College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 1, Problem 9CQ
To determine
The correctness of dimension.
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Suppose quantity s is a length and quantity t is a time. Suppose the quantities v and a are defined by v = ds/dt and a = dv/dt. (a) What is the dimension of v? (b) What is the dimension of the quantity a? What are the dimensions of (c) ∫vdt,∫vdt, (d) ∫adt,∫adt, and (e) da/dt?
Thank you for your help and time, I think I got this but I am a little confused.
The arc length formula says the length s of arc subtended by angle Ɵ in a circle of radius r is given by the equation s=rƟ. What are the dimensions of (a) s, (b) r, and (c) Ɵ?
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Chapter 1 Solutions
College Physics
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- 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?arrow_forwardIn general, when a derived unit becomes complicated (involves too many standard units), what is done?arrow_forwardThe 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.arrow_forward
- One student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?arrow_forwardRoughly how many heartbeats are there in a lifetime?arrow_forwardConsider the physical quantities m,s,v,a, and t with dimensions [m]=M,[s]=L,[v]=LT1 and [a]=LT2 . Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a)F=ma;(b)K=0.5mv2;(c)p=mv;(d)W=mas;(e)L=mvrarrow_forward
- A surveyor measures the distance across a straight river by the following method (Fig. P1.6). 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 0 = 35.0. How wide is the river? Figure P1.6arrow_forwardConsider the equation y=mt+b, where the dimension of y is length and the dimension of t is time, and mand bare constants. What are the dimensions and SI units of (a) mand (b) b ?arrow_forwardThree displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44arrow_forward
- 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 .arrow_forwardFigure P1.6 shows a frustum of a cone. Match each of the three expressions (a) (r1 + r2)[h2 + (r2 r1)2]1/2, (b) 2(r1 + r2), and (c) h(r12 + r1r2 + r22)/3 with the quantity it describes: (d) the total circumference of the flat circular faces, (e) the volume, or (f) the area of the curved surface. Figure P1.6arrow_forwardProblem 12: In this problem, the symbols M, L, and T represent the dimensions mass, length, and time, respectively. Consider the physical quantities V, ρ, and t with dimensions [V] = L3, [ρ] = ML-3, and [t] = T. (Here, the square bracket means “the dimensions of” so, for example, [V] represents the dimensions of the quantity V.) Part (a) What are the dimensions of ∫ρdV? dimensions = ______ Part (b) What are the dimensions of dV/dt? dimensions = ______ Part (c) What are the dimensions of ρ(dV/dt)? dimensions = ______arrow_forward
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