he crimping tool is used to crimp the end of the wire E. If a force of 25.6 lb is applied to the handles, determine the average shear stress (in ksi) in the pin at B. The pin is subjected to single shear and has a diameter of 0.28 in. Only vertical force is exerted on the wire. Note: You answer should include requested units and be to 3 decimal places.
Answers
Answer:
Shear Stress = 0.415 ksi
Explanation:
In order to find the shear stress we first need to find the cross sectional area of pin B. The area is given as follows:
A = πd²/4
where,
A = Area of cross section of pin = ?
d = diameter of pin = 0.28 in
Therefore,
A = π(0.28 in)²/4
A = 0.0615 in²
Now, the shear stress is given as:
Shear Stress = Shear Force/Area
Shear Stress = 25.6 lb/0.0615 in²
Shear Stress = 415.8 psi
Shear Stress = 0.415 ksi
Related Questions
(35-39) A student travels on a school bus in the middle of winter from home to school. The school bus temperature is 68.0° F. The student's skin temperature is 94.4° F. Determine the net energy transfer from the student's body during the 20.00 min ride to school due to electromagnetic radiation. Note: Skin emissivity is 0.90, and the surface area of the student is 1.50m2.
Answers
Answer:
The net energy transfer from the student's body during the 20-min ride to school is 139.164 BTU.
Explanation:
From Heat Transfer we determine that heat transfer rate due to electromagnetic radiation (\(\dot Q\)), measured in BTU per hour, is represented by this formula:
\(\dot Q = \epsilon\cdot A\cdot \sigma \cdot (T_{s}^{4}-T_{b}^{4})\) (1)
Where:
\(\epsilon\) - Emissivity, dimensionless.
\(A\) - Surface area of the student, measured in square feet.
\(\sigma\) - Stefan-Boltzmann constant, measured in BTU per hour-square feet-quartic Rankine.
\(T_{s}\) - Temperature of the student, measured in Rankine.
\(T_{b}\) - Temperature of the bus, measured in Rankine.
If we know that \(\epsilon = 0.90\), \(A = 16.188\,ft^{2}\), \(\sigma = 1.714\times 10^{-9}\,\frac{BTU}{h\cdot ft^{2}\cdot R^{4}}\), \(T_{s} = 554.07\,R\) and \(T_{b} = 527.67\,R\), then the heat transfer rate due to electromagnetic radiation is:
\(\dot Q = (0.90)\cdot (16.188\,ft^{2})\cdot \left(1.714\times 10^{-9}\,\frac{BTU}{h\cdot ft^{2}\cdot R^{4}} \right)\cdot [(554.07\,R)^{4}-(527.67\,R)^{4}]\)
\(\dot Q = 417.492\,\frac{BTU}{h}\)
Under the consideration of steady heat transfer we find that the net energy transfer from the student's body during the 20 min-ride to school is:
\(Q = \dot Q \cdot \Delta t\) (2)
Where \(\Delta t\) is the heat transfer time, measured in hours.
If we know that \(\dot Q = 417.492\,\frac{BTU}{h}\) and \(\Delta t = \frac{1}{3}\,h\), then the net energy transfer is:
\(Q = \left(417.492\,\frac{BTU}{h} \right)\cdot \left(\frac{1}{3}\,h \right)\)
\(Q = 139.164\,BTU\)
The net energy transfer from the student's body during the 20-min ride to school is 139.164 BTU.
Discuss the ethics of the circumstances that resulted in the Columbia shuttle disaster. Considering the predictions that were made years before the disaster, as well as the reliability of the Binomial distribution and its implications, what could or should the engineers associated with the program have done differently
Answers
Explanation:
This is not so much a mathematical issue as a case study, because the response will inevitably require us to test the special Columbic shuttle disaster scenario. I would suggest that you read this in detail and present the points accordingly. Here I give as many points as I think are relevant.
