Pretty much any real object takes up space. This can cause confusion when asking, for instance,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Pretty much any real object takes up space. This can cause confusion when asking, for instance, what is the r position of a car? Do we mean the front end of the car? The back end? Somewhere in between? To remove this confusion, if we don't explicitly describe the part of the object we care about, the assumption is that the location of any real object refers to the location of the object's *center of mass* You probably have an intuitive idea of where the center of mass for an extended object is, especially if that object is uniform. The idea of center of mass also applies to a collection of discrete objects. The position (vector) of the center of mass for a system of discrete objects can be found using the following formula: miri + mr2+... my + m + ... (1) where m, is the mass of object j and r; is the position (of the center of mass) of object j. This is essentially a weighted average of the position of each individual object: The position of a more massive object contributes more than the position of a less massive object to the overall position of the center of mass. Discuss this formula with your group to ensure it makes conceptual sense. It can be written more compactly as: mtot ;;. j (2) For what follows, assume that object I's position function is ri(t) = At + Bj, and that object 2's position function is 2(t) - Ce-Dti, where A, B, C, and D are all positive constants and can appear in your answers. You can also use that the mass of object 1 is my and the mass of object 2 is m. a) Draw a set of z-y axes and sketch the vectors 1 and 2 for t=0. Draw a second set of axes and sketch and 2 for some t > 0. Label any relevant points on the axes with knowns. b) Determine the position of the center of mass as a function of time Fem(t) for a system comprised of objects 1 and 2. Simplify your expression so that it is clear what the r- and y-components of your position vector are and label them rem, and rem,y c) You recently learned that the rate of change of the position vector is called the velocity vector. That is, 7 r. Use this idea to determine the velocity of the center of mass as a function of time em(t) for a system comprised of objects 1 and 2. d) If instead of the positions you were given just (t), 2(1), m, and m2, come up with expression could you use to calculate cm (t) that contains only those four quantities. Generalize this expression for a system comprised of N objects each with a different velocity. Hint: It should look very similar to the expression for the position of the center of mass. Pretty much any real object takes up space. This can cause confusion when asking, for instance, what is the r position of a car? Do we mean the front end of the car? The back end? Somewhere in between? To remove this confusion, if we don't explicitly describe the part of the object we care about, the assumption is that the location of any real object refers to the location of the object's *center of mass* You probably have an intuitive idea of where the center of mass for an extended object is, especially if that object is uniform. The idea of center of mass also applies to a collection of discrete objects. The position (vector) of the center of mass for a system of discrete objects can be found using the following formula: miri + mr2+... my + m + ... (1) where m, is the mass of object j and r; is the position (of the center of mass) of object j. This is essentially a weighted average of the position of each individual object: The position of a more massive object contributes more than the position of a less massive object to the overall position of the center of mass. Discuss this formula with your group to ensure it makes conceptual sense. It can be written more compactly as: mtot ;;. j (2) For what follows, assume that object I's position function is ri(t) = At + Bj, and that object 2's position function is 2(t) - Ce-Dti, where A, B, C, and D are all positive constants and can appear in your answers. You can also use that the mass of object 1 is my and the mass of object 2 is m. a) Draw a set of z-y axes and sketch the vectors 1 and 2 for t=0. Draw a second set of axes and sketch and 2 for some t > 0. Label any relevant points on the axes with knowns. b) Determine the position of the center of mass as a function of time Fem(t) for a system comprised of objects 1 and 2. Simplify your expression so that it is clear what the r- and y-components of your position vector are and label them rem, and rem,y c) You recently learned that the rate of change of the position vector is called the velocity vector. That is, 7 r. Use this idea to determine the velocity of the center of mass as a function of time em(t) for a system comprised of objects 1 and 2. d) If instead of the positions you were given just (t), 2(1), m, and m2, come up with expression could you use to calculate cm (t) that contains only those four quantities. Generalize this expression for a system comprised of N objects each with a different velocity. Hint: It should look very similar to the expression for the position of the center of mass.
