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# Equilibrium

### Determine the tension in the wires

Please see the attachment and answer problem 3 only. A uniform circular plate of radius 300 mm and mass 26 kg is supported by three vertical wires that are equally spaced arround its edge (see the attachment). A small 3 kg block E is placed on the plate at D and is then slowly moved along the diameter CD until it reaches C.

### Oscillations of Mass Suspended by a Spring

(Please see the attached file). Two small blocks, A and B , of masses 0.8 kg and 1.2 kg respectively, are stuck together. A spring has natural length 0.5 meters and stiffness of 98 N/m. One end of the spring is attached to the top of the block A and the other end of the spring is attached to a fixed point O. (a) The system

### Simple Harmonic Motion of a Floating Object

An object with height h, mass M, and a uniform cross-sectional area A floats upright in a liquid with density p. a). Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium. b). Calculate the vertical distance from the surface of the liquid to the bottom of the flo

### Spring Constant and Oscillatory Motion

A 5.0 kg block hangs from a spring with spring constant 2000 N/m. The block is pulled down 5.0 cm from the equilibrium position and given an initial velocity of 1.0 m/s back toward equilibrium. What are (a) the frequency, (b) amplitude, (c) phase constant and (d) the total mechanical energy of the motion (e) write the equation

### A horizontal, 10 m plank weighs 100N N.

Set of 10 problems on mechanics : forces, moment, springs, stress, strain, Young's modulus, shear, modulus

### Simple Harmonic Motion

A block with mass attached to a horizontal spring with force constant is moving with simple harmonic motion having amplitude. At the instant when the block passes through its equilibrium position, a lump of putty with mass m is dropped vertically onto the block from a very small height and sticks to it. For this value of m, w

### Lagrangian and Hamiltonian's Mechanics

Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity w about its vertical axis, as shown in figure 7.17. Use cylindrical polar coordinates and let the equation of the parabola be z=kp^2. Write down the Lagrangian in terms of p as the

### Torque Equilibrium Equation

See the attached file for further question details. A) What is the equation that results from choosing the pivot point to be the point from which the mass hangs (where W acts)? Express your answer in terms of the unknown quantities T_L and T_R and the known lengths x and L. Recall that counterclockwise torque is positive.

### Physics: Two pulley tension problem

Please help me with attached problem. Thanks in advance 1. Force Table is set up with 2 pulleys at 50 degrees and at 170 degrees as shown. A total of 200 grams is suspended from the pulley at 50 degrees and a total of 300 grams is suspended from the pulley at 170 degrees. A third string, tied to the big ring, is attache

### Final Temperature of Iron-Water System

A piece of iron of mass 200g at temperature 80 degrees C is added to a 300g of water at temp 10 degrees C. What is the final temperature of the system? [ The specific heat of water is 4190 J/(Kg . oC) and for iron is 450 J/(Kg . oC)]

### Potential Energy - Angular Frequency

Please see attached file for formatted problem description. The potential energy of a one-dimensional mass m at a distance r from the origin is U(r) = U_o(r/R + lambda^2(R/r) for 0 < r < infinity, with U_o, R, and lambda all positive constants. Find the equilibrium position r_o. Let x be the distance from equilibrium an

### Stable and unstable equilibrium

A metal ball (mass m) with a hole through it is threaded on a frictionless horizontal rod. A massless stirring (length l) attached to the ball runs over and massless, frictionless pully and supports a block of mass M. (a) Write down the potential energy U(ᶿ). (The PE is given easily in terms of the heights shown as H and h. Es

### One-Dimensional Spring

The force exerted by a one-dimensional spring, fixed at one end, is F=-kx, where x is the displacement of the other end from its equilibrium position. Assuming that this force is conservative (which it is) show that the corresponding potential energy is U=1/2kx^2, if we choose U to be zero at the equilibrium position. (b) Suppos

### Energy - An interesting one-dimensional system is the simple pendulum, consisting of a point mass m, fixed to the end of a massless rod (length l)

An interesting one-dimensional system is the simple pendulum, consisting of a point mass m, fixed to the end of a massless rod (length l), whose other end is pivoted from the ceiling to let it swing freely in a vertical plane, as shown in Figure 4.26. The pendulum's position can be specified by its angle &#963; from the equilibr