The failure of a space program is definitely a complex situation, more than a simple binomial distribution. It's definitely not as simple as repeating the flip of a coin. There are several coherent factors and situations that govern the overall coordination and execution of such an event. The problem is, those who are running a project like this are still making a trade off,It is never the case that they sealed the lid on any chance of failure between multiple parameters. You try to do something, but often, as is the case above, the potentially dangerous situation is impossible or uncontrollable. Since the root cause of failure, which is dried out tiles that can not withstand heat and water, it appears that owing to the constant use of the shuttle the head architects have not foreseen this.
a review on design of experiments and surrogate models in aircraft real-time and many-query aerodynamic analyses
Answers
Design of experiments (DoE) is a statistical approach that enables researchers to understand the impact of multiple variables on the output of a complex system by creating a model of the system and testing it with various combinations of input variables.
The benefits of DoE in the field of aerodynamics include reduced computational expense, improved analysis efficiency, and the capacity to examine the interrelationship between variables. DoE provides valuable knowledge into the design space of a problem, which is essential in the development of accurate surrogate models.In recent times, real-time simulation has evolved as a technique that is increasingly becoming applicable in the industry due to the optimization of computational performance.
It's critical to develop accurate surrogate models that can rapidly make inferences and decisions while guaranteeing precision. The primary aim of surrogate models in aerodynamic real-time analysis is to provide quick insights into the system response when input variables are changed.Surrogate models are created based on machine learning techniques or the analysis of the system using a reduced order model (ROM). Machine learning techniques allow surrogate models to learn from data obtained from simulations of the aerodynamic system.
In contrast, ROMs reduce the dimensions of the problem by extracting essential information using several methods such as the proper orthogonal decomposition (POD) or balanced truncation.Surrogate models are now widely used in aerodynamic analysis, providing the much-needed speed for conducting many-query analyses. They also enable researchers to run large-scale optimization studies, which is an essential requirement in the aerospace industry.
Despite the benefits of surrogate models in aerodynamic analysis, their accuracy needs to be improved to ensure they provide high-quality data that can be relied upon in the optimization process. Overall, DoE and surrogate models offer great potentials in many-query aerodynamic analyses, and researchers can make use of these techniques to increase the efficiency of their studies.
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Write a function named sum_nested_nums that takes a list as input having elements that are lists of numbers and returns the sum of all numbers in these sublists. For example, >>> sum_nested_nums([[0,5, 2], [-3, 4]]) Since 0 + 5 + 2 +-3 + 4 = 8. Note: Must use Nested for loops.
Answers
Here is the function definition:
```
def sum_nested_nums(lst):
total = 0
for sublist in lst:
for num in sublist:
total += num
return total
```
This function is named `sum_nested_nums` and it takes a list `lst` as input. The list has elements that are themselves lists of numbers. We need to loop through all these sublists and sum the numbers in them. We do this using nested for loops: the outer loop iterates over the sublists in `lst`, and the inner loop iterates over the numbers in each sublist.
Inside the inner loop, we add each `num` to the `total` variable. Finally, we return the total sum of all numbers in the sublists.
So, when we call `sum_nested_nums([[0,5, 2], [-3, 4]])`, the function returns the sum of all numbers in these sublists, which is 8.
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A student lives in an apartment with a floor area of 60 m2 and ceiling height of 1.8 m. The apartment has a fresh (outdoor) air exchange rate of 0.5/hr. The stove in the apartment heats by natural gas. The student cooks a meal using two gas burners that each emit carbon monoxide (CO) at a rate of 100 mg/hr. The outdoor CO concentration can be assumed to be negligible (0 ppm). The initial (time = 0) indoor CO concentration can be assumed to be 0 ppm (except for problem 4). Carbon monoxide can be considered as an inert gas, i.e., it does not stick to or react with any surfaces or other gases in air.
1. Assume that the student cooks for a long enough period of time to achieve a steady-state CO concentration in the apartment. What is that concentration in ppb?
2. Assume that the student cooks for only 45 minutes and turns off both burners at that time. What is the CO concentration in ppb at the end of 45 minutes?
3. Repeat problem 2 for air exchange rates that vary from 0.1 to 1/hr and plot the concentration at 45 minutes (in ppb) versus air exchange rate.
4. Assume that for the conditions of problem 2, the student waits 25 minutes after turning the burners off and then starts cooking again with two burners on. How long will it take to reach a concentration that is 95% of steady-state under this condition?
