Weekend AP 2D Quiz #11 KEY
(e) Calculate the distance that the 1.5 kg block descends in 0.40 s.
Block A of mass 2.0 kg is pulled along a horizontal table by a force of 15 N, which is applied
by a light string that passes over a light frictionless pulley, as shown above. The coefficient
of kinetic friction between the block and the surface is 0.25.
(a) On the dot below, which represents the block, draw and label the forces (not
components) that act on the
block as it is pulled across the table.
1998M3. Block 1 of mass m1 is placed on block 2 of mass m2 which is
then placed on a table. A string connecting block 2 to a hanging mass
M passes over a pulley attached to one end of the table, as shown
above. The mass and friction of the pulley are negligible. The
coefficients of friction between blocks 1 and 2 and between block 2 and
the tabletop are nonzero and are given in the following table.
(b) Calculate the magnitude of the acceleration of the block.
Express your answers in terms of the masses, coefficients of friction, and g, the acceleration
due to gravity.
a.
Suppose that the value of M is small enough that the blocks remain at rest when
released. For each of the following forces, determine the magnitude of the force and draw
a separate Free Body Diagram for:
i. The normal force N1 exerted on block 1 by block 2
ii. The friction force f1 exerted on block 1 by block 2
iii. The force T exerted on block 2 by the string
iv. The normal force N2 exerted on block 2 by the tabletop
v. The friction force f2 exerted on block 2 by the tabletop
The applied 15N force is removed. Block B of mass 1.5 kg is now hung downwards on the
string.. The system
is released from rest so that the 1.5 kg box descends and the 2.0 kg block is again pulled
across the table.
(c) Calculate the acceleration of the 1.5 kg block as it descends.
(d) Calculate the tension in the string connecting the two blocks.
b. Determine the largest value of M for which the blocks can remain at rest.
1997B1. A 0.20 kg object moves along a straight line.
The net force acting on the object varies with the object's
displacement as shown in the graph above. The object
starts from rest at displacement x = 0 and time t = 0 and is
displaced a distance of 20 m. Determine each of the
following.
a. The acceleration of the particle when its displacement x is 6 m.
c.
d.
Now suppose that M is large enough that the hanging block descends when the blocks
are released. Assume that blocks 1 and 2 are moving as a unit (no slippage). Determine
the magnitude a of their acceleration.
b.
The time taken for the object to be displaced the first 12 m.
c.
The amount of work done by the net force in displacing the object the first 12 m.
Now suppose that M is large enough that as the hanging block descends, block 1 is
slipping on block 2. Determine each of the following.
i. The magnitude a1 of the acceleration of block 1
ii. The magnitude a2 of the acceleration of block 2
d. The speed of the object at displacement x = 12 m.
b.
Block B strikes the floor and does not bounce. Determine the time t = t1 at which
block B strikes the floor.
1
2
(b) y  at 2
t
2y
a
2h
g
2


4h
g

c.
2
h
g
Describe the motion of block A from time t = 0 to the time when block B strikes the
floor.
Accelerate at g/2 till block B hits the deck
d.
Describe the motion of block A from the time block B strikes the floor to the time
block A leaves the table.
Moves at constant speed till it falls off table
e. Determine the distance between the landing points of the two blocks.
v 2  vo 2  2ay v  2ay
y
e.
The final speed of the object at displacement x = 20 m.
1 2
at
2
x  vt
f.
The change in the momentum of the object as it is displaced from x = 12 m to x = 20 m
1998B1 Two small blocks, each of mass m, are connected by a
string of constant length 4h and negligible mass. Block A is
placed on a smooth tabletop as shown above, and block B
hangs over the edge of the table. The tabletop is a distance 2h
above the floor. Block A is then released from rest at a
distance h above the floor at time t = 0. Express all algebraic answers in terms of h, m, and
g.
a.
Determine the acceleration of block A as it descends.
(a)
Block B: ma  mg  T Acceleration is the same
Block A:
ma  T
ma  ma  mg  T  T a  a  g
2a  g
a
g
2
t
2y
a
g
 2  h
2

2  2h 
g
 4h 
4 gh 2
 gh 
 
g
 g 


 4h 2
gh
4h
g

2h