A mass falling while attached to a massive pulley.
Section
Column
width
70%
Image Modified
Composition Setup
A bucket for collecting water from a well is suspended by a rope which is wound around a pulley. The empty bucket has a mass of 2.0 kg, and the pulley is essentially a uniform cylinder of mass 3.0 kg on a frictionless axle. Suppose a person drops the bucket (from rest) into the well.
We will consider two different methods to obtain the solution.
Deck of Cards
id
littledeck
Card
label
Method 1
Toggle Cloak
id
sysa1
Systems:
Cloak
id
sysa1
The pulley and the bucket are treated as separate objects. The bucket can be treated as a , but the pulley must be treated as a .
Toggle Cloak
id
inta1
Interactions:
Cloak
id
inta1
The pulley and the bucket are each subject to external influences from the rope and from . The pulley is also subject to a from the axle.
Toggle Cloak
id
moda1
Model:
Cloak
id
moda1
and
Toggle Cloak
id
appa1
Approach:
Cloak
id
appa1
Toggle Cloak
id
inta2
Interactions:
Cloak
id
inta2
The system is subject to external forces from the earth acting on the bucket and the pulley and from the normal force acting on the pulley.
Toggle Cloak
id
moda2
Model:
Cloak
id
moda2
Toggle Cloak
id
appa2
Approach:
Cloak
id
appa2
Card
Method 2
Method 2
Deck of Cards
littledeck
littledeck
Card
Part A
Part A
Card
label
Part B
Part B
What is the bucket's speed after falling 5.0 m down the well?
Solution
Again, we will use two methods.
Deck of Cards
id
littledeck2
Card
label
Method 1
Method 1
Toggle Cloak
id
sysb1
System:
Cloak
id
sysb1
Bucket as .
Toggle Cloak
id
intb1
Interactins:
Cloak
id
intb1
External influences from the earth (gravity) and the rope (tension).
Toggle Cloak
id
modb1
Model:
Cloak
id
modb1
One-Dimensional Motion with Constant Acceleration.
Toggle Cloak
id
appb1
Approach:
Cloak
id
appb1
Card
Method1
Method1
Card
label
Method 2
Method 2
Toggle Cloak
id
sysb2
System:
Cloak
id
sysb2
Treat the bucket, pulley and the earth as a single system.
Toggle Cloak
id
intb2
Interactions:
Cloak
id
intb2
Internal interactions of gravity (conservative) and tension from the rope (non-conservative) plus an external influence from the normal force on the pulley (non-conservative).
Toggle Cloak
id
modb2
Model:
Cloak
id
modb2
.
Toggle Cloak
id
appb2
Approach:
Cloak
id
appb2
Card
Method 2
Method 2
Deck of Cards
littledeck2
littledeck2
Card
Part B
Part B
Deck of Cards
bigdeck
bigdeck
Column
width
30%
Wiki Markup
{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box}
{tr}
{td:align=center|bgcolor=#F2F2F2}{*}[Examples from Rotation]*
{td}
{tr}
{tr}
{td}
{pagetree:root=Examples from Rotation}
{search-box}
{td}
{tr}
{table}