Note that you can actually address this question with an eloquent mathematical derivation (preferred) or simply by crunching the concentration profile in a spreadsheet.
What is the concentration at 95% of steady-state?
Compare your result with the time that would be required to reach 95% of steady-state had the initial indoor CO concentration been 0 ppm.
Answers
Answer:
4
Explanation:
A diagram and graphs describe an experiment to determine torque variation
Answers
The power of the braking system is fundamentally measured in brake torque. The effective radius, or how far away from the hub center the brake caliper acts on the disc, is that distance.
What is Brake torque?Utilizing the maximum power and efficiency of an internal combustion engine means using the best ignition timing to produce the most brake torque. For any engine running circumstances, there is always the ideal spark timing. Wide-open throttle is the best situation for MBT, however idle engine operation is not ideal. The power of the braking system can be summed up as brake torque. At a specific distance from the hub center, referred to as the effective radius, the brake caliper applies pressure to the disc. Braking torque is equal to the caliper's force times the system's effective radius. The force used to slow down the rotors is referred to as brake torque.To learn more about Brake torque refer to:
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Brake torque is the primary measurement of the braking system's power. This distance is the effective radius, or the distance the brake caliper acts on the disc from the hub center.
What does torque refer to?To get the most out of an internal combustion engine's power and efficiency, the best ignition timing is needed to generate the most brake torque.
The ideal spark timing is always available for any engine operation. MBT works best with the throttle open, but idle engine operation is not ideal.
The term "brake torque" can be used to summarize the braking system's power. The effective radius is the distance from the hub center at which the brake caliper applies pressure to the disc.
The caliper's force divided by the system's effective radius is the braking torque. Brake torque is the force applied to the rotors to slow them down.
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in software engineering how do you apply design for change?
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Answer:
it is reducely very iloretable chance for a software engineer to give an end to this question
Calculate the total charge stored in the channel of an NMOS device if Cox = 10 fF/μm2, W = 5 μm, L = 0. 1 μm, and VGS – VTH = 1 V. Assume VDS = 0
Answers
The total charge stored in the channel of the NMOS device is 5 femtocoulombs.
How to solveTo calculate the total charge stored in the channel of an NMOS device, we use the formula Q = Cox * W * L * (VGS - VTH),
where Q is the charge, Cox is the oxide capacitance, W is the width, L is the length, VGS is the gate-source voltage, and VTH is the threshold voltage.
Given the values: Cox = 10 fF/μm², W = 5 μm, L = 0.1 μm, and VGS - VTH = 1 V, we can calculate the charge as follows:
Q = (10 fF/μm²) * (5 μm) * (0.1 μm) * (1 V) = 5 fC
So, the total charge stored in the channel of the NMOS device is 5 femtocoulombs.
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A 36-mph wind blows against an outdoor movie screen that is 70 ft wide and 20 ft tall. Estimate the wind force on the screen. Use drag coefficient Cd = 1.15.
Answers
Answer:
The wind force on the screen is approximately 5,341.5936 \(lb_f\)
Explanation:
The speed of the wind, v = 36 mph
The width of the outdoor movie, w = 70 ft. wide
The height of the outdoor movie, h = 20 ft. tall
The drag coefficient, Cd = 1.15
We have;
\(C_d = \dfrac{F}{\dfrac{\rho \cdot v^2 \cdot A}{2} }\)
From which we have;
The wind force, F = 0.00256·\(C_d\)·v²·A
Where;
A = The cross sectional area of the rectangular outdoor movie screen, A = w × h
∴ A = 70 ft. × 20 ft. = 1,400 ft.²
The wind force, F = 0.00256 × 1.15 × (36 mph)² × 1,400 ft.² = 5,341.5936 \(lb_f\)
The wind force on the screen, F = 5,341.5936 \(lb_f\).
