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Classical Mechanics

Minimum Connecting Distance for Nodes

Given the following distances between destination nodes, what is the minimum distance that connects the nodes? Between nodes 1 - 2: 125; Between nodes 2 - 3: 150; Between nodes 1 - 3: 200 A. 125 B. 200 C. 275 D. 350 Given the following distances between destination nodes, what is the minimum distance that connects

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.

particle passes from potential U1 to potential U2

See attached file for full problem description. 7.8 Consider a region of space divided by a plane. The potential energy of a particle in region 01 is U1 and in region 02 it is U2. If a particle of mass m and with speed v1 in region 01 passes from region 01 to region 02 such that its path in region 01 makes an angle theta1

amplitude and phase of Driven harmoic oscillators

See attached file for full problem description. 1. Driven harmoic oscillators Suppose that a driven harmoic oscillators with belta = 1/3w0 is driven with force F = F0cos(wt) with driven frequency w = 1/3w0. Find the amplitude 'D' and phase a of the motino x(t) = Dcos(wt- a). expressing them purely in terms of F0, k and nume

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

Solid sphere and a cylinder kinetic energy

A solid sphere and a cylinder of the same mass and radius roll without slipping at the same speed. It is correct to say that the total kinetic energy of the solid sphere is more than the total kinetic energy of the cylinder. less than the total kinetic energy of the cylinder. equal to the total kinetic energy of

Disk, Hoop, and a Sphere Rolling Down an Incline

A disk, a hoop, and a sphere are released at the same time at the top of an inclined plane. They all roll without slipping. In what order do they reach the bottom? A. disk, hoop, sphere B. sphere, disk, hoop C. hoop, sphere, disk D. hoop, disk, sphere.

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?

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

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= 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.

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?