Name
Period
Date
Dynamics Worksheet 3
John
Ringo
Paul
Tension = 150 N
George
12.0 kg
20.0 kg
15.0 kg
Tension = 222 N
1. Four penguins (John, Paul, George, and Ringo) are being playfully pulled along
very slippery (frictionless) ice by a curator as in the diagram above. The masses of
three of the penguins and the tension in two of the cords are given. Remember,
objects that are moving together can be analyzed as a system. Draw and label the
forces acting on the chosen system in each part.
a. Calculate the acceleration of the
b. What is John’s mass?
penguins.
c. What is the tension in the rope that
pulls Ringo?
d. What is the tension in the rope
between George and Paul?
Dynamics Worksheet 3
page 2
m1
m2

2. A block of mass m1 on a frictionless inclined plane of angle  is connected by a cord
over a massless, frictionless physics pulley to a second block of mass m2 hanging
vertically as in the diagram above.
a. On the system diagram below, draw and label the forces (not components) that
act on the system as it accelerates.
m2
m1
b. What is the acceleration of each block? If you need to draw anything besides
what you have shown in part (a) to assist in your solution, use the space below.
Do NOT add anything to the figure in part (a). Express your answer in terms of
m1 , m2 ,  , and g .
m2
m1
c. Calculate the acceleration if m1  3.70 kg ,
m2  2.30 kg ,   30.0 and g  9.80 N .
kg
d. In what direction is
block m2 moving and
how do you know?
Dynamics Worksheet 3
page 3
e. Draw a separate force diagram for each box and calculate the tension acting on
each.
m2
m1
3. A 4.0 kg block is put on top of a 5.0 kg block. The
4.0 kg
coefficient of static friction between the blocks is 0.306 .

The assembly of blocks is now placed on a horizontal,
5.0 kg

F
frictionless table and a force F is applied to the bottom
Frictionless
block as shown so that the blocks move together.
a. Draw a force diagram of b. What is the maximum acceleration the blocks can
the top block.
achieve if they are to remain together?
4.0 kg

c. What is the magnitude of the maximum horizontal force F that can be applied to
the lower block so that the blocks will move together? Remember, objects that
are moving together can be analyzed as a single system.
4.0 kg
5.0 kg
Dynamics Worksheet 3
page 4

Fapplied
mA
mB
mC
4. Three boxes of mass m A  2.0 kg , mB  4.0 kg and mC  6.0 kg are side-by-side on

a frictionless surface as in the diagram. A force of Fapplied  60. N is applied
horizontally to the 2.0 kg box.
a. Draw and label the forces acting on b. Calculate the acceleration of the boxes.
the system of three boxes.
mA
mB
mC
c. Draw a quantitative force diagram for each box. Remember, the length of a
force arrow represents the magnitude of the force. Use the following interaction
notation.


FAB  Force of A acting on B
FBA  Force of B acting on A


FBC  Force of B acting on C
FCB  Force of C acting on B
mA
mB


d. Explain why FAB   FBA and


FBC   FCB .
mC
e. Explain why Fapplied  FBA and FAB  FCB .