The wind force on the outdoor movie screen is;
F = 23437.26 N
We are given;
Wind speed; v = 36 mph = 16.0934 m/s
Width of screen; w = 70 ft = 21.336 m
Height of screen; h = 20 ft = 6.096 m
Drag coefficient; Cd = 1.15
Now formula for the drag force is;
F = ½•C_d•ρ•A•v²
Where;
F is drag force
C_d is drag coefficient
ρ is density of object
v is speed of object
A is area
Let us use density as 1.21 kg/m³
Area; A = wh = (21.336 × 6.096)
Thus;
F = ½ × 1.15 × 1.21 × (21.336 × 6.096) × 16.0934²
F = 23437.26 N
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copy the drawing and mark on it the location at highest bending stress. make a three-dimensional mohr-circle representation of the stresses at this poin
Answers
The highest bending stress occurs on the uppermost surface, as shown in the figure. The neutral axis is located halfway between the top and bottom surfaces. In the case of flexure, bending stress increases linearly from the neutral axis to the top and bottom surfaces.
As a result, the highest bending stress will always be found on the surface furthest from the neutral axis, which in this case is the top surface. Three-dimensional Mohr Circle representation of the stresses at this point is given below: To determine the principal stresses, we must first construct a stress tensor. The stress tensor is a 3x3 matrix that contains the normal and shear stresses acting on a point in three dimensions.
We'll assume that our stress state is two-dimensional and that there is no shear stress acting on the z-axis. We can compute the principal stresses using the eigenvalues of the stress tensor. The eigenvalues of the stress tensor are the principal stresses. To put it another way, they are the values of σx and σy that are in line with the maximum shear stress. The equation for the maximum shear stress is as follows: τmax = σmax - σmin / 2 The Mohr Circle for this two-dimensional stress state is given below.
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The unit weight of soil is 17.3 KN/m3. The moisture content of this soil is 17% when the degree of saturation is 60%.
Answers
Answer:
degree of saturation at optimummoisture content is 78.1 %.
Explanation:
The maximum dry unit weight of the soilYa is 16.8kN/mThe optimum moisture content of the soilwis 17 %.The specific gravity of soil G is 2.73.Calculation:Determine the degree of saturation (S)using the relation.Yd = Gs Yw/ 1+Gsw/sHere, Yw is the unit weight of water.Substitute 16.8 kN/m' for a, 2.73 for G,9.81 kN/m' for u, and 17 % for w.16.8= 2.73x9.811/2.73x1 .4641 26.78S-1.594S =-0.4641-0.594S= -0.4641S= 0.4641S = 0.781x 100S = 78.1 %16.80.594Therefore, the degree of saturation atoptimum moisture content is 78.1 %.
5. According to the FMCSRs, you are qualified to operate a CMV if you:
A. are at least 15-years old.
B. have passed an IQ test.
C. have only one current CDL.
D. are currently disqualified from operating a motor vehicle.
Answers
Answer:
currently states that a person is qualified to drive a commercial motor vehicle if he/she “can read and speak the English language sufficiently to converse with the general public, to understand highway traffic signs and signals
So I think B
What is 90 to the power of 46
Answers
Answer:Just multiply 90 by itself 46 times
Explanation:
do it
Which step in the reverse-engineering process involves the identification of subsystems and their relationship to one another?
Answers
The answer is analyze
Things to be done before isolation
Answers
Answer every question of this quiz
Please note: you can answer each question only once.
Which number shows the intake valve?
OK
Answers
I'd say number 4, number 3 looks like an exhaust valve
If a rubber band is stretched adiabatically, its temperature increases. (a) If the rubber band is stretched isothermally, does its entropy in- (b) If the rubber band is stretched adiabatically, does the internal crease, decrease, or stay the same? Energy increase, decrease, or stay the same?
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Naturally found uranium consists of 99.274%, 238U, 0.720%235U, and 0.006% 233U (by mass). As we have seen, 235U is the isotope that can undergo a nuclear chain reaction. Most of the 235U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF6(g).
A.) What is the mass of UF6 in a 30.0-L vessel of UF6 at a pressure of 690 torr at 360 K?
B.) What is the mass of 235U in the sample described in part A? The atomic mass of uranium-235 is 235.044 u.
C.) Now suppose that the UF6 is diffused through a porous barrier and that the change in the ratio of 238U and 235U in the diffused gas can be described by the equation r1r2=urms1urms2=3RT/M13RT/M2ââââââââ=M2M1ââââ. What is the mass of 235U in a sample of the diffused gas analogous to that in part A?
