs by superimposing the individual responses.
Btech admission in india
This document discusses partial differential equations and the heat equation. It begins by defining partial differential equations and providing an example of the heat equation modeling heat transfer through a solid body. It then derives the one-dimensional heat equation to model heat flow through a uniform bar. The method of separation of variables is introduced to solve the heat equation under various boundary and initial conditions. Finally, examples are provided to demonstrate solving heat transfer problems using Fourier series expansions.
Numerical Methods in Mechanical Engineering - Final Project
Final Project for the class of "Numerical Methods in Mechanical Engineering" - MECH 309.
In this project, various engineering problems were analyzed and solved using advanced numerical approximation methods and MATLAB software.
1. (5 pts) Which of these graphs represent a one-to-one function .docx
1. (5 pts) Which of these graphs represent a one-to-one function?
Answer(s): ____________
(
no explanation required
.)
(There may be more than one graph that qualifies.)
(A)
(B)
(C)
(D)
2. (5 pts) Convert to a logarithmic equation: 7
x
= 2401.
(no explanation required)
2. ______
A.
B.
C.
D.
3. (10 pts) Based on data about the growth of a variety of ornamental cherry trees, the following logarithmic model about these trees was determined:
h
(
t
) = 6.47 ln(
t
) + 2.83,
where
t
= age of tree in years and
h
(
t
) = height of tree, in feet.
(Note that "ln" refers to the natural log function) (explanation optional)
Using the model,
(a) At age 3 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot?
(b) At age 12 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot?
4.
(5 pts)
Solve the equation.
Check
all proposed solutions.
Show work in solving and in checking, and state your final conclusion.
5. (10 pts)
(a)
_______ (fill in the blank)
(b) Let
State the exponential form of the equation.
(c) Determine the numerical value of
, in simplest form. Work optional.
6. (10 pts) Let
f
(
x
) = 2
x
2
–
x
– 10 and
g
(
x
) = 3
x
+ 1
(a) Find the composite function
and simplify the results. Show work.
(b) Find
. Show work.
7. (15 pts) Let
(a) Find
f
-
1
, the inverse function of
f
.
Show work
.
(b) What is the domain of
f
? What is the domain of the inverse function?
(c) What is
f
(2) ?
f
(2) = ______
work/explanation optional
(d) What is
f
-
1
( ____ ), where the number in the blank is your answer from part (c)?
work/explanation optional
8. (15 pts) Let
f
(
x
) =
e
x
– 1
+ 4.
Answers can be stated without additional work/explanation.
(a) Which describes how the graph of
f
can be obtained from the graph of
y
=
e
x
? Choice: ________
A. Shift the graph of
y
=
e
x
to the left by 1 unit and up by 4 units.
B. Shift the graph of
y
=
e
x
to the right by 1 unit and up by 4 units.
C. Reflect the graph of
y
=
e
x
across the
x
-axis and shift up by 4 units.
D. Reflect the graph of
y
=
e
x
across the
y
-axis and shift up by 4 units.
(b) What is the domain of
f
?
(c) What is the range of
f
?
(d) What is the horizontal asymptote?
(e) What is the
y
-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth).
(f) Which is the graph of
f
?
GRAPH A GRAPH B GRAPH C GRAPH D
NONLINEAR MODELS - For the latte.
Trigonometry docs
This document provides an overview of trigonometry, covering right triangle trigonometry and oscillating functions. It discusses key concepts like the Pythagorean theorem, SOH CAH TOA, trig identities, and converting between degrees and radians. Right triangle trigonometry focuses on ratios of sides, while oscillating functions deal with concepts like sine, cosine, and their roles in vibrations, circuits, and calculus.
CH EN 3453 Heat Transfer 2014 Fall Utah Homework HW 10 Solutions
Chemical Engineering CH EN 3453 Heat Transfer
from University of Utah, 2014 Fall
Homework HW 10 Solutions
Sect5 4
This document discusses various types of mechanical vibrations including undamped, underdamped, critically damped, and overdamped motion. It provides examples of solving differential equations describing simple harmonic motion under different damping conditions and applying the solutions to problems involving springs, pendulums, and other oscillating systems. Specific cases are worked through to determine characteristics like frequency, period, and damping behavior.
Problem and solution a ph o 6
The document describes a theoretical problem involving a child on a swing. It provides equations related to angular momentum and mechanical energy of rotation to analyze the motion. The key points are:
- As the child squats and stands, its distance from the swing pivot changes, altering the angular velocity.
- Each cycle increases the angular velocity by a factor determined by the ratio of distances when squatting vs. standing.
- Conservation laws are applied to calculate how many cycles are needed to double the maximum angular velocity/amplitude.
- The solution finds it takes 5 cycles to increase the angular velocity/amplitude by a factor of two, based on the given distance ratio of 1.072 when squatting vs. standing
Admission in india 2014
The document discusses heat transfer through multiple dimensions and steady-state conduction. It covers analytical solutions using separation of variables for simple geometries with various boundary conditions. Numerical techniques using finite difference methods are also introduced. The temperature field is discretized on a grid and the heat diffusion equation is expressed as algebraic equations at the grid points using Taylor series approximations. Thermal balance is enforced at interior points by equating heat conduction to neighboring points.
Similar to Turn Up The Heat (20)
Dynamic response of oscillators to general excitations
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Numerical Methods in Mechanical Engineering - Final Project
Numerical Methods in Mechanical Engineering - Final Project
1. (5 pts) Which of these graphs represent a one-to-one function .docx
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CH EN 3453 Heat Transfer 2014 Fall Utah Homework HW 10 Solutions
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Turn Up The Heat
- 1. TURN UP THE HEAT Andrea Spencer AP Calculus 2007