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Potential energy of the two-spring system; force on the junction point.

The ends of two identical springs are connected. Their unstretched lengths l are negligibly small and each has spring constant k. After being connected, both springs are stretched an amount L and their free ends are anchored at y = 0 and x = +/- L as shown (see attachment). The point where the springs are connected to each othe

Bernoulli's Theorem.

On a bet, you try to remove ethyl alcohol from a glass by blowing across the top of a vertical straw immersed in the ethyl alcohol. What is the minimum speed you must give the air at the top of the straw to draw ethyl alcohol upward through a height of 1.7 cm? ____m/s

Radiation (Stefan's law)

Assuming your skin temperature is 37.2°C and the temperature of your surroundings is 21.9°C, determine the length of time required for you to radiate away the energy gained by eating a 293 Calorie ice cream cone. Let the emmissivity of your skin be 0.915 and its area be 1.22 m2. _________ hours

Thermodynamics processes law

The figure below shows how 8 moles of a monatomic ideal gas follows the three-part cycle, the first part of which involves an isothermal expansion from point A, where V = 15 m3, to point B, where V = 90 m3. (a) Provide the missing entries in the following table. Q(J) W(J) ΔU(J) A>B ____ ___

Venturi meter to find speed and volume of gas

A venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed v2 through a horizontal section of pipe whose cross-sectional area A2 = 0.0600 m2. The gas has a density of ρ = 1.80 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0300 m2 and has been substitu

Motion of merry-go-round before and after person jumps onto it

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of .667 rev/s. A 59.4 kg person running tangential to the rim of the merry-go-round at 3.38 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-ro

Velocity of an object within a pulley system

The system consists of 60-lb and 20-lb blocks A and B, respectively, and 5-lb pulleys C and D that can be treated as thin disks (see the attachment). Determine the speed of block A after block B has risen 5 ft, starting from rest. Assume that the cord does not slip on the pulleys, and neglect the mass of the cord.

Hamiltonians and Motion

A simple pendulum of length l and mass m is suspended from a point on the circumference of a thin massless disc of radius a that rotates with a constant angular velocity [(w)omega] about its central axis. Find the equation of the motion of the mass m.

Lagrangian of Particle Moving in Electromagnetic Field

An electromagnetic field is given by the potential: phi = 0 and A = ay(z-hat) + bt(x-hat) with a and b constant where 'x-hat?'z-hat?are unit vectors along the x and z directions respectively. a. Write the Lagrangian for a particle of charge q moving in this field. b. Identify any constants of the motion c. Write the

The Time and Amplitude of an Oscillator

An oscillator with a mass of 420g and a period of 0.800s has an amplitude that decreases by 2.30% during each complete oscillation. A) If the initial amplitude is 7.00cm, what will be the amplitude after 31.0 oscillations? B) At what time will the energy be reduced to 65.0% of its initial value?

Finding the Amount of Energy Absorbed by an Eardrum

A 54 dB sound wave strikes an eardrum whose area is 4.0 x 10-5 m^2. (a) How much energy (in watts) is absorbed by the eardrum per second? (b) At this rate, how long (in years) would it take your eardrum to receive a total energy of 1.0 J?

Harnessing of hydro energy

I was looking at the Vortex Hydro Energy project and I am confused on how the energy is stored and then transferred. Can someone explain this to me?

Simple Harmonic Motion Energy

A 0.53 kg mass vibrates according to the equation x = 0.49 cos 8.42t, where x is in meters, and t is in seconds. Determine the frequency in hertz. Determine the total energy in joules. Determine the kinetic energy and potential energy in joules when x = 0.26 m.

Gas mileage of car engine

When one gallon of gasoline is burned in a car engine, 1.19 x 10^8 J of internal energy is released. Suppose that 1.00 x 10^8 J of this energy flows directly into the surroundings (engine block and exhaust system) in the form of heat. If 6.0 x 10^5 J of work is required to make the car go one mile, how many miles can the car tr

Rate of change in water's temperature due to current.

