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    Energy

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    Energy Conservation in oscillatory motion:

    A 0.321 kg mass is attached to a spring with a force constant of 12.3 N/m. If the mass is displaced 0.256 m from equilibrium and released, what is its speed when it is 0.128 m from equilibrium?

    Quantum Mechanics: Time Independent Perturbation

    I have a negative potential, -V in the center of an inifinite square well. The well extends from -a to +a and the unperturbed wave functions are: Si sub n (x) = sq root 1/a sin(n*pi*x/2*a) for n even Si sub n (x) = sq root 1/a cos(n*pi*x/2*a) for n odd The perturbation extends from -b to +b and is given by:

    Find the kinetic energy

    Find the kinetic energy of a cylindrical shaft of mass 2.0 kg and radius 10cm rotating about its central axis at 600 rad/s a. 1800 j b. 1200 j c. 18000 j d. 12000 j

    Kinetic energy

    A neutron in a nuclear reactor makes an elastic head-on collision with the nucleus of a uranium atom initially at rest. (a) What fraction of the neutron's kinetic energy is transferred to the uranium nucleus? (The mass of the uranium nucleus is about 238 times the mass of the neutron.) (b) If the initial kinetic energy of

    Rotational Dynamics of a Solid Sphere

    A solid sphere of mass 1.0 kg and radius 0.10 m rolls down a 10 m board which makes an angle of 30 degrees to the ground. (a) What will be the sphere's speed when it reaches the ground? (b) What will be it's rotational speed? (c) What total energy will it have?

    Rotational Dynamics

    A solid sphere of mass 1.0 kg and radius of .10 m rolls down a 10 m board which makes an angle of 30 degrees to the ground. (a) What will be sphere's speed when it reaches the ground? (b) What will be its rotational speed? (c) What total energy will it have?

    Energy and Momentum: Spring Goes Around Track

    The 0.31 kg mass slides on a frictionless wire that lies in the vertical plane. The ideal spring attached to the mass has an equilibrium length of 80 mm and its spring constant is 120 N/m. The mass is released at point A, from rest. Calculate the minimum distance b, if the mass is to slide all the way around the loop to poin

    Energy and Momentum: Rebounding Ball

    A 0.075 kg ball hits a frictionless, rigid, horizontal surface with a speed of 1.2 m/s at the angle q1 = 70 deg. The angle of rebound is q2 = 62 deg. Compute: a) the speed of the ball immediately after rebound. b) the resultant impulse acting on the ball during its time of contact with the surface. See attachment for

    Energy and Momentum: Orbiting Spacecraft

    A spacecraft is traveling in a circular orbit (see attached file) around the earth at an altitude of 210 miles. When the craft reaches point A, its engines are fired for a short period, reducing its speed by 7.5%. The resulting path is the (elliptical) crash trajectory AB. Determine the angle b, measured from the nonrotating x

    Energy and Momentum - Child on a Swing

    See the attachment for a diagram of the scenario below. A child with a mass of 22 kg sits on a swing and is held in the position shown by a second child. (35 deg from vertical). Neglecting the mass of the swing, determine the tension in rope AB... a) while the second child holds the swing with his arms outstretched horizont

    A hoop of radius 0.5m; inclined plane; speed

    A hoop of radius 0.5m and a mass of 0.2kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping from a vertical distance of 3m? a. 5.4m/s b. 3.8m/s c.7.7m/s d.2.2m/s

    Ball Rolling up an Incline

    A 10.0 kg bowling ball of radius 15 cm rolls without slipping along a horizontal surface with a speed of 4.0 m/s as it approaches an incline. What is the total kinetic energy of the ball as it rolls along the horizontal? How high above the floor level will the ball reach (with no slipping) as it rolls up the incline?

    One dimension collisions

    A ball of mass 1.5kg is thrown upward. it leaves the thrower's hand with a velocity of 10 m/s. Assuming the upward direction is positive: a. how long does it take for the ball to return to the throwers hand b.what is the ball's final velocity just before it reaches the hand? c. what is the change in momentum of the ball?

