Assignment 2

Problem 1:

A 90 kg fullback running east with a speed of 5 m/s is tackled by a 95 kg opponent running north with a speed of 3 m/s.  If the collision is perfectly inelastic, calculate the speed and the direction of the players just after the tackle.

Problem 2:

A ball of mass M on a frictionless horizontal table is pulled by a constant horizontal force F.  A coiled up rope of mass per unit length r is attached which uncoils as the body moves. 
(a)  By taking into account the uncoiling of the rope, derive an expression for the speed of the ball as a function of distance traveled.
(b)  Evaluate the terminal speed of the ball, assuming a very long rope.

Problem 3:

Three elastic spheres of equal size are suspended on light strings as shown; the spheres nearly touch each other.  The mass M of the middle sphere is unknown; the masses of the other two spheres are 4m and m.  The sphere of mass 4m is pulled sideways until it is elevated a distance h from its equilibrium position and then released.  What must the mass of the middle sphere be in order for the sphere of mass m to rise to a maximum possible elevation after the first collision with the middle sphere?  What is that maximum elevation H?


Problem 4:

A light flat ribbon is placed over the top of a triangular prism as shown in the diagram.   Two blocks are placed on the ribbon.   The coefficients of static and kinetic friction between the ribbon and the blocks are μs and μk, respectively.  There is no friction between the ribbon and the prism.  The angle θ and the masses of the blocks m and M are given.  Assuming that M > m, find the acceleration of the ribbon along the prism after the blocks are simultaneously released.  Consider all possible cases.

Problem 5:

A rocket of initial mass m0 ejects fuel at a constant rate km0 and at a velocity v' relative to the rocket shell of mass m1.
(a)  Show that the minimum rate of fuel consumption that will allow the rocket to rise at once is k = g/v' where g is the gravitational acceleration. 
(b)  Find the greatest speed achieved and the greatest height reached under that condition.