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    Classical Mechanics

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    Deformed cylinder and its final volume

    A cylindrical shell is deformed as shown in the diagrams. Find a relationship between the given quantities, if the initial and final volumes are the same.

    Physics: Magnitude and Direction

    Find the magnitude and direction of the resultant which has a component of -20 N and vertical component of -30 N. with graphic solution.

    Torque of Particles about the Origin

    What is the torque on the particle about the origin? [See the attached Question File.] Force = -12 N is exerted on a particle at = (5 + 5 ) m. What is the torque on the particle about the origin? ( + + ) N·m

    Example PhysicsProblem: Classical Mechanics

    The 1.4 kg, 20 cm diameter disk in Figure P13.69 is spinning at 200 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 4.0 s? (See the attached question file)

    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?

    Falling Bodies from the Plane

    A plane is traveling at a speed of 250 miles/hr at an altitude of 600 feet. How far before the target must the plane drop an object to insure it hits the target?: a.) 6.12 miles b.) 1.530 miles c.) 0.425 miles d.) 8.35 miles.

    Center of Mass of a Plate

    Calculate the centre of mass of the sheet in figure 1 attached. The sheet has a uniform thickness & density. See the attached file.

    Elasticity: Lifting a Mass with a Hoist

    The upper pulley of a hoist is bolted to an iron beam with two 16 diameter steel bolts. a) Is it safe to lift a 2-ton mass with the hoist? b) What is the largest mass that can be lifted with the hoist? Ssteel=7.0x10^10Pa. The maximum safe strain in the bolts is 10^-3.

    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

    Lagrangian and Hamiltonian's Mechanics: Write down the Lagrangian L for two particles of equal mass m1 = m2 = m, confined to the x-axis and connected by a spring with potential energy U = ½ k x^2. (Here x is the extension of the spring, x = (x1- x2 -l), where l is the spring's outstretched length, and that mass l remains to the right of mass 2 at all times.] (b) Rewrite L in terms of the new variables X = ½(x1+x2) (the CM position) and x (the extension) and write down the two Lagrange equation of X and x (c) Solve for X(t) and x(t) and describe the motion.

    Lagrangian and Hamiltonian's Mechanics: Write down the Lagrangian L for two particles of equal mass m1 = m2 = m, confined to the x-axis and connected by a spring with potential energy U = ½ k x^2. (Here x is the extension of the spring, x = (x1- x2 -l), where l is the spring's outstretched length, and that mass l remains to

    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

    Water Displacement Problem

    Assume that a 2400 ton (1 ton=2000 lbs) battleship with a length and width (approximated as a rectangle) of 110x12 meters is made out of just steel (density of steel=7.86 g/cm^3). If half of the metal of the ship is to be below the surface of the water then (a) how much volume will be available for storage in the ship below wa

    Hermitian Operator Matrix

    The operator Q is given by the matrix: Q ( 1 i ) (-i -1) a. Determine the matrix corresponding to Q. b. Is Q Hermitian? c. Find the Eigenvalues of Q d. For each eigenvalue in part (c), determine the corresponding eigenvector See attachment for better symbol representation.

    small piece of "post-it"-size paper and large wooden rectangle

    You have a small piece of "post-it"-size paper and a large wooden rectangular block. If you cannot crumple the paper or take both to a vacuum chamber, how would you ensure that both drop to the floor in the same time from the same height? Please list me two ways this can be accomplished without anything else (string, rubberband,

    The 150-lb ball shown is suspended on a string AB

    The 150-lb ball shown is suspended on a string AB and rests again the frictionless vertical wall. The string makes an angle of 30 with the wall. The tension in the string is: a. 173 lb b. 500 lb c. 300 lb d. 600 lb e. none of these Please see attached file for diagram

    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?

    Speed and Distance

    The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 53 miles per hour?

    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

    amplitude and phase of Driven harmoic oscillators

    See attached file for full problem description. 1. Driven harmoic oscillators Suppose that a driven harmoic oscillators with belta = 1/3w0 is driven with force F = F0cos(wt) with driven frequency w = 1/3w0. Find the amplitude 'D' and phase a of the motino x(t) = Dcos(wt- a). expressing them purely in terms of F0, k and nume

    Classical Mechanics: Fourier Problem.

    2. Obtain the Fourier representation of the output of a full-wave rectifier. Plot the first three terms of the expansion and compare with the exact function. Note: when they say the 'output of a full wave rectifier' they mean the function F(t) = [sin (w4*t)] The angular frequency of the unrectified signal is labeled w4. Think

    Solid sphere and a cylinder kinetic energy

    A solid sphere and a cylinder of the same mass and radius roll without slipping at the same speed. It is correct to say that the total kinetic energy of the solid sphere is more than the total kinetic energy of the cylinder. less than the total kinetic energy of the cylinder. equal to the total kinetic energy of

    Disk, Hoop, and a Sphere Rolling Down an Incline

    A disk, a hoop, and a sphere are released at the same time at the top of an inclined plane. They all roll without slipping. In what order do they reach the bottom? A. disk, hoop, sphere B. sphere, disk, hoop C. hoop, sphere, disk D. hoop, disk, sphere.