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Classical Mechanics

Waves

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)

Determining Horizontal Distance

A horizontal rifle is fired at a bull's eye. The muzzle speed of the bullet is 670 m/s. The barrel is pointed directly at the center of the bull's eye, but the bullet strikes the target .025 m below the center. What is the horizontal distance between the end of the rifle and the bull's eye?

Time question

A balloon is rising straight up with a speed of 3.0 m/s. A ballast bag is released from rest relative to the balloon when it is 9.5 m above the ground. How much time elapses before the ballast bag hits the ground?

Speed question

A diver runs horizontally with a speed of 1.20 m/s off a platform that is 10 m above the water. What is his speed just before striking the water?

Mechanics and Arbitrary Vectors

Show that: a. Sum of vectors i and j: epsilon(ijk)delta(ij) =0 b. Sum of vectors j,k: epsilon(ijk)epsilon(njk) = 2delta (in) c Sum of vectors i,j,k: epsilon(ijk)epsilon(ijk) = 6 Show that: Sum of vectors k: epsilon (jk)epsilon (mnk) = delta(im)delta (jn) - delta (in)delta (jm) Using the epsilon (ijk) notation and in f

Questions involving different gravities and masses

15. The height achieved in a jump is determined by the initial vertical velocity that the jumper is able to achieve. Assuming that this is a fixed number, how high can an athlete jump on Mars if she can clear 1.55 In on Earth? 22. The radius of a neutron star is T50 times smaller than Earth's radius, and its mass is 1.8 H 105

A system of two masses

A cart of weight m1 is pulled uphill on a 15 degrees slope by a bucket of weight m2 dropping vertically. Ignoring friction and the weight of the cable, determine how m1 and m2 must be related in order for the system to move with constant speed.

Radio frequency reception

A shortwave receiver has "90-m band" written on one end of the dial and "11-m band" on the other. What range of frequencies does this radio receive? Take the speed of radio waves to be 3.00 × 10^8 m/s.

Momentum of Automobile

I need to see each step and formula to solve this question: The momentum of an object traveling at 5.3 m/s is determined to be 350 kg m/s. Could the moving object be an automobile?

Smith chart and two wire lines

The two-wire lines shown in the attached figure are all lossless have Z0 = 200 ohms. Find d and the shortest possible value for d1 to provide a matched load if gamma = 100cm. Please show all steps using smith chart. (See attached file for full problem description)