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Pendulum and Spring Questions

____ 1. A simple pendulum, 2.0 m in length, is released with a push when the support string is at an angle of 25 deegree from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, what is its speed at the bottom of the swing? (g = 9.8 m/s2) a. 2.3 m/s b. 2.6 m/s c. 2.0 m/s d. 1.8 m/

The motion of spring when the length of string shortened

Consider a simple plane pendulum consisting of a mass m connected to a string of length L. After the pendulum is set in motion , the length of the string is shortened at a constant rate: dL/dt = -k The suspension point remains fixed. Compute the following: a) The Lagrangian and Hamiltonian functions b) Compare

Lagrange dynamics of a rolling ball inside a hollow cylinder

A sphere of radius r is constrained to roll without slipping on the inner surface of the lower half of a hollow cylinder of inside radius R. Determine the following: a) the Lagrangian function. b) The equation of constraint c) Lagrange's equation of motion d) Frequency of SMALL oscillations

Lagrange's Equation for a double pendulum

A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lengths of rigid, massless, rod and bobs of equal mass and if both pendula are confined to move in the same plane find Lagrange's equation of motion for the system...Do NOT assume small angles.

Non-linear problems in oscillation

A mass, m, moves in one dimension and is subject to a constant force +F1 when x<0 and to a constant force -F1 when x>0. a) Describe the motion with a phase diagram b) Calculate the period of the motion in terms of: m, F1, and the amplitude A (disregard damping)

Modern Physics: Determining Gravitational Potential Energy

When an 81.0 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.00 x 10^3 J. By how much does the potential energy of an 18.0 kg child increase when the child climbs a normal staircase to the second floor?

Gravitational potential energy

Relative to the ground, what is the gravitational potential energy of a 55.0 kg person who is at the top of the Sears Tower, a height of 443 m above the ground?

Solar Intensity on a space flight

A possible means of space flight is to place a perfectly reflecting aluminized sheet into Earth's orbit and use the light from the Sun to push this solar sail. Suppose a sail of area 6.00 X 10^4 m^2 and mass 6000 kg is placed in orbit facing the sun. The solar intensity of 1380 W/m^2. a. What force is exerted on the sail?

Millikan experiment, Compton effect, photoelectric effect

1. In a Millikan oil drop experiment the terminal velocity of the droplet is observed to be vt = 1.5 mm/s. The density of the oil is = 830 kg/m3 and the viscosity of air is = 1.82 10-5 kg/m s. Use the following equations to find the values below. Calculate the droplet radius. µm (b) Calculate the mass of the drop

motion of a cookie jar on an incline

Show ALL your work, including the equations used to solve the problems. A cookie jar is moving up a 40º incline. At a point 55 cm from the bottom of the incline (measured along the incline), it has a speed of 1.4 m/s. The coefficient of kinetic friction between jar and incline is 0.15. a) How much farther up the incline

Find Final Energy for Absorption of Photon by Electron

An electron in a 10.2 nm one dimensional box is excited from the ground state into a higher energy state by absorbing a photon of electromagnetic radiation with a wavelength of 1.369 10^-5 m. Determine the final energy state for this transition.

Classical mechanics: Motion in two dimension.

1. A river flows due east at 1.00 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.0 m/s due north relative to the water. (a) What is the velocity of the boat relative to shore? (b) If the river is 280 m wide, how far downstream has the boat moved by the time it rea

Classical Mechanics.

1. A flea is able to jump straight up about 0.64 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100 story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle

Elastic Collision of Air-Track Glider

An air-track glider with an initial speed of 4.0 m/s has a head-on collision with another glider at rest that is three times as massive. What are the final speed and directions of the gliders if the collision is elastic? I believe the answer is V1 = -2.0 m/s and V2 = +2.0 m/s. I need to see each step and formula to solve this qu

What is the ratio of the masses of the two marbles?

A child playing marbles shoots a marble directly at another marble at rest. The first marble stops, and the second marble continues in a straight line with the same speed that the first marble had initially. What is the ratio of the masses of the two marbles? I need to see each step and formula to solve this question.

A block slides on a semicircular frictionless track.

A block slides on a semicircular frictionless track. If it starts from rest at position (A), what is its speed at the point marked (B)? A picture of the block and slide is attached as a jpeg file. I believe the answer is 3.7 m/s. I need to see each step and formula to solve this question.

Rotational and Linear Speed & Kinetic Energy

A full keg of beer weighs 170 lbf. The beer inside the keg weighs 124lbf and the container weighs 46lbf. The keg is placed at the top of ramp length L=8ft. from the back of your pickup truck to the ground and released. Find: 1. The rotational and linear speed of the keg at the bottom of the ramp. 2. The kinetic engery of th

Illuminance and intensity of light.

1). According to its package, a 100 watt light bulb emits 1140 lumens. For simplicity, assume the bulb provides isotropic illumination and ALL its emission is at 555 nm. A video camera is advertised as having "0.2 lux sensitivity", meaning it can record objects which receive at least this illuminance. In a dark room with no

Window Energy Transfer

A window has a glass surface area of 1.6x10^3 cm^2 and a thickness of 3.0 mm. a) Find the rate of energy transfer by conduction through the windows when the temperature of the inside surface of the glass is 70 degrees F and the outside temperature is 90 degrees F. b) Repeat for the same inside temperature and an outside t

Peak Electric Field in the Wave

A point source emits light energy uniformly in all directions at an average rate Po with a a single frequency f. Show that the peak electric field in the wave is given by: Eo = (µocPo/2 r2) (Everything is under the square root) I think we have to prove that the peak electric field is that equation but once again I am lost

Particle in a potential well

A particle of mass m moves in the potential V(x) = -g*delta(x) x>-a infinity x<-a (delta (x) = dirac delta function) a. Without worrying about continuity or boundary conditions, write down the general solution of the Schrodinger equation for a bound state (energy E<0) in regions( -a less than x les

Oscillations: The spring with varying force constant

Please see attachment. Thanks. --- Many real springs are more easily stretched than compressed. We can represent this by using different spring constants for and for . As an example, consider a spring that exerts the following restoring force: A mass on a frictionless, horizontal surface is attached to this spring,

Force of Friction and Gravitation Potential Energy

An electric winch pulls a 30.9 kg case of soap up a roller incline 3.01 m high in 3.15 seconds. The case starts from rest at the bottom and is moving 4.02 m/s at the top of the incline. The force of friction on the box is 39.4 N. a) What is the increase in gravitational potential energy of the box? b) Calculate the length

Angular Speed of Rotating Hoop

A string is wrapped several times around the rim of a small hoop with radius r and mass m . The free end of the string is held in place and the hoop is released from rest. Calculate the angular speed of the rotating hoop after it has descended a distance, h. (See attached file for diagram and figures)