# Test 2 - Al Akhawayn University ```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 = &frac12; 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:
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