Write an expression for a with a dimensionless constant of proportionality k. (Use the following as necessary: v, r, k, n, and m.) m a = Substitute the dimensions of a, r, and v. (Use the following as necessary: n, m, L, and T.) (수)" m = L" Equate the exponents ofL and T so that the dimensional equation is balanced: n + m = 1 and m = -1 Solve the two equations for n: n =2 Write the acceleration expression. (Use the following as necessary: v, r, and k.) .- a =

Write an expression for a with a dimensionless constant of proportionality k. (Use the following as necessary: v, r, k, n, and m.) m a = Substitute the dimensions of a, r, and v. (Use the following as necessary: n, m, L, and T.) (수)" m = L" Equate the exponents ofL and T so that the dimensional equation is balanced: n + m = 1 and m = -1 Solve the two equations for n: n =2 Write the acceleration expression. (Use the following as necessary: v, r, and k.) .- a =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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1. Multiplication or division: keep the same number of significant figures in the product or quotient as is in the least precise factor. Examples: 3.1 * 25.6=79.360000... = 79 6.7/981.0=0.0068297655... = 0.0068 keep only 2 significant digits 2. Powers or roots: keep the same number of significant figures as in the original number. Example: Sqrt(38) 6.164414... keep only 2 significant digits = 6.2 (11.6)² = 134.5600000... = 135 Exercises 3. Addition or subtraction: Round off, to the number of decimal places determined by the number with the least number of places beyond the decimal point. Example: 31.5+24.61 +3.28+1.19 +0.762 +0.003 = 61.345 1. 3.9 * 78.9= = 61.3 (correct result) 2. 32.01 +96.321 +36.98 +0.00023 +28.9= 3. 26.9/98 = 4. 421 0.003 =
Practice) a. To convert feet (ft) to meters (m), the number of feet should be multiplied by which of the following conversion factors? i. 1 m/3.28 ft ii. 3.28 ft/1 m b. To convert sq.in to sq.ft, the number of sq.in should be multiplied by which of the following conversion factors? i. 144 sq.in/1 sq.ft ii. 1 sq.ft/144 sq.in c. To convert sq.yd to sq.ft, the number of sq.yd should be multiplied by which of the following conversion factors? i. 1 sq.yd/9 sq.ft ii. 9 sq.ft/1 sq.yd 3. (Practice) Determine the final units of the following expression: 9.8m/s2 ×100cm/1m×1in/2.54cm×1ft/12in 4. (Practice) a. Determine the conversion factors that can be used to convert miles per gallon (mpg = mi/gal) to kilometers per liter (km/liter), given that 1 liter = 0.22 gallons and 1 kilometer = 0.6214 miles. b. Using the conversion factors you determined in Exercise 4a, convert 25 mpg into km/liter. 5. (Automotive) a. An automobile engine’s performance can be determined by monitoring its rotations per…
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a) Acceleration is described as space divided by time squared. Determine the dimensions of acceleration and its SI units.b) Kinetic Energy K has dimensions kg m2/s2. It can be written in terms of momentum p and mass m following the equation below. Determine the dimensions of the momentum and its SI units. c) The unit of force is the newton N, where 1 N = 1 kg m/s2. Determine the dimensions and the SI units of the momentum in terms of newtons.d) Newton’s law of universal gravitation is F =Gm1m2/r2 , where F is the magnitude of the gravitational force exerted by one object on another, m1 and m2 are the masses of the objects, and r is the distance between them. Determine the dimensions and the SI units of the proportionality constant G.
1.3 The Role of Units in Problem Solving A particular convenience store offers a drink called the "MegaGulp". If the cup holds 107 fl oz. of liquid and we treat the "Mega" in the name as a metric prefix, how many mL are in a "Gulp"? O 0.000107 O 0.000000362 O 316000000 O 0.00317 Save for Later Submit Answer
1. The floor of a rectangular building has an area of 120 square meter. The length of the floor / is 4m bigger than its width, w. Solve for I. Hint: Start with the equation of the area in terms of I. What kind of equation do you get? /= 48.11 X feet ! No, that's not the correct answer.
Instructions: Answer must be in standard form scientific notation with SI units that do not have prefixes except for kg. Provide the answer with the correct amount of significant figures. Thank you I greatly appreciate it
Q1) A) Find the answers to the following problems using the rule of Significant Figures a) (10.4168) m – (6.0) m b) (1.31) cm x (2.3) cm c) (5.7621) m / (6.201) m d) (2.5000) m + (32.85) m B) Represent each answer above in the scientific notation
Complete the missing entries in the table of metric prefixes, symbols, and multiplication factors. Pay attention to capitalization in the Prefix Symbol column, and specify whether the prefix is upper or lower case in the right-most column. The rows are not in any particular order. Example 1. 2. 3. 4. 5. Multiplier 10-¹2 10-2 10-3 Prefix Name pico kilo mega Prefix Symbol Р G Upper or lower case prefix? lower upper
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A unit of time year (yr) is defined as 365.25 days. Y How many seconds are there in 1.10 yr ? Express your answer using three significant figures. 1.10 yr = Submit Part B 17| ΑΣΦ 1.10 yr F Request Answer How many nanoseconds are there in 1.10 yr ? Express your answer using three significant figures. VO ΑΣΦ w ? ns S
One of the most well-known equations in fluid mechanics is the Bernoulli equation. The standard form of the Bernoulli equation for incompressible irrotational fluid flow is (see pic below)(P is pressure, u is flow velocity of the fluid, z is the height of fluid relative to a reference line)a. Verify that each additive term in the Bernoulli equation has the samedimensions. b. What are the dimensions of the constant C?