Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 1, Problem 9P
(a)
To determine
The given equation is dimensionally correct or not.
(b)
To determine
The given equation is dimensionally correct or not.
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In the equation y = y0 + vt + 1/2at^2 y and y0 are distances, v is a velocity, a is an acceleration, and t is time. Is the equation dimensionally homogeneous?
Which of the following equations are dimensionally consistent? (a) v = at, (b) v = 12at2, (c) t = a>v, (d) v2 = 2ax.
Consider the physical quantities m, s, v, a, and t with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, and [t] = T. 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 = mvr.
Chapter 1 Solutions
Physics for Scientists and Engineers
Ch. 1.1 - In a machine shop, two cams are produced, one of...Ch. 1.3 - True or False: Dimensional analysis can give you...Ch. 1.4 - The distance between two cities is 100 mi. What is...Ch. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - Prob. 3PCh. 1 - Prob. 4PCh. 1 - You have been hired by the defense attorney as an...Ch. 1 - A surveyor measures the distance across a straight...Ch. 1 - A crystalline solid consists of atoms stacked up...
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- 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_forwardA calculator displays a result as 1.365 218 0 X 107 kg. The estimated uncertainty in the result is 2%. How many digits should be included as significant when the result is written down? (a) zero (b) one (c) two (d) three (e) fourarrow_forwardA 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_forward
- In general, when a derived unit becomes complicated (involves too many standard units), what is done?arrow_forwardA 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_forwardWhich of the following equations are dimensionally (units) consistent? 1. v = 1/2at2 2. t = v/a 3. v2 = 2as 4. v = taarrow_forward
- If an equation is not dimensionally correct, does that mean that the equation cannot be true? yes noarrow_forwardHow many significant figures are there in (a) 0.0000303 and(b) 6.201 * 105?arrow_forwardConsider the physical quantities m, s, v, a, t, and r with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, [t] = T, and [r] = L. 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 = mvr.arrow_forward
- The quantity p = 3.14159c is a number with no dimensions, since it is a ratio of two lengths. Describe two or three other geometrical or physical quantities that are dimensionless.arrow_forwardIn a situation in which data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 m = 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m = 6.38 m. We could equally well write 6.375 m = 6.37 m, “rounding down” instead of “rounding up,” because we would change the number 6.375 by equal increments in both cases. Now consider an order-of-magnitude estimate, in which factors of change rather than increments are important. We write 500 m ~ 103 m because 500 differs from 100 by a factor of 5 while it differs from 1 000 by only a factor of 2. We write 437 m ~ 103 m and 305 m ~ 102 m. What distance differs from 100 m and from 1 000 m by equal factors so that we could equally well choose to represent its order of magnitude as ~ 102 m or as ~ 103 m?arrow_forwardConsider the physical quantities s, v, a, and t with dimensions [s] = L, [v] = LT−1, [a] = LT−2, and [t] = T. Determine whether each of the following equations is dimensionally consistent. (a) v2 = 2as; (b) s = vt2 + 0.5at2; (c) v = s/t; (d) a = v/t.arrow_forward
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