Expert Answer:
Answer rating: 100% (QA)
The skin friction coefficient Cf for a laminar boundary ... View the full answer
Related Book For
Posted Date:
Students also viewed these physics questions
-
When using the right hand rule for negative charges, is it only the force that goes in the opposite direction? For example If I'm asked to find direction of B field given velocity and force do I flip...
-
Current Attempt in Progress Given the following list of items, Annual Ordering Holding Item Demand Cost ($) Cost (%) Unit Price ($) 101 750 10 102 1,910 10 30 20 20 0.50 0.20 103 5,230 25 30 1.00 4...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
The SEC Form 10-K of Google is reproduced online at www.wiley.com/college/pratt. REQUIRED: Review the Google 2012 SEC Form 10-K, and answer the following questions: a. Compute Googles long-term debt...
-
How is family ownership affecting ECCO? Comment on the corporate ownership structure and its implications for strategy-making and implementation. What alternatives exist?
-
a) In how many ways can one select two positive integers m,n, not necessarily distinct, so that 1 < m < 100, 1 < n < 100 and the last digit of 7m + 3n is 8? b) Answer part (a) for the case where l <...
-
Job-order costing is usually identified with manufacturing companies. However, service industries and not-for-profit organizations also use the method. Suppose a social service agency has a cost...
-
Scotts Miracle-Gro is the worlds leading supplier and marketer of do it yourself lawn and garden products; it is located in Marysville, Ohio. Although Scotts dominates many of its chosen markets, its...
-
A lease agreement that qualifies as a finance lease calls for annual lease payments of $50,000 over a four-year lease term (also the asset's useful life), with the first payment at January 1, the...
-
Perfect Parties, Inc. has several divisions, one of which provides birthday parties at their facility, and has provided the actual and planning budget results for the month of June. The Controller...
-
Fame Ltd is considering expanding its range of dance facilities by investing in 35 new studios. The following estimates have been made relating to the cash outflows and inflows: 1. Initial inv...
-
Based on your reading, what are some of the organizational benefits associated with having volunteer programs? What are some of the organizational disadvantages? Do you believe the benefits outweigh...
-
Only one of the following four statements, which compare confirmation of accounts payable with suppliers and confirmation of accounts receivable with customers, is true. The true statement is that a....
-
A random sample of size 29 from a normal distribution has standard deviation s = 49. Test H0: = 55 versus H1: < 55. Use the = 0.01 level of significance.
-
A random sample of size 8 from a normal distribution has standard deviation s = 75. Test H0: = 50 versus H1: 50. Use the = 0.01 level of significance.
-
When the sample size is large, some people treat the sample standard deviation s as if it were the population standard deviation , and use the standard normal distribution rather than the Students t...
-
Company 1 In Millions of GBP 12 Months Ending Income Statement P&G Ltd. - As Reported FY 2020 FY 2021 09/30/2020 09/30/2021 Revenue 32,562.0 32,791.0 Cost Of Sales (10,420.0) (10,535.0) Gross Profit...
-
If there is an unrealized holding gain on available-for-sale investments, it is reported as?
-
How can a firm select the best suited candidates from a large number of applicants?
-
Choose a service company you are familiar with, and show how each of the 7 Ps of services marketing applies to one of its service products.
-
Why do the marketing, operations, human resource management, and IT functions need to be closely coordinated in service organizations?
-
How can a profitable business fail? a Because it can't pay its bills b Because it has more current liabilities than current assets c Because it has a bank overdraft d Because it has too much cash
-
When adjusting an operating profit to calculate the 'cash flows from operating activities', an increase in inventories over the financial period would be: a Added to operating profit b Ignored c...
-
Cash has been described as: a The lifebuoy of the business b The lifeboat of the business c The lifeline of the business d The lifeblood of the business
Study smarter with the SolutionInn App