    Propulsive Efficiency

    Propulsive efficiency can be defined as the useful power output over the rate of change in energy of the airflow through the engine. If useful power is thrust x velocity, and the rate of change of KE is expressed in terms of air mass flow rate, provide an expression for ηP in these terms. If the efflux pressure is brought

    Derive Expression Where Needed

    1. A motorcyclist is coasting with the engine off at a steady speed 17 m/s but enters a sandy stretch where the coefficient of friction is .80. Will the cyclist emerge from the sandy stretch without having to start the engine if the sand lasts for 15 m. If so, what will be the speed upon emerging? 2. One car has twice the

    Weather Forecasts Physical Origins

    Question: It is the middle of winter and the weatherman forecasts a cold, overcast, but dry day, with an average temperatures of -2 degrees Celsius. However, he highlights the presence of a strong wind with a wind chill factor that will make it feel like -10 degrees Celsius. What is meant by the term 'wind chill'? How can it be

    Elastic and Inelastic Collisions

    A 10 gram bullet is fired horizontally into, and becomes embedded in, a suspended block of wood whose mass is 0.890 kg. (a) How does the speed of the block with the embedded bullet immediately after the collision compare with the initial speed of the bullet? (b) If the block with the embedded bullet swings upward and its center

    Relative Motion : Kinetic and potential energy

    You (A) are in a sledge sliding down an inclined plane. (Friction is neglected). An observer (B) at the foot of the plane looks at your initial position at the top of the slide and sees your energy as potential energy (mgh). You (A) slide down to the bottom of the plane and have a velocity of V0. So the observer sees mgh = mV0

    Yet More Simple Physics

    Think about a rollercoaster. If it loaded at a height of about 500m and then dropped down to almost ground level and was followed by 7 circles where the circles height was about the same it would not work well. Explain in terms of kinetic energy, potential energy, etc. why not. (Picture included if needed).

    Thermodynamics

    An ideal gas mixture consists of 3 kg of Ar and 6 kg of CO2 gases. The mixture is now heated at constant volume from 250 K to 350 K. The amount of heat transfer is:

    Molecules in vacuum

    In an ultra-high vacuum system, the pressure is measured to be 1.00 * 10^-10 torr, the average molecular diameter is 1.00 * 10^-10 m, the average molecular speed is 500 m/s and the temperature is 300 K. Find the number of molecules in a volume of 1.00 m^3 and the mean free path of the molecules.

    Friction/Newtons Law

    Question: A child slides down a slide with a 30 degree incline, and at the bottom her speed is precisely two-thirds what it would have been if the slide had been friction-less. Calculate the coefficient of kinetic friction between the slide and the child.

    Mixed Energy Photon Beam

    A collimated gamma ray beam consists of equal numbers of 0.1 MeV and 1.0 MeV photons. If the beam enters a 15 cm thick concrete shield, what is the relative portion of 1 MeV photons to 0.1 MeV photons in the emergent beam?

    Projectile Motion of a Kicked Ball

    A soccer player kicks a ball straight up at an initial speed of 11.0 m/s: a) How high will the ball rise above his foot? b) How long does it take to return to his foot?

    Finding the lagrangian of a system

    A triangular piece of wood is free to slide, without friction, in one dimension along a table, forming a moving inclined plane. A block of wood, placed on this inclined plane only moves as the result of the triangular block moving. There is no friction between the triangular piece of wood and the block. Find the lagrangian fo

    Find the wavelength of the electron.

    Find the wavelength of an electron with energy E = 2MeV. [Hint: The deBroglie relation lambda = h/p is correct at all energies, but since this energy is relativistic, you will have to use the relation E^2 = (pc)^2 + (mc^2)^2 to find p.]

    Electrical Potential Energy

    A 100-µF parallel-plate capacitor is charged to 500 V. It is then disconnected from the charging source and insulated. (a) How much energy is stored on the capacitor? (b) If the plates are pulled apart to a separation that is twice their initial separation, what energy is stored on the capacitor? (c) If the answers are not i

    Special Relativity and Schwarzschild Radius

    1. A particle is measured to have a kinetic energy that is four times its rest as energy. How fast is the particle moving? Express the speed as a fraction of c. 2. Write down the transformations that relate the electric field E and the magnetic field B in two different inertial frames. Use your result to show that E*B is the

    Harmonic Oscillator and Wave Packets

    Consider the 1-D harmonic oscillator, with Hamiltonian H=p²/2m+½mw²x²=hw(a¬a+1/2), and with energy eigenstates H|n}=En|n}=hw(n+1/2)|n}. The eigenvectors of the annihilation operator a are known as coherent states: a|z}=z|z}, where z is in general a complex number (a is not Hermitian, so z is not necessarily real). Take |z}