Transcript A body acted on by no net force moves with constant velocity

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 13, 14, 15
Newton’s Laws
1st Law: A body acted on by no net force moves with
constant velocity (which may be zero) and zero acceleration
2nd Law: The acceleration of an object is directly
proportional to the net force acting on it and is inversely
proportional to its mass. The direction of the acceleration
is in the direction of the net force acting on the object.
3rd Law: For every action there is an equal, but
opposite reaction
Newton’s law of gravitation
Falling with air resistance
dv
2
a
 g  kv
dt
Terminal Velocity with Coffee Filters
mg  Fr  ma
where Fr is the resistance force.
Fr
ag
m
1. A penny and a quarter dropped from a ladder land at the
same time (air resistance is negligible).

2. A coin dropped in a coffee filter from a ladder lands later
 coffee filter (the terminal velocity is
than a coin without
smaller for larger cross-section area).
3. A quarter dropped in a coffee filter will land faster than a
penny in a coffee filter (the terminal velocity is larger for
larger mass)
4. Two identical coins dropped in coffee filters of different
diameters land at different times (the terminal velocity is
smaller for larger cross-section area).
Resistance force: Fr  Av
2
A – area of the projectile
2
4


0.25
N

s
/m
For a spherical projectile in air at
STP:
Terminal velocity:
Fr
ag
0
m
Fr  mg
Av 2  mg

vT 
mg
A
A 70-kg man with a parachute: vT ~ 5 m/s
A 70-kg man without a parachute: vT ~ 70
m/s
Newton’s
st
1
Law
A body acted on by no net force moves
with constant velocity (which may be zero)
and zero acceleration
Aristotle: a natural state of
an object is at rest; a force
is necessary to keep an
object in motion. It follows
from common sense.
384-322 B.C.
Galileo: was able to
identify a hidden force of
friction behind commonsense experiments
1564-1642
Galileo: If no force is applied to
a moving object, it will continue
to move with constant speed in
a straight line
Inertial reference frames
Galilean principle of relativity: Laws of
physics (and everything in the Universe)
look the same for all observers who move
with a constant velocity with respect to
each other.
Kinetic Friction
• For kinetic friction, it turns out that the
larger the Normal Force the larger the
friction. We can write
FFriction = mKineticN
Here m is a constant
• Warning:
– THIS IS NOT A VECTOR EQUATION!
Static Friction
• This is more complicated
• For static friction, the friction force can vary
FFriction  mStaticN
Example of the refrigerator:
– If I don’t push, what is the static friction
force?
– What if I push a little?
Coefficient of friction: m
H
What is the normal force?
What is the velocity of the block when
it reaches the bottom?
Newton’s
rd
3
Law
For every action there is an
equal, but opposite, reaction
Skater
• Skater pushes on a wall
• The wall pushes back
– Equal and opposite
force
• The push from the wall is
a force
– Force provides an
acceleration
– She flies off with some
non-zero speed
P
P
No friction
m1
m1
m2
Free body diagram
N1
F12
F21
m1
N2
m2
m2g
m1g
F12=F21
Quiz
a) A crate of mass m is on the flat bed of a pick up
truck. The coefficient of friction between the crate
and the truck is m. The truck is traveling at the
constant velocity of magnitude V1. Draw the free
body diagram for the crate.
b) The truck starts to accelerate with an
acceleration ac. Draw the free body diagram for
the crate, if the crate does not slip.
A small block, mass 2kg, rests on top of a larger
block, mass 20 kg. The coefficient of friction
between the blocks is 0.25. If the larger block is
on a frictionless table, what is the largest
horizontal force that can be applied to it without
the small block slipping?
F
N1
N2
mN1
mN1
F
N1
m1 g
m2 g
A block of mass 20 kg is pushed against a vertical
surface as shown. The coefficient of friction
between the surface and the block is 0.2. If θ=300,
what is the minimum magnitude of P to hold the
block still?
P
θ
V0

A block of mass m is given an initial velocity V0 up an
inclined plane with angle of incline θ. Find acceleration
of the block if
a) m = 0
b) non-zero m
A wedge with mass M rests on a frictionless
horizontal tabletop. A block with mass m is
placed on the wedge and a horizontal force F
is applied to the wedge. What must the
magnitude of F be if the block is to remain
at a constant height above the tabletop?

F

A Problem With First Year Physics Strings
and Pulleys
m1
m1, m2 are given
m2>m1
String is massless
and unstretchable
m2
Find accelerations of m1 and m2 (assume
no friction in pulley)
Block 1, of mass m1, is placed at rest on an inclined plane. It is
attached by a massless, unstretchable string to block 2, of mass
m2. The pulley is massless and frictionless and just changes the
direction of the tension in the string. The coefficient of friction
between the plane and m1 is the constant m.
1
2

Determine what range of values for mass m2 will keep the system at rest.
Find acceleration if mass 2 goes down.
Friction everywhere.
2
F
1
Find F necessary to drag the box 1 at constant speed.
The advantage of a pulley
What minimum force F is needed
to lift the piano of mass M?
The Elevator Problem
Have a great day!
Reading: Chapter 7
Hw: Chapter 6 problems and
exercises