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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

Normal modes of oscillation

AB and BC are two rods, smoothly jointed at B, and suspended from a smooth fixed support A. The rods AB and BC are each of length l. AB has mass m, BC has mass 3m/2. Calculate the periods of the normal modes of oscillation in the vertical plane.

Conservative Forces and Potential Energy

How does on check a force to see if the force is conservative (using the curl)? Given a force how does one calculate the potential energy? Are the following forces conservative a) F(subx) = axz+bx+c, F(suby) = axz + bz, F(subz) = axy + by b) F(a vector) = e(sub r) a/r where a, b, c are constants and e(sub r) is

energy band structure of the material

1. A material is tested at 1 atmosphere and found to be an insulator. It is then very strongly compressed and found to have very much increased conductivity. Speculate on what changes may be happening to the energy band structure of the material.

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

Elastic Collisions

A ball tossed upward with a speed of 4.27 m/s from 1.52 meters above the floor fall to the floor and bounces to a height of 2.38 meters. Is the collision with the floor elastic? I need to see each step and formula to solve this question.

Determining the elasticity of a collision

A steel ball is dropped from a height of 2.37 meters onto a flat stone slab. On rebounding, the sped of the ball is 3.94 m/s when it is 1.52 meters above the stone slab. Is the collision elastic?

Two Pendulums

Two pendulums are hung adjacent to each other as shown in the picture. Bob #1 has a mass m, and bob #2 has a mass 2m. Bob #1 is pulled aside until the support string makes an angle of 45 degrees with the vertical direction and then released. When the bobs collide, they stick together. What is the maximum angle made by the suppor

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.

Motion of a freely falling body

An egg falls from a nest at a height of 3.08 meters. What speed will it have when it is 0.5 meters from the ground? Neglect air friction. 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.

Value of the spring constant k

A 750-gram air-track glider slides along at a speed of 0.85 m/s until it hits a spring attached to the end of the very heavy track. The spring is compressed by 1.35 cm at the maximum compression. What is the value of the spring constant k? I need to see each step and formula to solve this question.

Potential Energy Example Questions

A 0.302-kg coffee mug rests on a table top 0.740 meters above the floor. A) What is the potential energy of the mug with respect to the floor? B) What is the potential energy with respect to the counter top 1.100 meters above the floor? I need to see each step and formula to solve this question.

Ratio of Kinetic Energies

Sam can throw a baseball twice as fast as can his little brother, Bill. How many time as much kinetic energy can Sam give the baseball as Bill can?