D.) After one more cycle of gaseous diffusion, what is the percentageof 235UF6 in the sample? (In your calculations unrounded values from previous parts should be used.)
Answers
A. The mass of UF6 in a 30.0-L vessel of UF6 at a pressure of 690 torr at 360 K is 2298.4 g
B. The mass of 235U in the sample described in part A is 16.44 g
C. The mass of 235U in a sample of the diffused gas analogous to that in part A is 16.47 g.
D. The percentage of 235UF6 in the sample is 0.7179%
How do we arrive at the values given above?The values of the equations or problems given above are determined as follows:
A) To find the mass of UF6 in the 30.0 L vessel at a pressure of 690 torr and a temperature of 360 K, we need to use the ideal gas law:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
We can rearrange the equation to solve for n:
n = PV/RT
Plugging in the values, we get:
n = (690 torr)(30.0 L)/(8.31 J/mol*K)(360 K)
= 6.52 moles of UF6
To find the mass of UF6, we can multiply the number of moles by the molar mass of UF6, which is 352.0 g/mol:
mass = n * molar mass
= 6.52 moles * 352.0 g/mol
= 2298.4 g
B) To find the mass of 235U in the sample, we first need to calculate the mass of UF6 in the sample that is made up of 235U. We know that naturally occurring uranium consists of 99.274% 238U, 0.720% 235U, and 0.006% 233U by mass. Since the mass of the UF6 in the sample is 2298.4 g, the mass of 235U in the sample is (0.720%)(2298.4 g) = 16.44 g.
C) To find the mass of 235U in the diffused gas, we can use the equation provided:
r1r2 = urms1urms2 = (3RT/M1)(3RT/M2) = M2/M1
Where r1 and r2 are the ratios of 238U and 235U in the initial and final samples, respectively, and M1 and M2 are the molar masses of 238U and 235U, respectively.
We can rearrange the equation to solve for r2:
r2 = r1 * M2/M1
Plugging in the values, we get:
r2 = (16.44 g/2298.4 g) * (235.044 g/mol) / (238.05 g/mol)
= 0.7202
This means that the diffused gas has a ratio of 0.7202 235U to 238U. Since the mass of the UF6 in the sample is 2298.4 g, the mass of 235U in the diffused gas is (0.7202)(2298.4 g) = 16.47 g.
D) After one more cycle of gaseous diffusion, the ratio of 235U to 238U in the sample will be the same as it was in the diffused gas after the first cycle, 0.7202. The mass of 235U in the sample will also be the same, 16.47 g. To find the percentage of 235UF6 in the sample, we can divide the mass of 235U by the total mass of the UF6 and multiply by 100:
percentage = (16.47 g / 2298.4 g) * 100%
= 0.7179%
Therefore, the correct answers are as given above
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why we use the lagrange Equation?
Answers
Answer:
It is used for solving optimization problems in which,given some functional,one seeks the function minimizing or minimizing it.
Explanation:
Please i need a Brainliest.
Constant practice would be most effective in learning a skill under which conditions?
Answers
Constant practice would be most effective in learning a skill under these conditions:
When the conditions under which the skill is executed do not changeWhen students are just starting to learn the skill.What is a skill acquisition plan?A skill acquisition plan can be defined as a written plan that is used to outline the goals, objectives, materials, teaching methods, and data collection techniques for teaching trainees or employees, a specific skill or set of skills.
This ultimately implies that, skill acquisition plans include all of the following:
GoalsObjectivesMaterialsData collectionIn conclusion, we can infer and logically deduce that constant practice would be most effective in learning a skill under these conditions:
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Fast fourier transforms (FFT) are algorithms that speed up the computation of fourier coefficients compared to the traditional direct form discuss how the speed up is achieved
Answers
Answer:
Fast Fourier ( FFT ) algorithms speed up computation of Fourier coefficients by simply reducing the the computing time of a traditional direct form Fourier series. it achieves this by breaking complex DFTS into smaller DFTS to reduce its complexity and in turn reduce its computing time
Explanation:
Fast Fourier ( FFT ) algorithms speed up computation of Fourier coefficients by simply reducing the the computing time of a traditional direct form Fourier series. it achieves this by breaking complex DFTS into smaller DFTS to reduce its complexity and in turn reduce its computing time. an example of such FFT is Cooley-Tukey algorithm
which option identifies the AFNR pathway in the following scenarios? Jalal works for a prestigious golf course that hosts an annual PGA Tour event. His employers depend on him to use cutting-edge science and technology to prepare the course and maintain it with the utmost care.
