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School of Science and Engineering Al Akhawayn University Test # 2 Phy1401-01, Spring 2003 Instructor: Dr. H. Darhmaoui Date: April 18, 2003 1) A spool of wire of mass M and radius R is unwound under a constant force F (Figure 1). Assuming the spool is a uniform cylinder (Icylinder = ½ M R2) that doesn’t slip (friction is present). Show that (a) The acceleration of the center of mass is 4F/3M and (b) The force of friction is to the right and equal in magnitude to F/3. (c) If the cylinder starts from rest and rolls without slipping, what is the speed of its center of gravity after it rolled through a distance d? F M R Figure 1 2) An 8.00 g bullet is fired into a 2.50 kg block initially a rest at the edge of a frictionless table of height 1.00 m (Figure 2). The bullet remains in the block, and after impact the block lands 2.00 m from the bottom of the table. Determine the initial speed of the bullet. 8.00 g Figure 2 2.50 kg 1.00 m 2.00 m 3) A 10 kg monkey climbs up a 120 N uniform ladder of length L as in figure 3. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is attached to the wall by a horizontal rope. (a) Draw a free body diagram for the ladder. (d) Find the tension in the rope when the monkey is one third the way up the ladder. Figure 3 Solution: