When an object is in motion on a surface, there will be a resistance to the motion. Frictional Relationship.
Friction is proportional to the normal force.
ƒk= µk N
ƒs  µs N
W
F= fs
fs≤μsN
N
No Slippage
F>fk
W
fk=μkN
N
Slippage
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2
F denotes field force
F denotes contact force Fij is the force exerted by object i on object j 
 F A  FBA+FEA+fsBA
FEA Substitute FEA= mA g and
Normal Force on A
acceleration=a
A
N= ‐ mA g
= mA g FBA=N Static Friction
270o
FAE
FEA
FBE
FEB
B
θ
FEA
θ
FEB
FBE
Earth
3
Feel the Tension
When you can attach a rope to something and pull, a force is exerted on the rope and the rope then exerts the force on the block.
The reason it is called tension is that because of the third law, the block also pulls back on the rope with equal and opposite force. Thus as far as the rope is concerned, it is being pulled by both ends. The forces tend to pull the rope apart.
When you pull on a string or rope, it becomes
taut. We say that there is tension in the string.
Suppose the rope were the massless type (btw, these are very inexpensive)
and cut at any point, the force required to hold the ends together is T.
The tension in a “real” rope will vary along its
length, due to the weight of the rope.
Uniform rope = 2N
Here, we will assume that
all ropes, strings, wires,
etc. are massless unless
otherwise stated.
box weighs 100N
Once tension is define in a segment of a taut massless
rope, tension is define everywhere on the rope.
This also applies in a pulley system if static friction in
pulley axles can be neglected.
Pulley simply redirects the tension.
Assuming massless rope is generally not a bad approximation in cases where the tension is factor of 100 greater than the weigh of the rope. Demonstration
Clicker
You tie a rope to a tree and you
a) 0 N
pull on the rope with a force of
b) 50 N
100 N. What is the tension in
the rope?
c) 100 N
d) 150 N
e) 200 N
You tie a rope to a tree and you
a) 0 N
pull on the rope with a force of
b) 50 N
100 N. What is the tension in
the rope?
c) 100 N
d) 150 N
e) 200 N
The tension in the rope is the force that the rope
“feels” across any section of it (or that you would
feel if you replaced a piece of the rope). Because
you are pulling with a force of 100 N, that is the
tension in the rope.
Clicker
Two tug-of-war opponents each
a) 0 N
pull with a force of 100 N on
b) 50 N
opposite ends of a rope. What
c) 100 N
is the tension in the rope?
d) 150 N
e) 200 N
Two tug-of-war opponents each
a) 0 N
pull with a force of 100 N on
b) 50 N
opposite ends of a rope. What
c) 100 N
is the tension in the rope?
d) 150 N
e) 200 N
This is literally the identical situation to the
previous question. The tension is not 200 N !!
Whether the other end of the rope is pulled by a
person, or pulled by a tree, the tension in the rope
is still 100 N !!
An ideal pulley is one that simply changes the
direction of the tension without affecting the
magnitude
While we are on the subject of pulleys
Translational Equilibrium
When an object is in translational equilibrium,
the net force on it is zero:
From Newton’s second law, this is equivalent to saying
that the object’s acceleration is zero.
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