Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 7, Problem 5P
To determine
To Show: That
Introduction: The dot production of two vectors is a scalar quantity. It may be positive or a negative number.
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In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with
particles or rigid bodies that can be treated as particles, the Lagrangian can be defined
as:
L = T-V where T is the kinetic energy of the particle, and V the potential energy of the
particle. It is also advised to start with Cartesian coordinates when expressing the
kinetic energy and potential energy components of the Lagrangian
e.g. T = m (x² + y² + 2²). To express the kinetic energy and potential energy in
some other coordinate system requires a set of transformation equations.
3.1 Taking into consideration the information given above, show that the Lagrangian
for a pendulum of length 1, mass m, free to with angular displacement - i.e.
angle between the string and the perpendicular is given by:
3.2
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.2
L = T-V = ²² +mg | Cos
Write down the Lagrange equation for a single generalised coordinate q.
State name the number of generalised coordinates in problem 3.1.
Hence write…
In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with
particles or rigid bodies that can be treated as particles, the Lagrangian can be defined
as:
L = T-V where T is the kinetic energy of the particle, and V the potential energy of the
particle. It is also advised to start with Cartesian coordinates when expressing the
kinetic energy and potential energy components of the Lagrangian
e.g. T = m (x² + y² + ż²). To express the kinetic energy and potential energy in
some other coordinate system requires a set of transformation equations.
3.1 Taking into consideration the information given above, show that the Lagrangian
for a pendulum of length 1, mass m, free to with angular displacement 0- i.e.
angle between the string and the perpendicular is given by:
L=T-V=1²0² + mg | Cos
In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with
particles or rigid bodies that can be treated as particles, the Lagrangian can be defined
as:
L = T-V where T is the kinetic energy of the particle, and V the potential energy of the
particle. It is also advised to start with Cartesian coordinates when expressing the
kinetic energy and potential energy components of the Lagrangian
e.g. T = m (x² + y² + ²). To express the kinetic energy and potential energy in
some other coordinate system requires a set of transformation equations.
3.1 Taking into consideration the information given above, show that the Lagrangian
for a pendulum of length 1, mass m, free to with angular displacement - i.e.
angle between the string and the perpendicular is given by:
L=T-V = 1²0² + mg | Cos 0
3.2
Write down the Lagrange equation for a single generalised coordinate q.
State name the number of generalised coordinates in problem 3.1.
Hence write down the Lagrange equation of…
Chapter 7 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 7.2 - Prob. 7.1QQCh. 7.2 - shows four situations in which a force is applied...Ch. 7.3 - Which of the following statements is true about...Ch. 7.4 - A dart is inserted into a spring-loaded dart gun...Ch. 7.5 - A dart is inserted into a spring-loaded dart gun...Ch. 7.6 - Choose the correct answer. The gravitational...Ch. 7.6 - A ball is connected to a light spring suspended...Ch. 7.8 - What does the slope of a graph of U(x) versus x...Ch. 7 - A shopper in a supermarket pushes a cart with a...Ch. 7 - The record number of boat lifts, including the...
Ch. 7 - In 1990, Walter Arfeuille of Belgium lifted a...Ch. 7 - Spiderman, whose mass is 80.0 kg, is dangling on...Ch. 7 - Prob. 5PCh. 7 - Vector A has a magnitude of 5.00 units, and vector...Ch. 7 - Find the scalar product of the vectors in Figure...Ch. 7 - Using the definition of the scalar product, find...Ch. 7 - A particle is subject to a force Fx that varies...Ch. 7 - In a control system, an accelerometer consists of...Ch. 7 - When a 4.00-kg object is hung vertically on a...Ch. 7 - Prob. 12PCh. 7 - The tray dispenser in your cafeteria has broken...Ch. 7 - Prob. 14PCh. 7 - A small particle of mass m is pulled to the top of...Ch. 7 - The force acting on a particle is Fx = (8x 16),...Ch. 7 - When different loads hang on a spring, the spring...Ch. 7 - Prob. 18PCh. 7 - (a) A force F=(4xi+3yj), where F is in newtons and...Ch. 7 - Review. The graph in Figure P7.20 specifies a...Ch. 7 - A 0.600-kg particle has a speed of 2.00 m/s at...Ch. 7 - A 4.00-kg particle is subject to a net force that...Ch. 7 - A 2 100-kg pile driver is used to drive a steel...Ch. 7 - Review. In an electron microscope, there is an...Ch. 7 - Review. You can think of the workkinetic energy...Ch. 7 - You are lying in your bedroom, resting after doing...Ch. 7 - Review. A 5.75-kg object passes through the origin...Ch. 7 - Prob. 28PCh. 7 - A 0.20-kg stone is held 1.3 m above the top edge...Ch. 7 - A 1 000-kg roller coaster car is initially at the...Ch. 7 - A 4.00-kg particle moves from the origin to...Ch. 7 - (a) Suppose a constant force acts on an object....Ch. 7 - A force acting on a particle moving in the xy...Ch. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - For the potential energy curve shown in Figure...Ch. 7 - A right circular cone can theoretically be...Ch. 7 - The potential energy function for a system of...Ch. 7 - You have a new internship, where you are helping...Ch. 7 - Prob. 42APCh. 7 - A particle moves along the xaxis from x = 12.8 m...Ch. 7 - Why is the following situation impossible? In a...Ch. 7 - Prob. 45APCh. 7 - Prob. 46APCh. 7 - An inclined plane of angle = 20.0 has a spring of...Ch. 7 - Prob. 48APCh. 7 - Over the Christmas break, you are making some...Ch. 7 - A particle of mass m = 1.18 kg is attached between...
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