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A particle of mass m moves in a potential given by:
\(V(x)=-V_{0}a^{2}(a^{2}+x^{2})/8a^{4}+x^{4}\)
a) Sketch V(x) and F(x)
b) Discuss the motions which may occur. Locate all equilibrium points and determine the frequency of motion about any that are stable.
c) A particle starts at a great distance from the potential well with a velocity v0 towards the well. As it passes the point x=a, it suffers a collision with another particle during which it loses a fraction (%u03B1) of its kinetic energy. How large must %u03B1 be in order that the particle is trapped in the well? How large must %u03B1 be in order that the particle by trapped in one side of the well? Find the turning points of the new motion if %u03B1=1.
A neutron of initial kinetic energy (Eini) scatters elastically from a target nucleus which is initiallt at rest. Find the maximum and average fractional kinetic energy loss F=1-(Efinal/Einitial)
The uncertainty in the position of an electron along an x axis is given as 56 pm, which is about equal to the radius of a hydrogen atom. What is the least uncertainty in any simultaneous measurement of the momentum component px of this electron?
A) Find v so that the rod swings up and is horizontal at the max height of the bob. B) Find the minimum v so that the rod will make a complete circle C) Find v so that the tension in the rod is zero at the top of its swing.
X rays with a wavelength of 0.18 nm undergo first-order diffraction from a crystal at a 74 degree angle of incidence
A hydrulic jack in a mechanic's shop supports a car of mass M= 2.1 x 10^3 kg. What force must the pump exert on the fluid at the input to support the weight of the car
A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.73 m/s, What is the maximum possible value for d
A pump flows 100 gal/min of water. The inlet pressure is 0 psig and the outlet pressure is 20 pisg. How much electricity (kW) is required to power the motor
a)What is its velocity b)The charged ion then enters a magnetic field, B = 0.20 T, perpendicular to the field. What is the radius of the particle's circular orbit in the field
A 1.9cm × 1.9cm × 1.9cm box with its edgesaligned with the xyz-axes is in the electric field E? =(360x+150)i^N/C, where x is in meters
A dynamite blast at a quarry launches a rock straight upward, and 2s later it is rising at a rate of 15m/s. assume air resistance has no effect on the rock, analyse its speed (a) at launch and (b) 5s after launch.
Imagine that you calibrate a constant-volume gas thermometer in dry ice which has a temperature of -80.0°C and the pressure reading is 0.900atm. What is the pressure reading at the boiling point of water
A uniform diving board, 12m long and 20kg mass is placed on a platform. How far can a 60kg person walk down the board from the edge of the platform without board tipping over.
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