Download 4.3. Tension and Pulleys

4.3. Tension and Pulleys
Demonstration
1. Calibrate 2 spring scales, put them
together horizontally, and pull apart.
Do they always show the same force?
What are they measuring?
2. Put 2 spring scales together vertically,
and calibrate both to zero. If a weight
is added at the bottom, will both scales
show that weight, or half that weight?
Why?
Strings and Tension
When you pull on a string or rope, it becomes
taut. We say that there is tension in the string.
Tension is a force. How does its magnitude and
direction vary along the string?
Strings and Tension
If the string were cut in any place, equal and opposite
forces would be needed to hold the string together again.
All along an uncut string are equal and opposite forces, for
no net acceleration.
Demonstration
• Have two people hold a string under high
tension. Have a third person cut the string
in half. What happens? Why?
Strings and Tension
In a sense, the string transmits forces from one
end to the other. Tie a string to a chair, and pull.
The force of the chair’s resistance is transmitted
to your hand, and you hand’s force to the chair.
Strings and Tension
The tension in a real rope will vary along its
length due to the weight of the rope itself.
Here, we will assume that
all ropes, strings, wires,
etc. are massless unless
otherwise stated.
Strings and Tension
Consider a heavy box suspended on a rope
attached to a crane.
Does the tension on the rope
increase or decrease if:
(a) the crane accelerates
upward?
(b) the crane accelerates
downward?
(c) the crane moves upward
with constant velocity?
What about a fishing pole?
Pulleys: Demonstration
1. How might a pulley change tension?
2. What would the free-body diagram of the
balance of forces be for a rope and a
pulley:
a. For the rope turned 90 degrees?
b. For the rope turned 180 degrees?
3. Experiment!
Strings, Tension and Pulleys
An ideal pulley is one that simply changes the
direction of the tension.
A man is holding a box
at a constant height off
the ground by means of
a pulley. What are the
forces on the box, the
rope, the pulley, and the
man?
Translational Equilibrium
Objects with zero acceleration are said to be in
equilibrium. For this to happen, the net force on it
must be zero:
This allows the calculation of unknown forces.
Note that the velocity does not need to be zero;
just zero acceleration.
“Translational” refers to motion through space.
Translational Equilibrium
A man is pulling up a bucket at constant velocity.
What are the forces acting on the various parts of
the system?
Translational Equilibrium
What are the forces if the man ties the free end of
the rope also to the bucket?
Translational Equilibrium
What are the forces if the man ties the free end of
the rope also to the bucket?
Example
A 1.84-kg bag of clothespins hangs in the middle
of a clothesline, causing it to sag by an angle of
3.50 degrees. Find the tension in the line.
Demonstration
• Have two people hold a string under
tension. Place a weight in the middle.
How much force must they apply to
straighten out the string?
• In a “cause-and-effect” relationship, the
angle is the “effect”, i.e. the result. What
is(are) the cause(s)?
Two Pulley System
How much force is
required to lift a 52-kg
box at constant
velocity with a twopulley system?
Four Pulley System
Static Connected Objects
What are the forces in these two cases?
Pulling Connected Objects
When forces are exerted on connected objects,
their accelerations are the same.
If there are two objects connected by a string,
and we know the force and the masses, we can
find the acceleration and the tension:
Pulling Connected Objects
We treat each box as a separate system:
Pushing Connected Objects:
Contact Forces
Since both objects
have the same
acceleration, F =
(m1+m2)a. However
in the top case
F21=m1a, while in
the bottom case
F12=m2a. Note the
middle box may get
crushed.
Pulling Connected Objects
If there is a pulley, it is easiest to have the
coordinate system follow the string:
Pulleys and …
• Counter-weights
– Atwood Machine
– Elevator
• Springs
– Garage Door Opener
– Compound Bow
Demonstration
• Falling Ball Chain