


Problem 2. A massless string of length L passes through horizontal table. A hole in a a end of the string mo ves fricti...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
A mass m0.2kg is attached to the end of a massless string. The mass is rotating in a circular orbit of radius r 0.6m on a frictionless table with period T 1.2s. The string is pulled slowly downwards 0.2m through hole in the table. φ What is the new period of circular orbit for mass m? (ii) How much work is done on the mass?
In each of the following problems, please show each of the
following steps.
- draw the picture, specify the coordinate system, indicate your
generalized coordinates
- write the KE as a function of your generalized velocities and
coordinate system.
- write the PE as a function of your generalized coordinates and
coordinate system.
- write the Lagrangian
- derive the equations of motion, one each for each generalized
coordinate
1) Shown is a simple pendulum bob of mass m attached...
A mass on a horizontal table is attached by a thin string that passes over a frictionless, massless pulley to a 2.5 kg mass that hangs over the side of the table 1 m above the ground. The system is released from rest and the 2.5 kg mass strikes the ground at 0.83 s later. The system is now placed in its initial position and a 1.1 kg mass is placed on top of the block of mass m1. Released...
14. Two masses are connected by a string which passes over a pulley with negligible mass and friction. One mass hangs vertically and one mass slides on a frictionless 30.0 degree incline. The vertically hanging mass is 6.00 kg and the mass on the incline is 4.00 kg. The magnitude of the acceleration of the 4.00 kg mass is 15. Two masses are connected by a string which passes over a pulley with negligible mass and friction. One mass hangs...
A massless spring with a spring constant k = 22.0 N/m is hanging vertically from the ceiling neither stretched nor compressed as shown in part (1). A 0.45-kg ball is attached to its free end, then slowly lowered to its equilibrium (E) position (2). Finally, the ball is pulled down a distance of 15.0 cm before being released (3). a) Using the provided information derive the algebraic expression for the stretched distance in the spring while at equilibrium. b) Calculate...
2. (35 points) A pendulum consists of a point mass (m) attached to the end of a spring (massless spring, equilibrium length-Lo and spring constant- k). The other end of the spring is attached to the ceiling. Initially the spring is un-sketched but is making an angle θ° with the vertical, the mass is released from rest, see figure below. Let the instantaneous length of the spring be r. Let the acceleration due to gravity be g celing (a) (10...
Problem (1) (40 points) A pendulum consisting of a ball of mass m and a massless string of length L 5.00 m is released from an angle of a 69 88 shown in the figure and strikes a block of mass M 2m. The block slides a distance D before stopping under the action of a constant friction force with the frio- tion constant μ": 0.50. The ball rebounds to an angle of Hints: Take g= 10 m/?. sin 16"...
TRIAL 1 600 2.610 9.91 o.2 0.39 2.62 43 Average Result: The average speed of the given ball is velas hralels 1) Pull the penduum to the side, insert the ball into the gun, and compress and latch the gun spring Release the pendulum so that it hangs vertically 2) Fire the gun. The pendulum will latch near the highest point of its swing. Measure ne height ha·the vertical distance from the pendulum platform to the center of the ball...
10. Write a one-page summary of the attached paper? INTRODUCTION Many problems can develop in activated sludge operation that adversely affect effluent quality with origins in the engineering, hydraulic and microbiological components of the process. The real "heart" of the activated sludge system is the development and maintenance of a mixed microbial culture (activated sludge) that treats wastewater and which can be managed. One definition of a wastewater treatment plant operator is a "bug farmer", one who controls the aeration...