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Classical Mechanics

Physics - Mechanics - Buoyant Force

An undersea research chamber is spherical with an external diameter of 5.40 m. The mass of the chamber, when occupied, is 70400 kg. It is anchored to the sea bottom by a cable. Calculate the following. (a) the buoyant force on the chamber N (b) the tension in the cable N

Harmonic and Annihilation Operators

An important set of operators that are often used in discussing the harmonic oscillator are the creation and annihilation operators a and a^t. a = (1/ (2^(1/2)) )(X + iP) a^t = (1/ (2^(1/2)) )(X - iP) X and P are the coordinate and the conjugate momentum so that [X,P] = i©¤ 1. Show that a is not a Hermitian ope

Classical Mechanics

A satellite of mass 205 kg is launched from a site on the Earth's Equator into an orbit at 175 km above the surface of Earth. (a) If the orbit is circular, what is the orbital period of this satellite? s (b) What is the satellite's speed in orbit? m/s (c) What is the minimum energy necessary to place this satellite in

Classical Mechanics

A satellite has a mass of 100 kg and is located at 2.00 x 10^ 6 m above the surface of earth. (A) What is the potential energy associated with the satellite at this location? (B) What is the magnitude of the gravitational force on the satellite?

Physics - Mechanics - Rotational Motion.

A sample of blood is placed in a centrifuge of radius 15.0 cm. The mass of a red blood cell is 3.0 x 10^ -16 kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.0 x 10^ -11 N. At how many revolutions per second should the centrifuge be operated?

Physics - Classical Mechanics - Motion

A race car starts from rest on a circular track of radius 293 m. The car's speed increases at the constant rate of 0.800 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, find the following. (a) the speed of the race car (b) the distance traveled (c) the elapsed time

Question about Physics - Mechanics - Force

A cubic box of volume 4.2 x 10^ -2 cubic meters is filled with air at atmospheric pressure at 20.0 degrees Centigrade. The box is closed and heated to 175 degrees C. What is the net force on each side of the box?

Physics - Mechanics - Rotational Motion..

A constant torque of 25.0 N M is applied to a grindstone whose moment of inertia is 0.130kg m^2. Using energy principles and neglecting friction, find the angular speed after the grindstone has made 15.0 revolutions.

Physics - Mechanics - Rotational Motion..

A coin with a diameter of 1.80 cm is dropped onto a horizontal surface. The coin starts out with an initial angular speed of 17.6 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.72 rad/s2, how far does the coin roll before coming to rest?

Classical Mechanics for Tangential Direction

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s^2. The child is standing 4.65m from the center of the merry-go-round. What angle does the acceleration of the child make with the tangential direction?

Physics - Work-Energy Theorem

A 70 kg person uses 204.0 kJ of energy to walk a kilometer. This energy comes from "burning" glucose, but only about 30.0% of the heat of combustion of glucose can be used for propulsion. The rest is used for other body functions or is wasted as heat. Assuming that a sugar-coated cereal contains 30.0% sugar (which can be conside

Physics - Mechanics - Force..

A 0.500 kg mass is suspended from a spring. A force of 1.00 N stretches it an additional 45.0 mm. Find the force constant of the spring, and the period of the motion which results when the mass is released.

Example Physics Word Problems

See the attached file. 1. A piece of string wraps around a cylinder 8 times. The length of the string is 14 cm. calculate the circumference of the cylinder. 2. The mass of full bottle of cooking oil is 1.30 kg, when exactly half of the oil has been used; the mass of the bottle plus the remaining oil is 0.90kg.what is the ma

Mechanics: Determining Center of Mass

A 60 kg woman and a 90 kg man stand 10.0 m apart on frictionless ice. (a) If they hold on to the two ends of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now? In meters. (b) How far will the man have moved when he collides with the woman? In meters.

Finding Tension in a Cable

Find the tension of (T) in the cable and the magnitude and direction of the force (C) exerted on the strut of the picot. Let the weight of the suspended object be 1000LBS (neglect the weight of the strut). Please see the attached diagram.

Eigenvalues and eigenvectors of sample matrix

2. Show that the operator delta^2/delta(x^2) is Hermitian given square integrable functions. 3a. Find the eigenvalues and eigenvectors of the matrix below. Show all steps. A = [1, 0, 1; 0, 2, 0; 1, 0, 1] 3b. Construct the matrix U and show that is diagonal with the appropriate values along the diagonal elem

Physics - Classical Mechanics Problem

Please help with the following problem. A 2.50 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 7.50 kg object, as shown in the figure. Find the magnitude of the acceleration of the two objects and the tension in the string. Show all wor

Physics - Classical Mechanics - Projectile Motion

1. Derive the formula for the vertical distance, y and horizontal distance, x traveled by a projectile fired at an angle of projection 0, below the horizontal. 2. A man throws a stone upward at an angle of 30° with the horizontal. It lands 60 m measured horizontally and 2 m below his arm measured vertically. Determine the ti

Circular motion and Gravitation

Circular motion and Gravitation - 1. A car is traveling at 20 mi/h on a level road where the coefficient of static friction between the tires and the road is 0.8. Find the minimum turning radius of the car. 2. The acceleration of gravity on the surface of Mars is 0.4 g. How much will a person weigh on the surface of Mars i

Calculating Rope Tension

A weight of 100N is supported vertically by two ropes, one making 60° above to the horizontal to the right and the other making an angle of 37° above the horizontal to the left. Find the tension in the ropes.

Projectile Motion - Tennis

A tennis player standing 12.6 m from the net hits the ball at 3.00 degrees above the horizontal. To clear the net , the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

Simple Harmonic Motion: Equivalent force constant of springs

Two springs with the same unstretched length, but different force constants and are attached to a block with mass on a level, frictionless surface. Calculate the effective force constant in each of the three cases depicted in the figure. a). Express your answer in terms of the variables k1, m, k2 k_eff -c = b) An object

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?

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