Solution Found!

Physics / Classical Mechanics 0 / Chapter 7 / Problem 7.1

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

Change Question

Write down the Lagrangian for a projectile (subject to no

Chapter 7, Problem 7.1

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Write down the Lagrangian for a projectile (subject to no air resistance) in terms of its Cartesian coordinates (x, y, z), with z measured vertically upward. Find the three Lagrange equations and show that they are exactly what you would expect for the equations of motion.

Questions & Answers

QUESTION:

Write down the Lagrangian for a projectile (subject to no air resistance) in terms of its Cartesian coordinates (x, y, z), with z measured vertically upward. Find the three Lagrange equations and show that they are exactly what you would expect for the equations of motion.

ANSWER:

Step 1 of 5

The Lagrangian of the projectile system is given by,

Here, is kinetic energy and is potential energy of the system.

The expression of kinetic energy is given by,

Here, is the mass of the projectile, and is the velocity of the projectile.

The velocity of the projectile in terms of Cartesian coordinates is given by,

Rewrite the equation of kinetic energy as follows.

Study Tools You Might Need

Chapter: 6 Problem: 99P

Introductory Chemistry 5
A compound containing carbon and hydrogen has a molar mass of 56.11 g/mol and an empirical formula of \(\mathrm{CH}_{2}\). Determine its molecular formula. Equation Transcription: Text Transcription: CH_2

Chapter: 5 Problem: 14

Physics: Principles with Applications 6
A sports car of mass 950 kg (including the driver) crosses the rounded top of a hill (radius = 95 m) at 22 m/s. Determine (a) the normal force exerted by the road on the car. (b) the normal force exerted by the car on the 72-kg driver, and (c) the car speed at which the normal force on the driver equ

Chapter: 27 Problem: 45

Physics: Principles with Applications 6
45. (Ill) A Ferrari with a mass of 1400 kg approaches a freeway underpass that is 10 m across. At what speed must the car be moving, in order for it to have a wavelength such that it might somehow diffract" after passing through this single slit"? How do these conditions compare to normal freeway spe

Chapter: 21 Problem: 95

Physics 4
Consider the circuit shown in Figure 2146, in which three lights, each with a resistance R, are connected in parallel. The circuit also contains an open switch. (a) When the switch is closed, does the intensity of light 3 increase, decrease, or stay the same? Explain. (b) Do the intensities of lights

Chapter: 23 Problem: 23.85

Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs 1-36) 4
A plastic rod with linear charge density l is bent into the quarter circle shown in FIGURE P23.48. We want to find the electric field at the origin. a. Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle u. b. Write, but do not eva

Chapter: 5 Problem: 8

Urban Economics 8
Consider a city that imposes a new pollution tax that increases the average cost (and price) of the good produced by a polluting industry by 4 percent and improves the citys environmental quality by 20 percent. The price elasticity of demand for the citys export goods is -1.50. a. The total output of

Chapter: 31 Problem: 4

Principles of Economics 9
Describe the economic logic behind the theory of purchasing-power parity.

Chapter: 10 Problem: 10.12

Chemistry for today : general, organic, and biochemistry 9
Write balanced equations to represent decay reactions of the following isotopes. The decay process or daughter isotope is given in parentheses. a. \({ }_{63}^{157} \mathrm{Eu}\) (beta emission) b. \({ }_{78}^{190} \mathrm{Pt}\) (daughter = osmium - 186) c. \({ }_{62}^{138} \mathrm{Sm}\) (

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account