A. Agricultural System
B. Plant System
C. Biotechnology System
D. Natural Resource System
Answers
Answer: C. Biotechnology system
Explanation:
what is settling velocity? what factors influence settling velocity? does settling velocity affect the dissolved load?
Answers
A particle's settling velocity is the rate at which it travels through a still fluid. The specific gravity of the particles, their size, and their shape all have an impact on settling velocity.
A particle in still air will gravitationally settle and reach its terminal velocity fairly quickly. A particle's terminal velocity in a still fluid is referred to as the settling velocity (also known as the "sedimentation velocity"). Understanding variations in the hydraulic regime and interactions between sediment and fluid in the surf zone depends heavily on the particle settling velocity at the foreshore region. In contrast to sedimentation, which is the end product of the settling process, settling is the movement of suspended particles through the liquid. Sedimentation in geology is the process by which sediments are deposited and sedimentary rock is created. The process of sedimentation involves allowing particles suspended in water to separate under the influence of gravity.
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It describes the physical and social elements common to this work. Note that common contexts are listed toward the top, and less common contexts are listed toward the bottom. According to O*NET, what are common work contexts for Reporters and Correspondents? Check all that apply.
Answers
Answer:
Acef
Explanation:
Edginuity 2021
Answer:
2,3,4,5
Explanation:
guy above me is wrong
12-kW 240 V range contributes __ watts to the load when calculating the service by the standard method
Answers
12-kW 240 V range contributes 12000 watts to the load when calculating the service by the standard method
How to complete the statementThe standard method for calculating the service size of an electrical system involves adding up the wattage of all the electrical appliances and devices that are expected to be in use at the same time.
Assuming that the 12-kW 240 V range is the only electrical appliance in use, then it contributes 12,000 watts to the load.
However, if there are other appliances and devices in use at the same time, then their wattage should also be taken into account when calculating the overall load.
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Anyone got a pc that can run 240 fps? Around like 1,300 dollars that can run 240 fps on fortnite whoever answers and gives me a good pc I will give brainliest
Answers
Answer:
What do u need it for just gaming or for streaming and other things
2-design a set of simple test programs to determine the type compatibility rules of a c compiler to which you have access. Write a report of your findings
Answers
When designing a set of simple test programs to determine the type compatibility rules of a C compiler to which you have access, it is important to consider the different data types that are used in C programming. An example of a set of test programs that can be used to determine the type compatibility rules of a C compiler:
Integer Test the compatibility of the C compiler with integer data types. It declares two variables of type int, initializes them with values, and then adds them together. The result is printed to the screen. If the program compiles and runs without any errors, then the C compiler is compatible with integer data types.
Floating-Point Test the compatibility of the C compiler with floating-point data types. It declares two variables of type float, initializes them with values, and then adds them together. The result is printed to the screen. If the program compiles and runs without any errors, then the C compiler is compatible with floating-point data types.
By running the set of simple test programs described above, you can determine the type compatibility rules of a C compiler to which you have access. If any of the programs do not compile or run without errors, then you can determine which data types are not compatible with the C compiler and adjust your code accordingly.
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Match the term to the correct definition. bus full mesh ring star
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Bus: linear arrangement Round in the form of a ring Systems are arranged in the form of a star using wire in this topology. Mesh: A non-synchronized arrangement of systems.
What is star bus topology?This topology is referred to as a star bus topology since it incorporates different star topologies into a single bus. A bus or star topology is comparable to the widely used tree topology in networks.
What distinguishes mesh topology from star star?The most popular topology in home and office networks is the star topology because it is so simple to deploy, operate, and troubleshoot. A redundant network of connections between nodes forms a mesh topology.
