Equation for distance of the closest approach to the origin

Assignment Help Mechanical Engineering

Reference no: EM13709667

Consider a particle of mass m moving in two dimensions between two perfectly reflecting walls which intersect at an angle alpha at the origin. Assume that when the particle is reflected, its speed is unchanged and its angle of incidence equals its angle of reflection. The particles is attracted to the origin by a potential U(r)=-c/r^3 where c is some constant and r is the distance of the particle to the origin. Now start the particle at a distance R from the origin on the x-axis with a speed v and initial angle with x-axis theta. Show that the magnitude of the angular momentum is conserved when it reflects off a wall. Show that the angular momentum of the particle is conserved in between collisions (i.e. when the particle is moving in free space under the potential field U(r)). Determine the equation for distance of the closest approach to the origin.

Reference no: EM13709667

Questions Cloud

Determine the pressure drop across the turbine : A turbine is supplied with 0.6 m3 /s of water from a 0.3 m diameter pipe. The discharge pipe is 0.4 m in diameter. Determine the pressure drop across the turbine if it delivers 60 kW of power.

Power cycle operating between hot and cold reservoirs : The data listed below are claimed for a power cycle operating between hot and cold reservoirs at 1500 K and 450 K, respectively. For each case, determine whether the cycle operates reversibly, operates irreversibly, or is impossible.

Description of the implications of covert research : In what circumstances might covert research be justified and How would you deal ethically with this. Define me what covert research is.

Air behaves as an ideal gas for steady-state operation : Air enters a one-inlet, one-exit control volume at 6 bar, the pressure is 3 bar, the temperature is 456.5 K, and the velocity is 300 m/s. The air behaves as an ideal gas for steady-state operation, determine: (a) the mass flow rate in kg/s (b) the ex..

Equation for distance of the closest approach to the origin : Consider a particle of mass m moving in two dimensions between two perfectly reflecting walls which intersect at an angle alpha at the origin. Assume that when the particle is reflected, its speed is unchanged and its angle of incidence equals its an..

Single crystal wire of iron at room temperature : A single crystal wire of iron at room temperature is subjected to a tensile stress along [010]. Calculate the resolved shear stress in the (110) plane, along the [-111] direction, if the applied stress is 7500 psi.

In metal injection molding what is the green part made of : In metal injection molding what is the green part made of?, when is the green part made?, how is a brown part created?, and how does the final metal molded part become fully dense with cast metal properties?

Explanation of add a new location- tesla''s decision : Using a real service or manufacturing operation that you have experience with, evaluate the elements that they would have to consider to expand their operation to another facility.

Find the speed of the water leaving the nozzle : A fire truck draws water from an open constant-level reservoir through a hose of 0.2 ft2 cross section. The water is discharged from the pump through another 0.2 ft2 hose to a surge tank pressurized to 120 psig with air at the top. The pump adds 970 ..

User Account

All Pages