Problem 1:

Sandra, who has a mass m = 40 kg stands on a M = 28 kg flatboat.  Her distance to the shore is 9.4 m.  She walks 2.6 m along the boat toward the shore and then stops.  How far is she away from the shore?  Assume there is no friction between the boat and the water.

Problem 2:

A small mass slides without friction down the loop track shown in the figure below.
(a)  Show that the speed at point B must be at least as large as (gR)^1/2 if the mass does not fall away from the track.
(b) What must be the height h required to achieve the speed found in (a)?  Give your answers in terms of R.

Problem: 3

A uniform carpenter's square has the shape of an L, as shown in the figure.  Locate the center of mass relative to the origin of the coordinate system.

Problem 4:

A solid iron cylinder (density = 7.87 g/cm³) of radius r = 5 cm and length l = 20 cm rolls down a ramp which has an incline of 20^o (no sliding).  The initial height is 3m above ground.
(a)  What is the magnitude of the linear acceleration at half the height?
(b)  The cylinder arrives at the bottom of the ramp. What is the angular momentum of the cylinder about its central axis if it suddenly lifted up from the ground at the two ends of this axis?

Problem 5:

A homogeneous thin rod of mass m and length 2a slides on a smooth, horizontal table, one end being constrained to slide without friction in a fixed straight line.  It is initially at rest, with its extension normal to the line, when it is struck at the free end with an impulse Q parallel to the line.
(a)  Determine the initial motion of the rod.
(b)  Show that the force exerted by the line on the rod is given by 
Q²sinq/[ma((4/3) -sin²q)²], where q is the angle between the rod and the line.

Problem 6:

Two identical uniform cylinders of radius R each are placed on top of each other next to a wall as shown.  After a disturbance, the bottom cylinder slightly moves to the right and the system comes into motion.  Find the maximum subsequent speed of the bottom cylinder.  Neglect friction between all surfaces.

Problem 7:

A pencil of length L is held vertically with its point on a desk and then allowed to fall over.  Assuming that the point does not slip, find the speed of the eraser just as it strikes the desk.  Compare this with the speed that would result from free fall from a height equal to the length of the pencil.