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Ball A of mass mA and ball B of mass mB are connected with a string of length l. Initially, the string is loose and the distance between the two balls is b. At time t0, ball B is given a velocity of v0 perpendicular to the line connecting A and B. At time t1, the distance between A and B becomes l and the string becomes taut. We want to find the velocities of each ball right after the string becomes taut.
(a) Choose an inertial frame and a set of coordinates to describe the motion of the balls. Write the position, velocity, and acceleration (kinematics) of both
the balls.
(b) Is the linear momentum of the two-ball system conserved? Why?
(c) Is the angular momentum of ball B conserved right before and right
after the string becomes taut around any point or points? Explain (one to two sentences).
(d) What are the linear momenta of A, B and the two-ball system right
before and right after the string becomes taut?
(e) Find the position and velocity of the center of mass of the system right
before and right after the string becomes taut?
(f) What is the linear impulse applied by the string on A as the string becomes taut?
Answers
In this case, if there are no external forces (such as friction or external impulses), the linear momentum of the system will be conserved.
(a) Inertial Frame and Coordinates:
Let's choose an inertial frame of reference where ball A is at the origin (0,0) and ball B initially has a position of (b,0).
We can choose the x-axis along the line connecting A and B, and the y-axis perpendicular to it. The positive x-direction is from A to B, and the positive y-direction is upward.
The position, velocity, and acceleration of each ball can be described as follows:
Ball A:
Position: rA(t) = (0, 0) [remains fixed at the origin]
Velocity: vA(t) = (0, 0) [no initial velocity or acceleration]
Acceleration: aA(t) = (0, 0) [no initial velocity or acceleration]
Ball B:
Position: rB(t) = (b, 0) [initial position at (b, 0)]
Velocity: vB(t) = (v0, 0) [given initial velocity in the positive x-direction]
Acceleration: aB(t) = (0, 0) [no initial acceleration]
(b) Conservation of Linear Momentum:
The linear momentum of the two-ball system is conserved if there are no external forces acting on the system.
(c) Conservation of Angular Momentum:
Right before and right after the string becomes taut, the angular momentum of ball B is conserved around any point because no external torques act on the system. The string only provides tension forces along the line connecting A and B, causing no torque.
(d) Linear Momenta:
Right before the string becomes taut:
Linear momentum of ball A: pA = mAvA = (0, 0) [zero initial velocity]
Linear momentum of ball B: pB = mBvB = (mBv0, 0) [initial velocity in the positive x-direction]
Linear momentum of the two-ball system: pSystem = pA + pB = (mBv0, 0)
Right after the string becomes taut:
Linear momentum of ball A: p'A = mAvA = (0, 0) [zero velocity]
Linear momentum of ball B: p'B = mBv'B [velocity to be determined]
Linear momentum of the two-ball system: p'System = p'A + p'B = (0, 0) + (mBv'B, 0) = (mBv'B, 0)
(e) Center of Mass:
Right before the string becomes taut:
Position of the center of mass: rCM = (mArA + mBrB) / (mA + mB) = (mBb, 0) / (mA + mB)
Right after the string becomes taut:
Position of the center of mass: r'CM = (mAr'A + mBr'B) / (mA + mB) = (0, 0) [both balls are at the origin]
Velocity of the center of mass remains zero throughout since the balls have zero net momentum.
(f) Linear Impulse:
The linear impulse applied by the string on ball A as the string becomes taut is equal to the change in momentum of ball A.
Thus, since ball A has zero initial velocity and final velocity, the linear impulse is zero.
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Question 1 [10 Marks] In materials science, reinforcement is a constituent of a composite material which increases the composite's stiffness and tensile strength. How will you design a reinforcement material that is made of ceramic matrix. Also give the reasons why you chose that specific material.
Answers
Note as far as material science is concerned, that to create a ceramic matrix reinforcement material, I would use a ceramic material with high strength and stiffness such as silicon carbide.
Why is this so?This is because it has a high melting point.
I would next use chemical vapor deposition or melt spinning to convert the ceramic material into a fibrous shape, resulting in a fibrous ceramic matrix composite.
Because of the intrinsic qualities of the ceramic matrix, the resultant composite would have high stiffness and tensile strength, making it perfect for applications requiring great strength and endurance, such as aerospace or automotive components.
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