Answered: If an equation is not dimensionally…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 5P

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Similar questions

(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.
(a) If your speedometer has an uncertainty of 2.0 km/h at a speed of 90 km/h, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h, what is the range of speeds you could be going?
(a) Estimate the number of times your heart beats in a month, (b) Estimate the number of human heartbeats in an average lifetime.
(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.
Suppose quantity s is a length and quantity t is a time. Suppose the quantities vand 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 , (d) adt, and (e) da/dt?
Answer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (h) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?
(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?
If you live in the United States, you probably know your height in feet and inches. In other countries, metric units are commonly used for measuring such quantities. First, find your height in inches. Then determine your height in a. centimetens and b. meters
(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?
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.
For the triangle shown in Figure P1.45, what are (a) the length of the unknown side, (b) the tangent of , and (c) the sine of ? Figure P1.45
(a) A person's blood pressure is measured to be 1202 mm Hg. What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?

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If an equation is not dimensionally correct, does that mean that the equation cannot be true?