The area of a circle is given by ar? where r is the radius. This can be written as area = (ar) x r. Can we regard this equation as being of the form: z = xy 1 PHY1509 PHYSICS SECTION: UNIQUE NUMBER (714489) where z = area, x = ar and y = r so that one can use equation (10.12) or (10.13) instead of equation (10.15) for determining the error in the area? Give reasons for your answer.

The area of a circle is given by ar? where r is the radius. This can be written as area = (ar) x r. Can we regard this equation as being of the form: z = xy 1 PHY1509 PHYSICS SECTION: UNIQUE NUMBER (714489) where z = area, x = ar and y = r so that one can use equation (10.12) or (10.13) instead of equation (10.15) for determining the error in the area? Give reasons for your answer.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter6: Some Methods In The Calculus Of Variations

Section: Chapter Questions

Problem 6.10P

See similar textbooks

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?
If the DNA strand in a molecule could be stretched out, it would have a length on the order of 2.0 m. What would this be in feet and inches?
One mole of atoms consists of 6.02 × 1023 individual atoms. If one mole of unicorn atoms were spread uniformly over the surface of a sphere the size of the Earth, approximately how many atoms would be found per square meter? The average radius of the Earth is 6.38 × 103 km. how do I set up this unit conversion?
A student wanted to calculate the radius, r, of the base of a spherical cylinder. The student measured both the volume of the cylinder and its height and obtained the following: Volume, V = (92± 1) cm^3 . Height, h = (11.5 ± 0.1) cm. V = π * (r^2) * h. Calculate the radius of the base of the cylinder.
A hot tub with a surface area of 28 ft2 is filled with water to a depth of 29 in . Hint: volume is calculated as area × height (A × h). A) What is the volume of water in the tub, in liters? Express your answer to two significant figures and include the appropriate units. B) How many kilojoules are needed to heat the water from 59∘F to 103 ∘F? Express your answer to two significant figures and include the appropriate units. C) If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 59∘F to 103∘F? Express your answer to two significant figures and include the appropriate units.
The surface area S (r) (in square meters) of a spherical balloon with radius r meters is given by S() =4ar. The radius P(1) (in meters) after t seconds is given by P() =-1 !! Write a formula for the surface area N (1) (in square meters) of the balloon after / seconds. It is not necessary to simplify. N (1) - 0 JT
In measuring the external surface of a building, the builder uses SI units and the contractor only reads English units. At the end of the work, the contractor receives a document in which he says that the surface of the property is 18887 m2, so he asks that they make the conversion to units that he can understand, for example yards2. If it is known that 1 m 1. 0936 yards, what was the measurement that the contractor finally received? a) 22588.1147 Yards b) 20654.8232 Yards? C) 17270.4828 Yards d) 15792.3215 Yards?
Convert the volume (SCF) of natural gas to tons of natural gas. Given: volume of gas is 42,201 standard cubic feet (SCF) at 60°F and 14.7psia. NOTE: this answer will NOT be in metric tons, but English tons. Choose your answer with TWO decimals. O 1.60 10^5 tons O 3.20*10^8 tons O 1.11 tons O 2.78 10^-3 tons
A new physics unit of distance is created and called the Zarkov. A student informs you 1 Zarkov (1 Za) is exactly equivalent to 8 inches. Convert 4.44 × 10 5 Z a 3 m i n u t e 2to m 3 h r 2. If hard to read: asking you to convert Zarkov's squared over minutes cubed to meters squared over hours cubed. Answer in E notation without units in the box. I am assuming your output units are m 3 h r 2. Note: for some numbers the computer will convert your E notion to another notation without the E...that will not cost you points. To be clear regarding E notation, I will provide an example of what I'm talking about:
The atmospheric pressure P decreases exponentially with elevation h as follows, P(h) = P,e-gh/A ,where Po ([Pa]) is the atmospheric pressure at sea level, g ([m/s²1) is the acceleration due to gravity, and A is some dimensional constant. Determine the SI unit of the constant A and argue your key assumption. %3D B.
Kinetic energy K (Chapter 5) has dimensions kg · m2/s2. It can be written in terms of the momentum p (Chapter 6) and mass m as K= p 2m (a) Determine the proper units for momentum using dimensional analysis. (Use the following as necessary: kg, m, and s.) [p] = (b) The unit of force is the newton N, where 1 N = 1 kg • m/s?. What are the units of momentum p in terms of a newton and another fundamental SI unit? (Use the following as necessary: N, m, and s.) [p] =
So we take a pile of paper, we count the number of sheets, and obtain 226. Then, we measure how tall the pile is with a ruler: 24.0 mm. As discussed in section 1, we could have a long argument about how much exactly should the uncertainty of this measurement be. Let’s settle to ± 0.5 mm