A rectangular block of aluminum30 mm×60 mm×90 mm is placed in apressurechamber and subjected to a pressure of 100 MPa. If the modulus of elasticity is 75GPa andPoisson's ratio is 0.35, what will be the decrease in the longest side of the block, assuming thatthe material remains within the linear elastic region? What will be the decrease in the volume oftheblock? g
we know that change is length is calculated by following strain relation
where strain is given as
plugging strain value in change in length formula
calculate the length on the longer side
= 90 - 0.04008 = 89.95 mm
change in volume
Calculations involve determining strain from given pressure and Modulus of Elasticity and then determining the decrease in length of the longest side and total volume of the aluminum block when subjected to pressure.
The question is about applying principles of material science under conditions of pressure. The decrease in length and volume of a rectangular block of aluminum when subjected to pressure can be calculated by using the concepts of Modulus of Elasticity and Poisson's Ratio.
First, the strain experienced can be calculated using the formula:
Strain = Pressure / Modulus of Elasticity
Substituting the given values, the strain is found. The change in the longest side (90mm) is calculated by multiplying the original length by the strain. The volume change is calculated using the formula:
Change in volume = Original volume * (-3) * strain
Where original volume is = 30mm * 60mm * 90mm. Here the negative indicates a decrease. This will provide the decrease in the longest side and the total volume of the block when subjected to the given pressure.
Learn more about Material Deformation under Pressure here:
A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested to estimate the average force required to break the binding to within 0.08 lb with 99% confidence? Assume that σ is known to be 0.72. (Exact answer required.)
538 books should be tested.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
How many books should be tested to estimate the average force required to break the binding to within 0.08 lb with 99% confidence?
n books should be tested.
n is found when
We have that
538 books should be tested.
A sphere has a diameter of 4(x + 3) centimeters and a surface area of 7847 squarecentimeters. Find the value of x.
Toy company produces rubber balls that have a radius of 1.7 cm.A sphere has a radius of 1.7 centimeters. What is the volume of one rubber ball? Round to the nearest hundredth of a centimeter.
The volume of one rubber ball is 20.58 cubic centimeters.
The rubber ball has a spheric format.
A sphere with radius r has volume given by the following equation:
In this question:
r = 1.7 cm.
The radius is in centimeters, so the volume will be in cubic centimeters.
What is the volume of one rubber ball?
The volume of one rubber ball is 20.58 cubic centimeters.
1) 20.58 cm
The health of the bear population in yellowstone national park is monitored by periodic measurements. a sample of 54 bears has a mean weight of 182.9 lb. assuming the standard deviation is known to be 121.8lb find a 99% confidence intreval estimate
The 99% confidence interval will be found as follows: x_bar +/- z(σ/√n) where z- z-score σ-sigma n=sample size thus from the information given we shall have: 182.9+/-2.58(121.8/√54) =182.9+/-42.7632 =225.6632 or 140.1368
1. Dyani says she identified a quantitative variable and conducted a survey when she asked her fellow classmates in her homeroom about their favorite style of sweatshirt from the categories: hoodie, pullover, or zip-up. Explain her error. 2. Suppose Hana wants to find out the most commonly driven type of the vehicle among the students at her high schoo;. Since 1,560 students attend her high school, she asks every tenth student who enters the building one morning what kind of vehicle he or she drives. What is the population in this scenario?
The variable "favorite style of sweatshirt" is a qualitative variable instead of a quantitative one. This is because the categories "hoodie", "pullover" and "zip-up" are not quantitative in nature. They are simply labels or names. Yes we can assign a frequency tally for each one, which is likely what she's doing, but that's a slightly different story from what your teacher is asking.
An example of a quantitative variable is "height". This variable can take on any positive numeric value, within realistic reason of course. Theoretically there are infinitely many possible height values if we allow as much precision as we want. Even in a more finitely restricted space, we still have a lot of values to work with. We don't consider each number a different label or category or class. It's just a number. So that's what makes "height" a quantitative variable.
Keep in mind that just because you have a number, doesn't mean it's automatically quantitative. A phone number or a basketball player jersey number are two examples of numbers that are labels. We cannot add up a bunch of phone numbers to get something meaningful. Ask yourself "can I do math operations on these numbers?". If the answer is "yes", then you have quantitative data. Be careful to ask this question for any kind of data you have. Going back to Dyani's data, the category names cannot have math operations applied to them, so that's more evidence we're not dealing with quantitative data.
In short, Dyani has qualitative data instead of quantitative data. Specifically, she has nominal data because each label can be thought of as a name. There is no order to each choice, which means the data is not ordinal.
The answer to this question is found at the top, in the very first sentence. She wants to know what the most common car is. The population is the set of all student drivers at that school. Let's say there are 400 students who drive to school. That would mean the population would be those 400 people.
Because it's likely too time consuming to survey every member of the population, a sample is used instead to make the best estimate of what the population is. So this is what she's doing when she asks every 10th student to take part of the survey. This is known as systematic sampling because there's a pattern or rule to her choices. This form of sampling can be fairly unbiased assuming that she does this on various different days to get a good snapshot. If she only did it on one day, then it could be likely that some students skipped school or some were out sick. The more she samples, the better look she'll have at the population.
Dyani's mistake was identifying a categorical variable as quantitative. The population in Hana's scenario is 1,560 students.
1. Dyani's error: Dyani mistakenly identified the type of variable she collected as quantitative, when it is actually categorical. A quantitative variable represents numerical values that can be measured, while a categorical variable represents non-numerical values or categories. In this case, the variable is the style of sweatshirt, which falls under the categorical variable as it can be classified into distinct categories - hoodie, pullover, or zip-up.
2. Population in Hana's scenario: In Hana's scenario, the population refers to the total number of students at her high school. Since there are 1,560 students in total, that would be considered the population.
Learn more about Categorical and Quantitative Variables here:
A subject conference is scheduling 20-minute sessions and 25-minute sessions with 10 minutes between sessions. The sessions at the conference begin at 8 A.M. What is the next time at which all sessions will begin at the same time again?
30=2*3*5 and 35=5*7, then the least common multiple is 2*3*5*7=210 minutes. This means that 7 20-minutes sessions with 10-minutes breaks and 6 25-minutes sessions with 10-minutes breaks will end together after 210 passed minutes and at 11:30 A.M. all sessions will begin at the same time.