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# Classical Mechanics

### Minimum Coefficient of Static Friction

For the situation shown in the figure, what is the minimum coefficient of static friction between the block and the surface that will keep the block from moving? (F1 = 5.0 N, F2 = 4.0 N, and m = 5.0 kg.) See Attached

### Classical Mechanics: Crate and Friction

A student could either pull or push, at an angle of 300 from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is 0.20. The crate is to be moved a horizontal distance of 15 m. (a) Compared with pushing, pulling requires the student to do (1) less,

### Physics - Classical Mechanics - Inclined Plane

A packing crate is placed on a plane inclined at an angle of 350 from horizontal. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane? Justify your answer.

### Residence Time of Water

A stable and highly soluble pollutant is dumped into a lake at the rate of 0.19 tonnes per day. The lake volume is 2E7 m3 and the average water flow-through rate is 8E4 m3 per day. Ignore evaporation from the lake surface and assume the pollutant is uniformly mixed in the lake. What eventual steady-state concentration will t

### 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 - Rotational Motion for Classical Motion

A 1.2 kg grindstone in the shape of a uniform cylinder of radius 0.25 m acquires a rotational rate of 1800 rev/s from rest over a 6.0 s interval at constant angular acceleration. Calculate the torque delivered by the motor.

### 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.

### A ball with a mass of 200 g is whirled in a circle at the end of a string 100cm long whose breaking strength is 100 N. ...

1. A ball with a mass of 200 g is whirled in a circle at the end of a string 100cm long whose breaking strength is 100 N. neglecting gravity, the maximum speed of the ball is approximately. 2m/s 7m/s 10m/s 50m/s 2.A 1-kg object is moving at 10m/s. To double its kinetic energy, its speed should be increased to approximatel

### 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?

### Grey Construction Case Study: Minimizing Cable Distance

12-23) Grey Construction would like to determine the least expensive way of connecting houses it is building with cable TV. It has identified 11 possible branches or routes that could be used to connect the houses. The cost in hundreds of dollars and the branches are summarized in the following table. (a) What is the least expe

### Harmonic Oscillations 2 - A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b_1, the amplitude is A_1 when the driving angular frequency equals sqaureroot {k/m}. a) In terms of A_1, what is the amplitude for the same driving frequency and the same driving force amplitude F_{max}, if the damping constant is 3b_{1}? b) In terms of A_1, what is the amplitude for the same driving frequency and the same driving force amplitude F_{max}, if the damping constant is b_{1}/2?

A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b_1, the amplitude is A_1 when the driving angular frequency equals sqaureroot {k/m}. a) In terms of A_1, what is the amplitude for the same driving frequency and the same driving

### 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