Number 3 show all work please ? 2) Check the following equations for dimensional consistency where t is time (s), v is speed(m/s), a is acceleration (m/s?), and x is position (m): a) x =v2b)x %3D 글 at c)t%=2x2aV a3) A can of paint that covers 20 m? costs $24.60. The walls of a room 13 ft x 18 ft are 8 ft high.What is the cost of paint for the walls?4) A runner covers 100 m in 11.2 s. What was her average speed?5) A human noworod

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Answered: 3) A can of paint that covers 20 m2…

3) A can of paint that covers 20 m2 costs $24.60. The walls of a room 13 ft x 18 ft are 8 ft high. What is the cost of paint for the walls?

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Introduction

Section: Chapter Questions

Problem 4P: Each of the following equations was given by a student during an examination: (a) 12mv2=12mv02+mgh...

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(a) One of lire fundamental laws of motion states that the acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (b) The newton is the SI unit of force. According to the results for (a), how can you express a force having units of newtons by using the fundamental units of mass, length, and time?
In SI units, speeds are measured in meters per second (m/s). But, depending on where you live, you’re probably mole comfortable of thinking of speeds in terms of either kilometers per hour (km/h) or miles per hour (mi/h). In this problem, you will see that 1 m/s is roughly 4 km/h or 2 mi/h, which is handy to use when developing your physical Intuition. More precisely, show that (a) 1.0m/s=3.6km/h and 1.0m/s=2.2mi/h .
The Hoover Dam Bridge connecting Arizona and Nevada opened in October 2010 ( Fig. 1.18). It is the highest and longest arched concrete bridge in the Western Hemisphere, rising 890 ft above the Colorado River and extending 1900 ft in length. What are these dimensions in meters? Figure 1.18 High and Wide An aerial view of the new four-lane Hoover Dam Bridge between Arizona and Nevada with the Colorado River beneath (as seen from behind the dam). See Exercise 16.
A map suggests that Atlanta is 730. miles in a direction 5.00 north of east from Dallas. The same map shows that Chicago is 560. miles in a direction 21.0 west of north from Atlanta. Figure P1.68 shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago. Figure P1.68
A surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.53
A sidewalk is to be constructed around a swimming pool that measures (10.0 0.1) m by (17.0 0.1) m. If the sidewalk is to measure (1.00 0.01) m wide by (9.0 0.1) cm thick, what volume of concrete is needed and what is the approximate uncertainty of this volume?
A surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.53
A surveyor measures the distance across a straight river by the following method (Fig. P3.7). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is = 35.0. How wide is the river?
Assume it takes 7.00 min to fill a 30.0-gal gasoline tank, (a) (Calculate the rate at which the tank is filled in gallons per second. (b) (Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in hours, required to fill a 1.00-m3 volume at the same rate. (1 U.S. gal = 231 in.3)
Each of the following equations was given by a student during an examination: (a) 12mv2=12mv02+mgh (b) v = v0 + at2 (c) ma = v2. Do a dimensional analysis of each equation and explain why the equation cant be correct.
(a) Suppose the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? (b) A displacement is related to time as x = A sin (2ft), where A and f are constants. Find the dimensions of A. Hint: A trigonometric function appearing in an equation must be dimensionless.
The purpose of this problem is to show the entire concept of dimensional consistency can be summarized but the old saying “You can’t add apples and oranges.” It you have studied power series expansions in a calculus course, you know the standard mathematical funstions such as trigonometric functions, logarithms, and exponential function can be expressed as infinite sums of the form where the an are dimensionless constants for all n = 0, 1, 2, … and x is the argument of the function. (If you have not studied power series in calculus yet, just trust us.) Use this fact to explain why the requirement that all terms in an equation have the same dimensions is sufficient as a definition of dimensional consistency. That is, it actually implies the arguments of standard mathematical funstions must be dimensional consistency. That is, it actually implies the arguments of standard mathematical functions must be dimensionless, so it is not really necessary to make this latter condition a separate requirement of the definition of dimensional consistency as we have done in this section.