1. Consider a particle of mass m constrained to move on a frictionless cylinder of radius R, given by the equation ρ=R in cylindrical polar coordinates (ρ, φ, z). Besides the force of constraint, the only force on the mass is force F=-kr directed toward the originUsing z and φ as generalized coordinates find the Lagrangian L, solve Lagrange’s equations and describe the motion. 2. Show that the kinetic energy of any holonomic mechanical system has the form.

T a jk (q) q ( j ) q(k )
j 1 k 1

n

n

. .

3. Consider a double pendulum (fig. 1) made up of two masses, m1 and m2 and two lengths l1 and l2. Find the equation of motion.

Fig. 1

4. A point mass glides without friction on a cycloid, which is given by x= a(v-sinθ) and y=a(1+cosθ) with 0≤v≤2π. Determine the Lagrangian and solve the equation of motion.

5. Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table so that m1 rests on the table surface and m2 hangs suspended. Assuming m2 moves only in a vertical line, what are the generalized coordinates for the system? Write the Lagrange equations for the system and, if possible, discuss the physical significance

any of them might have. Reduce the problem to a single second-order differential equation and obtain a first integral of the equation. What is its physical significance? (Consider the motion only until m1 reaches the hole.). 6. The term generalized mechanics has come to designate a variety of classical mechanics in which the Lagrangian contains time derivatives of qi higher than the first order. Problems

for which

x f x, x, x, t have

been referred to as ‘jerky’ mechanics. Such

equations of motion have interesting applications in chaos theory. By applying the methods of the calculus of variations, show that if there is a Lagrangian of the form

...
Daily Use of Physics
Jason L. McDuffy
University of Memphis
Physics 1 (online)
Project 1
Daily Use of PhysicsPhysics is considered to be a powerful lens that helps people view the everyday world. Physics is reflected in the everyday phenomena, puzzles and toys that offer a variety of interesting challenges leading to deep and interesting problems that derive from science and...

...Christopher Gooden
Dr. Jan Yarrison-Rice
Physics 101
5 April 2005
Physics in Sports
When many people think of sports, the topic of physics doesn't always come to mind. They usually don't think about connecting athletics with academics. In reality math, science, and especially physics, tie into every aspect of sports. Sports are a commonality that brings nations together, Soccer, known as football to most of the world, is said to an...

...Science in the Big City:
Exploring Career Opportunities in the Natural and Physical Sciences
New York City
May 13-18, 2014
Students in the Natural Sciences at the University of Houston-Downtown are generally accomplished and motivated students with strong interests in science. However, students typically have a very limited perception of the science careers available to them outside of medicine. To educate students as to the array of potential careers available in the sciences (not...

...Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been...

...be great at whatever sport we would participate in and understanding simple physics in Cosmetology, I never realized how much physics comes into play when playing sports. We don’t call it physics when were playing, football, basketball, baseball because it’s just a natural feeling when were throwing a ball or trying to tackle someone. When we began to learn about Newton’s law of Gravity. All sports in the world today have all...

...Physics End of Year Reflection Paper
At the beginning of this course you were given some overarching enduring understandings and essential questions. These were:
Overarching Enduring Understandings:
Students will uncover and use appropriate scientific models to describe and quantify the nature and interactions of matter and energy.
Students should understand that there is a network of rules and relationships that determine what will happen in a given...

...Student Exploration: Fan Cart Physics
Vocabulary: acceleration, force, friction, mass, newton, Newton’s first law, Newton’s second law, Newton’s third law, velocity
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
1. Imagine a horse pulling a cart. What would happen to the speed of the cart if several bags of cement were added to the cart? The speed of the cart would decrease.
2. Suppose several more horses were hitched up to the same cart. How would...

...Science Teaching: Yesterday, Today, and Tomorrow
Science instruction can take on many forms. From the lecture hall, to the laboratory there are a variety of ways science can be taught. This essay explores the historical events and changes that have effected science education and made it what it is today and where it may be heading in the future. (Martin, 2009)
Science education was created to share scientific data and events with students who are not part of...

812 Words |
3 Pages

Share this Document

Let your classmates know about this document and more at StudyMode.com

## Share this Document

Let your classmates know about this document and more at StudyMode.com