Transcript Balanced Force Example 3 (print version)

Newton’s First Law (Balanced Forces) Examples
Example 3
Modified Atwood’s Machine
A
5.0 kg
2.0 kg
Constant Velocity

FN
Box
A

FT
Method 1
B

F fk

FT
String
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.
Floor

FgA
Box
B
Treat as two separate objects
tied together by a string.
Earth

FgB
Since Box A has four
interactions it has four forces
acting upon it.
Since Box B has two
interactions it has two forces
acting upon it.
Newton’s First Law (Balanced Forces) Examples
Example 3
Modified Atwood’s Machine
A
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.
5.0 kg
2.0 kg
Constant Velocity
Method 1
B
FN  FgA
FT  F fk

F fk
Treat as two separate objects
tied together by a string.

FN
A

FgA
 F F
gB
FT T

FT
The two FT are the same
B

FgB
magnitude since it is a single
string with a single massless,
frictionless pulley.
Newton’s First Law (Balanced Forces) Examples
Example 3 continued
Modified Atwood’s Machine
A
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.
5.0 kg
2.0 kg
Constant Velocity
Method 1
B
Treat as two separate objects
tied together by a string.
Method 1

FN

F fk
A

FgA

FT

FT
Begin by writing an equation for the
horizontal forces acting on Box A.
F fk  FT
B

FgB

Since vx  constant
Newton’s First Law (Balanced Forces) Examples
Example 3 continued
Modified Atwood’s Machine
A
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.
5.0 kg
2.0 kg
Constant Velocity
Method 1
B
Treat as two separate objects
tied together by a string.
Method 1

FN

F fk
A

FgA

FT

FT
B

FgB
F fk  FT
F fk  mB g
Write an equation for the vertical
forces acting on Box B.
FT  FgB Since vy  constant
FT  mB g
F fk  2.0 kg  9.8 N 
kg 

F fk  20. N
Newton’s First Law (Balanced Forces) Examples
Example 3 continued
Modified Atwood’s Machine
A
5.0 kg
2.0 kg
Constant Velocity

FN
Box
A
B

F fk

FT
String
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.

FT
Floor

FgA
Box
B
Method 2
Treat as a single system since all
of the parts move together.
Earth

FgB
Since the forces of tension are
internal to the system, we can
ignore those interactions.
Newton’s First Law (Balanced Forces) Examples
Example 3 continued
Modified Atwood’s Machine
A
5.0 kg
2.0 kg
Constant Velocity

FN
Box
A
B

F fk

FT
String
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.

FT
Floor

FgA
Box
B
Method 2
Treat as a single system since all
of the parts move together.
Earth

FgB
Since the system has four
external interactions, it has
four forces acting upon it.
Newton’s First Law (Balanced Forces) Examples
Example 3 continued
Modified Atwood’s Machine
A
Given the Modified Atwood' s Machine shown in the
diagram, what force of friction must exist to keep
the system moving at a constant velocity?
Assume a frictionless, massless pulley.
5.0 kg
2.0 kg
Constant Velocity
B
FN  FgA
F fk  FgB

FN
A
B

F fk

FgA

FgB
Method 2
Treat as a single system since all
of the parts move together.
Write an equation for the horizontal
forces acting on the system.
F fk  FgB
F fk  mB g
F fk  2.0 kg  9.8 N 
kg 

F fk  20. N