Two square metal plates, each 0.1m on a side are parallel to each other and separated by distance 0.01m. the region between the plates is filled with water with conductivity 0.001 (ohm-meter)^(-1) If a potential difference is maintained between the plates, find the rate of change of temperature of the water.

Rate of production of heat

1. A certain sedentary person uses energy at an average rate of 123.29Watts. All of this energy has its ultimate origin in the sun. How much matter is converted to energy in the sun per day to supply this person? 2. If 1 kcal = 4.18 kJoule. What is the rate of energy production in kilowatts from a college student producing 1

Launching of satellite from Earth to Mars.

Assume the Earth has a circular orbit around the sun of radius and that Mars has a circular orbit around the sun of radius . To send a satellite to Mars that requires the least amount of energy the satellite is given an elliptical orbit whose perihelion corresponds to Earth's orbital distance and whose aphelion corresponds to

The Maximum Speed of Protons

Two protons are released from the res when they are 0.8nm apart. 1. What is the maximum speed they will reach? 2. When does this speed occur? 3. What is the maximum acceleration they will achieve? 4. When does this acceleration occur?

Physics - Sodium Light Wavelength and Energy

For a yellow sodium light emission, with a frequency of 5.09 x 1011 Hz a) What is the wavelength in nm? b) Calculate the energy of the light. (c = 3.00 x 108 m/s, h = 6.63 x 10-34 j-s, Rh = 2.18 x 10-18J)

Explanation of Energy Considertions in Motion

#1 A water slide is constructed so that right before the water you are moving horizontally and you fall a certain distance vertically and travel a certain distance horizontally. Given a certain amount of time (ignoring friction and air resistance). a) Find height from which you started at You are given how far person trav

Newton's laws of motion: Conservation of momentum

1) An astronaut loses contact with the hull of a space station and finds himself floating 16m from the station with zero velocity relative to it. Fortunately, he is carrying a 200W flashlight. Turning on the torch he uses it as a "light rocket? If he weighs 150kg, how long will it take to get back to the ship? Is there another w

Rotational motion and kinetic energy lost

PROBLEM 2: A playground whirl consists of a uniform disk of mass 10M and radius R. It is spinning at a rate of 2.0 rmp. A child mass M, originally at rest, steps on to the whirl. She does not slide back off. What is the final angular velocity of the whirl and the child (assuming the axis is frictionless)? What fractio

Determining Angle and Speed: Helium Example

A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times that of the neutron. The helium nucleus is observed to rebound at an angle of 43° from the neutron's initial direction. The neutron's initial speed is 6.6 x 10^5 m/s. Determine the angle at which the neutron rebounds, measured

Conservation of angular and linear momentum

(1) A particle of mass m at the end of a light string wraps itself about a fixed vertical cylinder of radius a. All the motion is in the horizontal plane. the angular velocity of the cord is w0 when the distance from the particle to the point of contact of the cylinder and string is b. find the angular velocity and tension in t

Four problems on rotational dynamics

1) How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.3 cm and a mass of 15.1 g. The laser scans at a constant tangential velocity of 1.26 m/s. Assume that the music is first detected at a radius of 20.3 mm from the center of the disk. Ignore the small circular ho

coefficient of kinetic friction between the block and table

A 0.510 kg wood block is firmly attached to a very light horizontal spring (k = 190 N/m). It is noted that the block-spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the tabl

Work done with torque and angular momentum

How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.8 cm and a mass of 15.5 g. The laser scans at a constant tangential velocity of 1.16 m/s. If we assume that the music is first detected at a radius of 20.3 mm from the center of the disk. Ignore the small circular

Oscillation and escape velocity of a particle

The potential energy function of a particle of mass is V = cx/(x^2 + a^2), where c and a are positive constants. Sketch V as a function of x. Find the position of stable equilibrium, and the period of small oscillations about it. Given that the particle starts from this points with velocity v, find the ranges of values of v for