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

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 13-15
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
Reading quizzes (Chs 5,6)
Hockey Puck
• Which of these three best
represents a hockey puck
in the real world?
a)
b)
c)
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.
Newton’s second law


F  ma
The vector acceleration of an object is in the same
direction as the vector force applied to the object
and the magnitudes are related by a constant called
the mass of the object.
A Recipe for Solving Problems
1. Sketch
Isolate the body (only external forces but not forces
that one part of the object exert on another part)
2. Write down 2nd Newton’s law


F  ma
Choose a coordinate system
Write 2nd Newton’s law in component form:





F  Fx i  Fy j  max i  ma y j
Fx  max , Fy  ma y
3. Solve for acceleration
Is it better to push or pull a
sled?
You can pull or push a sled with the same force
magnitude, FP, and angle Q, as shown in the figures.
Assuming the sled doesn’t leave the ground and has a
constant coefficient of friction, m, which is better?
FP
FP
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
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
Force of tension
Massless, unstretchable string; frictionless pulley
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)
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

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?
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.
The Elevator Problem
Have a great day!
Reading: Chapter 7
Hw: Chapter 6 problems and
exercises