Name
Period
Date
Dynamics Worksheet 4
1. In the diagram to the right, blocks A and B have masses
of m A and mB , respectively. Answer all question in terms
of m A , mB , mC ,  sA ,  kA ,  sC ,  kC and g .
a. Determine the minimum mass ( mC of block C ) that
must be placed on A to keep A from sliding if the
coefficient of static friction between A and the table is
 sA . Begin by drawing and labeling the forces acting
on the system.
C
A
C
A
B
Suppose that block C has less mass than that found in (a), but enough mass to keep
it moving without sliding on A. The coefficient of kinetic friction between the table
and A is  kA .
b. Find an expression for the acceleration of the system. Begin by drawing and
labeling the forces that now act on the system.
C
A
B
B
Dynamics Worksheet 4
c. Draw and label the forces
acting only on block C as
it moves without slipping
on block A.
page 2
d. The coefficient of static friction between
block C and block A is  sC . What is the
minimum mass block C can have if it is to
move without slipping on block A as the system
accelerates as found in (b)?
C
Suppose that block C has even less mass than that found in (d), so that it slips on
block A. The coefficient of kinetic friction between block C and block A is  kC .
e. Draw and label the
forces acting only on
block C as it slips on
block A.
f. What is the new acceleration of block C?
C
g. Block C is suddenly lifted off of block A . What is the acceleration of block A , if
the coefficient of kinetic friction between the table and A is  kA ? Begin by
drawing and labeling the forces acting on the new system.
A
B
Dynamics Worksheet 4
page 3
2. A 40. kg slab rests on a frictionless floor. A 10. kg
100. N
10. kg
block rests on top of the slab. The coefficient of
static friction between the block and the slab is
40. kg
 s  0.60 , whereas the coefficient of kinetic friction
Frictionless
is  k  0.40 . The 10. kg block is pulled by a
horizontal force with a magnitude of 100. N .
a. Draw and label the forces acting on each block. Be sure to include all forces of
interaction between the blocks.
10. kg
40. kg
b. Does the top block accelerate with respect to the slab? How do you know?
c. What is the resulting acceleration of the top block?
Dynamics Worksheet 4
page 4
d. What is the magnitude of the resulting acceleration of the slab?
.

3. A 25 kg box moves with a position given by x (t )  (3.5 m 4 )t 4  (6.0 m )t  4.0 m .
s
s
What is the net force acting upon the box at t  4.0 s and t  7.0 s ?