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Solution of Problem 43, Chapter 8, Fundamentals Of Physics 9th - Halliday & Resnick

pada tanggal Januari 30, 2023

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Solution of Problem 42, Chapter 8, Fundamentals of Physics 9th - Halliday & Resnick

pada tanggal Januari 30, 2023

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Solution of Problem 1, Section 13, Mathematical Method in the Physical Sciences 3th - Mary L. Boas

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Solution of Problem 1, Section 6 Mathematical Method in the Physical Sciences 3th - Mary L. Boas

pada tanggal Januari 29, 2023

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Solution of Problem 42, Chapter 8, Fundamentals of Physics 9th - Halliday & Resnick

Solution of Problem 42, Chapter 8 Fundamentals of Physics 9th - Halliday & Resnick Question: A worker pushed a 27 kg block 9.2 m along a level floor at constant speed with a force direction 32° below the horizontal. If the coefficient of kinetic friction between block and floor was 0.20, what were (a) the work done by the worker's force and (b) the increase in thermal energy of the block - floor system? Answer: a) Work done by worker's force: Work = force * distance * cos 𝚹 Force = 𝚺F = ma = m (g - friction force) friction force = μk * N ( Where N is the normal force) N = mg Substituting the values Work = (27 kg) (9.8 m/s^2 - 0.2 * 9.8 m/s^2) * 9.2 m * cos(32°) Work = 227.6 J b) Increase in thermal energy: ΔQ = work done by friction force = friction force * distance friction force = μk * N = μk * m * g Substituting the values...

Solution of Problem 1, Section 13, Mathematical Method in the Physical Sciences 3th - Mary L. Boas

Solution of Problem 1, Section 13 Mathematical Method in the Physical Sciences 3th - Mary L. Boas Question: Use the ratio test to show that a binomial series converges for |x| < 1. Answer: The ratio test is a method used to determine the convergence of a series. Given a series with terms a_n, the ratio test states that if the limit of |a(n+1) / an | as n approaches infinity is less than 1, then the series converges. Consider the binomial series: (1 + x)^m = Σ_{n=0}^∞ ( m choose n) x^n where (m choose n) = m! / (n! (m-n)!) Taking the ratio of consecutive terms, we have: |a(n+1) / an| = | (m choose n+1) x^(n+1) / (m choose n) x^n| = | (m-n) x / (n+1)| = |x| (m-n) / (n+1) As n approaches infinity, (m-n) approaches m and (n+1) apporaches infinity. Since |x| < 1, we have that |x| * (m-n) / (n+1) approaches infinity. Therefore, the limit of | a(n+1) / an| as n approaches infinity is less than 1. By the ratio test, binomial series converges for |x| < 1.

Solution of Problem 1, Section 6 Mathematical Method in the Physical Sciences 3th - Mary L. Boas

Solution of Problem 1, Section 6 Mathematical Method in the Physical Sciences 3th - Mary L. Boas Question: Show that n! > 2^n for all n > 3. Hint: Write out a few terms; then consider what you multiply by to go from, say 5! to 6! and from 2^5 to 2^6. Answer: To show that n! > 2^n for all n > 3, we can proceed as follows: 1. Write out the first few terms of both n! and 2^n to get a sense of their behavior: n = 4: 4! = 24, 2^4 = 16 n = 5: 5! = 120, 2^5 = 32 n = 6: 6! = 720, 2^6 = 64 2. Consider what happens when we multiply by n+1 to go from n! to (n+1)! and from 2^n to 2^(n+1): For n!, we multiply by n+1 to get (n+1)!. This means that (n+1)! = n! * (n+1) > n! For 2^n, we multiply by 2 to get 2^(n+1). This means that 2^(n+1) = 2^n * 2 = 2 * 2^n < 2^n Therefore, n! > 2^n, and n! will continue to grow faster than 2^n as n increases. Therefore, we can conclude that for all n...

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