No Strings Attached:
Normal Forces, Force Vectors,
Strings, Springs and Pulleys
Chapter 6.1-6.3
Important Vocabulary:
Normal Force
Contact Force
Tension
Coefficient of Friction
Friction: the most important everyday force,
next to gravity!
F
Ff
The force of friction ..…..
N
Fg
•Is the result of contact between two bodies.
•Always acts to oppose (slow down) the motion.
•Is proportional to the Normal force.
•Does not depend on area of contact. Why not?
F f  N
Friction depends on whether or not the
object is moving.
• Static friction: friction for object at rest.
• Kinetic friction: friction for moving object.
Kinetic
Static
V=0
V>0
Two more notes about friction:
-Coefficient of static friction is higher than that of kinetic friction
(frictional force decreases when object begins to move).
-Coefficient of kinetic friction does not change with speed
And finally(?)….frictional force “laws” are an approximation, but a good one.
A problem of friction
A block of mass M = 1.5 kg sits on a hinged inclined plane. The
coefficient of static friction is =0.15. At what angle of the
inclined plane does the block begin to slide?
1. Draw the picture showing the forces on the block.
What are they?
2. Draw the free-body diagram.
3. Write down Newton’s law, Fnet = M a
4. Think about the problem. When does the acceleration
become greater than zero?
Science Friction.
V0
=0
=.05
A block of mass M=1 kg slides with speed Vo over a frictionless surface.
Then, it hits a rough surface with kinetic coefficient of friction =0.05 .
How much further does it slide before it stops?
Have I got a tension headache!
• Tension, T, is the “contact
force” for pulling objects
• Tension is a real force—
you can measure it by
cutting the string and
inserting a force scale
TENSION
Tension is real—it can be
measured.
Tension Problem
•
•
•
•
Given, M1, M2, and F
What is acceleration?
What is the Tension, T in the line?
What is the force on each block?
T
M2
F
M1
IMPORTANT:
Blocks move together,
so each has the same
acceleration “a” and
speed “v”.
F
a
M1  M 2
Case of NO FRICTION.
F1=T
T  F1
 M 1a

M1
F
M1  M 2
F2=F-T
F
T
F2  F  T

M2
F
M1  M 2
Check work: Look a limits of large and small M1, M2.
Pulleys: the beginnings of technology.
A pulley changes the direction of Tension
Compare the tension in the left and right cases.
1.
2.
3.
The left is higher.
The right is higher since the mass is
double.
They are the same.
Simplest pulley system.
What happens to the tension?
1.
2.
3.
It is the same in both cases, the
bucket mass doesn’t change.
The tension doubles in the right
side.
The tension is reduced by ½ in the
right side.
The “bosun’s chair” problem.
Accelerating blocks: more of a challenge
Given M2, M1 and g.
What is a?
What is the tension?
What are the forces?
(ignore friction)
Accelerated blocks and tension.
CAUTION: The TOTAL force on M2 is NOT JUST
THE WEIGHT!
Freebody diagram
a
a
NOTE: Why is the diagram for mass 2 correct? Isn’t it moving in the y axis?
Accelerating tethered blocks.
a
T  M 1a
M 2 g  T  M 2a
M2
a
g
M1  M 2
Block on the table.
Block dropping down.
Does this make sense? Check it
by looking at limits of M2.
Tethered blocks: add one more!
T1
T2
T2
M3g
T1  M 1a
T2  T1  M 2 a
Add all three equations together.
( M 1  M 2  M 3 )a  M 3 g
Do on “board” then reveal
M 3 g  T2  M 3 a
M3
a
g
M1  M 2  M 3