{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# a6 - (c Discuss the path that the particle takes in its...

This preview shows page 1. Sign up to view the full content.

Phys 263/Amath 261 Assignment 6 Due: Friday, July 11, 2008 (in class) 1. A central force-ﬁeld allows a particle to move in a logarithmic spiral: r = ke αθ (1) where k and α are constants. (a) Find the force law associated with this orbit. (b) Determine r ( t ) and θ ( t ) for the orbit. (c) What is the total energy of the orbit? 2. A particle with mass m = 1 in straight-line motion with speed V approaches an exotic planet from a large distance. Far away, it appears as though the body will miss the planet by a distance p . The planet however exerts a central force ﬁeld with strength F = - r 3 , (2) where the constant γ = 8 p 2 V 2 9 . (3) (a) Find the orbit of the particle, r ( θ ). (b) Find the distance of closest approach of the particle, and its speed at that instant.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (c) Discuss the path that the particle takes in its orbit, including a rough sketch. 3. Integrate directly the equation θ ( r ) = Z ( L/μr 2 ) dr r 2 μ ± E-V ( r )-L 2 2 μr 2 ² (4) to obtain the equation of motion r ( θ ) for the inverse-squared attractive force ﬁeld. 4. A particle moves in an elliptical orbit in an inverse-square law central force ﬁeld. If the ratio of the maximum angular velocity to the minimum angular velocity of the particle in its orbit is n , then show that the eccentricity of the orbit is ± = √ n-1 √ n + 1 . (5) 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online