### Capillary Rise: Determining the Rise of a Liquid in a Straw

See the attached file. Problem Statement: A double walled straw with an outer diameter of ½" and an inner diameter of ¼" is placed in a glass of water as shown and described below: a) Determine the volume of water in the 4" diameter by 4" high cup of water b) Determine how high the water will rise in both the outer lay

### Oscillations: Simple Harmonic Motion.

Question: A particle of mass m is placed on a friction-less horizontal table and attached by two identical massless spiral springs of natural length b and stiffness k, to two fixed points A and B on the table. Points A and B are a distance 2a apart, where 2a > 2b, so that the springs are stretched. The particle is then given a d

### the tensions in all pieces of string

Please see the file attached. It's one question. Find the tensions in all pieces of string in the figure below. The system is at static equilibrium.

### Melting of Lead and Phase Diagrams

See attached file.

### Equilibrium: Contact force and tension in the ring.

Three identical steel balls, each of mass m, are placed in a cylindrical ring which rests on a horizontal surface and whose height is slightly greater than the radius of the balls. The diameter of the ring is such that the balls are virtually touching one another. A fourth identical ball is then placed on top of the other three

### Harmonic Motion

A person bounces up and down on a trampoline, while always staying in contact with it. The motion is simple harmonic motion, and it takes 1.98 s to complete one cycle. The height of each bounce above the equilibrium position is 54.0 cm. (a) Determine the amplitude of the motion. (b) Determine the angular frequency of the

### Steady State & Plotting Trajectories in MATLAB

Please see attached files regarding specifics. This problem has two parts (written & programming). The Brusselator is a simple model for oscillatory chemical systems such as the Belousov-Zhabotinski reaction. The time evolution of the concentration of two chemical species, x and y, is described by the ODE's: AND ,

### Motion in 1D

See attached file for full problem description.

### Torque, Static Equilibrium, and Rotational Dynamics

A solid cylinder of mass 10 kg and radius 1 rn rotates with an angular speed of 10 rad / s about a vertical axis through its center. A 0.5 kg piece of putty is dropped vertically on the cylinder at a point 0.5 m from the center of rotation and sticks there. What is the final angular speed of the cylinder?

### Woman skating across ice lake

A 500 N woman stands in the middle of a frozen lake of radius lOOm. The ice is frictionless so she can't walk. She decides to sacrifice one of her 0.5 kg shoes and throws it horizontally at 5 m/s. How long does it take her to reach the shore?

### Torque, Static Equilibrium, and Rotational Dynamics

2. If two particles have equal kinetic energies, does that mean that they must have equal momenta? Explain.

### 1. Radio engineers are erecting a communications tower stabilized with cables running from the top of the tower to the ground.

1. Radio engineers are erecting a communications tower that is 16.0 m high. During the installation they stabilize the tower with 32.0 m long cables running from the top of the tower to the ground. The anchors consist of concrete blocks to which the cables can be secured. Each block weighs 1590 N. If the coefficient of static fr

### Archimedes principle.

A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown in the picture (attached). a) Derive a formula for the block density in terms of the fluid densities, P1 and P2, the heights h0, h1, and h2 and the cross-sectional area A. (it is not necess

### Problems involving tension in the string

A transverse wave is traveling on a string. The displacement y of a particle from its equilibrium position is given by y= (0.021 m) sin (25t - 2.0x). The phase angle 25t - 2.0x is in radians, t is in seconds and x is in meters. The linear density of the string is 1.6 x 10^-2 kg/m. What is the tension in the string?

### Equilibrium, translational & rotational equilibrium

Please help with the following problem. Provide detailed calculations. A scale is attached to the ceiling and a mass of 1.00 kg hangs from it. It reads 9.81 N. Another identical scale at the right is connected by perfect strings passing over perfect pulleys to two 1.00 kg masses hanging vertically at the end of the strings (

### Lagrangian for a bead in a frictionless hoop

A bead slides on a frictionless hoop. The hoop is spinning at rate w on vertical axis. Find Lagrangian. See attached file for full problem description.