Download Forces and newton`s laws

Forces and Newton’s Laws
Forces and newton’s laws
The Normal Force
The normal force
The Friction Force
Friction
Static Friction
Static Friction a
Static Friction
Static Friction b
Static Friction
Static Friction c
Block in motion
(kinetic)
Kinetic Friction
When an object is in motion, the motion is hindered by
the “kinetic friction force” fk. The kinetic friction is
constant in magnitude, independent of the applied force.
Kinetic Friction a
Moving block
Static and Kinetic Friction
A force is applied to an
object originally at rest. As
the applied force increases
how does the friction force
behave?
Static and Kinetic Friction b
For most materials s > k
Block at rest
(static)
Static and Kinetic Friction
A force is applied to an
object originally at rest. As
the applied force increases
how does the friction force
behave?
Static and Kinetic Friction c
For most materials s > k
Block in motion
(kinetic)
Friction Ex3
Prob 4.74
The Tension Force
Tension, T, is the force
within a rope or cable that
is used to pull an object.
Tension Force
When a force is applied to a rope at one end, the force is
transmitted through the rope to exert a tension at the other
end. The force exerted by the rope on the block is the
tension force
. Here
.
The Tension Force
The condition
holds for an ideal rope
(“massless”). The magnitude of the tension is the
same everywhere inside the rope.
Tension Force
The force exerted by the rope on the hand is the
tension force
(Newton’s 3rd Law).
The Tension Force
Forces on a knot (or any segment) in an ideal rope:
Tension Force
For the knot to be in a state of uniform motion (eg rest),
the tension exerted on the knot by the right portion of
the rope must be balanced by the tension on the knot
from the left portion of rope.
The Tension Force and Pulleys
An ideal
pulley (massless,
Tension Force and
pulleys
frictionless) changes the
direction of the tension
force, T, but doesn’t
change its magnitude.
The Tension Force and Pulleys
Tension Force and pulleys
For a stationary block,
the free body diagram
of the block shows that:
m
Thus, for a stationary
block, T = mg.
The Tension Force and Pulleys
Tension Force and pulleys
Force of rope on block.
Force of rope on man.
Force of man on rope.
The Tension Force and Pulleys
Example b
Prob 4.102
Problem 4-67 (4-76 8e)
Problem 4-67 (76 8e)
67. In the drawing, the weight
of the block on the table is 422
N and that of the hanging
block is 185 N. Ignoring all
frictional effects and assuming
the pulley to be massless, find
(a) the acceleration of the two
blocks and (b) the tension in
the cord.
Prob 4.83
Chapter 5: Uniform Circular Motion
Uniform Circular Motion
Consider a car driving a circular path at
constant speed. (Remember that speed
is the magnitude of the instantaneous
velocity vector.)
2D Kinematics b
Over the course of the circular path, the
length of the velocity vector is constant
but its direction changes.
Uniform Circular Motion
2D Kinematics c
There is an acceleration whenever the
speed and / or the direction changes!
Uniform Circular Motion
Uniform circular motion 2
Uniform Circular Motion
Uniform circular motion 2
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc1
Since the velocity (direction) changes with time there is an
acceleration present.
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc1
Since the velocity (direction) changes with time there is an
acceleration present. For very short t ie the limit t → 0 :
(centripetal
acceleration)
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc2
Consider the displacement of the object from O to P. For very small
elapsed time intervals t – t0 = t , the arc segment OP becomes
approximately a straight line segment of length s and an isosceles
triangle COP is formed.
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc3
Considering the velocity vectors, we see that another isosceles
triangle with interior angle  is generated.
Uniform Circular Motion – Centripetal Acceleration
Uniform
circular
motion
–acc4
Proof of the geometry:
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc5
We now have two similar isosceles triangles.
“Similar” 
Uniform Circular Motion – Centripetal Acceleration
Recall “similar triangles”: Generally, if two triangles have the same 2
interior angles ( and  below) then their side lengths are related by
the ratios below. Isosceles triangle: 2 equal side lengths  2 interior
angles are equal.
Uniform circular motion –acc5a
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc6
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc7
For very short t , we see that the
vector
points toward toward the
centre of the circle. Hence,
points
toward the centre of the circle.
“centripetal”  “centre seeking”
Uniform Circular Motion – Centripetal Acceleration
Uniform circular motion –acc7