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Classical Mechanics

Simple Harmonic Motion: Equivalent force constant of springs

Two springs with the same unstretched length, but different force constants and are attached to a block with mass on a level, frictionless surface. Calculate the effective force constant in each of the three cases depicted in the figure. a). Express your answer in terms of the variables k1, m, k2 k_eff -c = b) An object

Displacement Problem

Assume that a 2400 ton (1 ton=2000 lbs) battleship with a length and width (approximated as a rectangle) of 110x12 meters is made out of just steel (density of steel=7.86 g/cm^3). If half of the metal of the ship is to be below the surface of the water then (a) how much volume will be available for storage in the ship below wa

Hermitian Operator Matrix

The operator Q is given by the matrix: Q ( 1 i ) (-i -1) a. Determine the matrix corresponding to Q. b. Is Q Hermitian? c. Find the Eigenvalues of Q d. For each eigenvalue in part (c), determine the corresponding eigenvector See attachment for better symbol representation.

The 150-lb ball shown is suspended on a string AB

The 150-lb ball shown is suspended on a string AB and rests again the frictionless vertical wall. The string makes an angle of 30 with the wall. The tension in the string is: a. 173 lb b. 500 lb c. 300 lb d. 600 lb e. none of these Please see attached file for diagram

Meeting in a circle

Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 1.3 10-3 rad/s, while the other has an angular speed of 3.3 10-3 rad/s. How long will it be before they meet?

Speed and Distance

The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 53 miles per hour?

Classical Mechanics: Lagrange of a simple pendulum.

A pendulum consists of a mass m suspended by a massless spring with unextended length of b and spring constant k. Find Lagrange's equation of motion. Assume that the pendulum is constrained to swing in a single plane.

Classical Mechanics: Fourier Problem.

2. Obtain the Fourier representation of the output of a full-wave rectifier. Plot the first three terms of the expansion and compare with the exact function. Note: when they say the 'output of a full wave rectifier' they mean the function F(t) = [sin (w4*t)] The angular frequency of the unrectified signal is labeled w4. Think

How high will 145 g baseball go?

A good, professional baseball pitcher throws a ball straight up in the air. Estimate how high the 145 g ball will go. (A good throw can reach 90 mph.) Explain your answer.


The G string on a guitar has a fundamental frequency of 196 Hz and a length of 0.62 m. This string is pressed against the proper fret to produce the note C, whose fundamental frequency is 262 Hz. What is the distance L between the fret and the end of the string at the bridge of the guitar?

Standing wave in a pipe

If a pipe is closed at one end and opened at the other end, at what fractions of a wavelength will a standing wave be produced within the pipe?

Two Objects Dropped

Two objects are dropped from a bridge an interval of 1.00 s apart. What is their separation 1.00 s after the second object is released? 4.90 m 9.80 m 14.7 m 19.8 m

Transverse wave meet on two parallel wires with tension

Please help with the following problem. Provide step by step calculations. Two wires are parallel, and one is directly above the other. Each has a length of 50.0 m and a mass per unit length of 0.020 kg/m. However, the tension in wire A is 6.00 x 10^2 N and the tension in wire B is 3.00 x 10^2 N. Transverse wave pulses ar

Oscillators and Classical Spring Concepts

See attachment for better formula representation. 1) Consider the two-dimensional anisotropic oscillator with motion given by: x(t) = Ax cos (ωxt) y(t) = Ay cos (ωyt - δ). (a) Prove that if the ratio of frequencies is rational (that is ωx / ωy = p/q where p and q are integers) then the motion is periodic. What i

Physics Questions

See attached file for full problem description. 1. Conversion factors: A Joule is the MKS unit for energy; the cgs (centimeter- gram-second) unit of energy is the erg. I have started the conversion from Joules to ergs for you. Write down conversion factors and convert the following MKS units to cgs units to find how many

Radial free fall in Schwarztchild metric.

Consider a Schwarzchild black hole of mass M=15Ms where Ms is the mass of the sun. A particle that was initially at rest at r= falls radially inward. Determine the proper time along the particle's worldline for it to reach (a) the event horizon and (b) the singularity, starting from r0 = 5rs. See attached file for f

Orbital mechanics problem.

Show the integral below can be integrated to give Equation 1 θ(r) = ∫ {[(L/r^2) dr] / [ 2μ (E+(k/r) - (L^2/ 2μr^2))]^.5} + Constant Using : U= L/r and r = minimum at θ = 0 Equation 1----------cos (θ) =[ (L^2/(μkr)) - 1]/ [{1+((2EL^2)/(μk^2))}^.5] S

Net average force acting on a diver

A 62.0 kg person, standing on a diving board, dives straight down into the water. Just before striking the water, her speed is 5.50 m/s. At a time of 1.65 s after she enters the water, her speed is reduced to 1.10 m/s. What is the net average force (magnitude and direction) that acts on her when she is in the water?

Static Friction and Dual Block System

One block rests upon a horizontal surface. A second identical block rests upon the first one. The coefficient of static friction between the blocks is the same as the coefficient of static friction between the lower block and the horizontal surface. A horizontal force is applied to the upper block, and its magnitude is slowly in

Irradiance of a Source

Show that the height of a light bulb (assumed to be a point source) from the center of a circular table radius = a that provides a maximum irradiance at its edges is given by 2(a) ^ (1/2)