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# Classical Mechanics

### Frequency of transverse standing waves on stretched string.

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?

### The A string on a string bass is tuned to vibrate at a fundamental frequency of 55.0 Hz. If the tension in the string were increased by a factor of four, what would be the new fundamental frequency?

The A string on a string bass is tuned to vibrate at a fundamental frequency of 55.0 Hz. If the tension in the string were increased by a factor of four, what would be the new fundamental frequency?

### 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

### Classical Mechanics: Mass, acceleration, velocity

See attached for full problems description.

### Classical Dynamics: Coefficient of kinetic friction in car accident litigation

Please see attached files for problem specifics.

### The amplitude of a transverse wave on a string is 4.5 cm

The amplitude of a transverse wave on a string is 4.5 cm. The ratio of the maximum particle speed to the speed of the wave is 3.1. What is the wavelength (in cm) of the wave?

### 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

### Tension of a Rope

A tightrope walker with a mass of 60.0 kg stands at the center of a rope which was initially strung horizontally between two poles. His weight causes the rope to sag symmetrically, making an angle of 4.80 with the horizontal. What is the tension in the rope? 359 N 589 N 2470 N 3520 N A tightrope wal

### 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

### Various classical physics questions

See attached file for a full problem description with correct formatting. 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 cg

### 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=&#61605; 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 solved by using substitution integrals

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] See attached file for full proble

### Sum of momenta of two joggers

A 85 kg jogger is heading due east at a speed of 2.0 m/s. A 55 kg jogger is heading 32 degrees north of east at a speed of 3.0 m/s. Find the magnitude and direction of the sum of the momenta of the two joggers.

### 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?

### Tension in the String Used to Hang a Block Over a Pulley

A 9.00 kg hanging weight is connected to a string over a pulley to a 5.00 kg block that is sliding on a flat table (see figure P5.24, page 142). If the coefficient of kinetic friction is 0.15, find the tension in the string.

### Acceleration: Speed of the Car When It Went Over the Cliff

A car drives straight off the edge of a cliff that is 54 m high. The police at the scene of the accident note that the point of impact is 130 m from the base of the cliff. How fast was the car traveling when it went over the cliff?

### Modern Physics: What is the final speed of the probe?

A 5.0 x 104 kg space probe is traveling at a speed of 11000 m/s through deep space. Retrorockets are fired along the line of motion to reduce the probe/s speed. The retrorockets generate a force of 4.0 x 10^5 N over a distance of 2500 km. What is the final speed of the probe?

### What is the magnitude and direction of the tension that the right section of the wire sustains.?

A tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 11 N on the wire. The left section of the wire makes an angle of 14 degree relative to the horizontal and sustains a tension of 447 N. What is the magnitude and dir

### 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

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)

### A truck covers 40.0 m in 8.50 s while smoothy slowing down to a final speed of 2.80m/s . Find orginal speed.

A truck covers 40.0 m in 8.50 s while smoothy slowing down to a final speed of 2.80m/s . Find orginal speed.

### Finding the Frequency of Oscillatory Motion

Two masses M=100gms. and Q = 200gms. slide freely on a horizontal, frictionless track and are connected by a spring whose force constant is k = .5 Newtons/meter. Find the frequency of oscillatory motion for this system.

### 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?

### ballast bag released from a rising balloon

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.