Transcript HP Unit 3 - student handout

Unit 3
Newton’s Laws of Motion
Aristotle vs Galileo
• What enables an object to
move?
• Galileo…What enables an
object to continue moving?
• Force =
• Net force =
Newton’s First Law of Motion
Newton’s 1st Law is often called the law of
inertia.
Mass
Mass is the measure
Mass is not weight.
Weight can
Why do all objects fall
at the same rate? (|a|=g=9.8m/s2)
• Aristotle felt heavy
things fell faster
than lighter ones.
However, without
air resistance, a
light object falls
the same as a
heavy object…
Newton’s Third Law of Motion
Weight & the Force of Gravity:
Weight
Weight or the force of gravity
Normal Force (FN)
A normal force (FN)
Tension Force (FT)
Tension forces exist in cables,
ropes, wires, strings, etc. The
tension force pulls on an
object where the direction of
the tension is always away
from the surface of the object
to which the ‘rope’ is attached.
m
FT
m
Force Body Diagrams (FBD)
In order to solve problems involving forces, we
need to draw an FBD.
Draw all forces acting on a box that is being
dragged to the right across a very smooth floor.
v
Newton’s 2nd Law of Motion
Example1
A Mazda Miata has a mass of 1080kg and can go
from zero to 26.8m/s (0 to 60 mph) in 7.9s. What
magnitude of net force acts on the car?
Example 2
A crane lowers a cable with a 1306kg car with an
acceleration of 0.73 m/s2. The car starts 20.0m
above the ground with an initial speed of zero.
a) What is the tension in the cable?
b) How much time will it take the car to reach the
ground?
Example 3
A person stands on a bathroom scale in an elevator at rest on
the ground floor of a building. The scale reads 836N. As the
elevator begins to move upward, the scale reading briefly
increases to 935N but then returns to 836N after reaching a
constant speed.
a) Determine the acceleration of the elevator.
b) If the elevator was moving at 3.0m/s upwards and then
uniformly decelerated to rest in 4.7s, determine the scale
reading.
Example4
A 35.0 kg lawn mower is pushed
across a level lawn in a direction of
0.0. The force exerted on the
handle is 100 N @ 310.0. Assume
friction is negligible.
(a) Determine the acceleration of the mower.
(b) Determine the normal force acting on the lawn mower.
Bird in a box
A bird sits on a sensitive
scale inside a large
cardboard box.
Falling apple
Force of gravity is the
action force for a falling
apple.
True or False: The Earth
accelerates towards
apple as apple falls
towards ground.
Equilibrium
Object is in equilibrium or is balanced when ΣF=0 in
a particular direction.
Determine the weight
of the hanging picture.
Force of Friction (Ff)
On a microscopic scale, most
surfaces are rough.
Two Types of Friction:
1) Static Friction (Ffs)
2) Kinetic Friction (Ffk )
Force of friction
tends to oppose the
motion of objects
Friction depends on two things:
1) The normal force
2) The coefficient of friction (μ)
In the case of static friction, there is a maximum
value at which the static friction force will resist
motion between surfaces.
F fs   s FN
This means that if you push a table with 50N of
force where maximum static friction is 75N, the
table won’t break free. You need to push with
just a smidge over 75N.
The static frictional force increases as the applied
force increases, until it reaches its maximum.
Example1
What minimum amount of force is needed to start to
make a 250N crate move across a floor if the
coefficient of static friction is 0.65?
Example2
A traveler pulls a suitcase of mass 8.00kg across a
level surface by pulling on the handle with 20.0N at an
angle of 50.0° relative to horizontal. Coefficient of
kinetic friction against the suitcase is μk = 0.100.
Determine the acceleration of the suitcase.
Example3
A physics book is sent sliding across a lab table with a
speed of 4.3m/s. If it takes the book 1.6m to stop,
determine the value of the coefficient of kinetic friction.
Terminal Velocity
Consider a skydiver who steps off a hovering helicopter at
high altitude. NOW consider the effect of air resistance
(friction) during the fall.
Initially at t=0, what forces act on the skydiver?
Initially at t=0, what is the acceleration and velocity of the
skydiver?
As the skydiver begins to fall, what happens to the force
of air resistance on skydiver?
As the skydiver continues to fall, describe what happens
to their speed and acceleration? Why?
Eventually what happens to the speed of the skydiver?
System of Bodies:
Multiple bodies connected together is called a
system where all bodies MUST accelerate at the
same value.
Assume mA = 1kg, mB = 3kg, mC = 4kg and the
surface on which they sit to be smooth. If block C
is pulled with a force F equal to 15N, determine:
a) The acceleration of the system.
b) The tension in each string btw A & B and
btw B & C.
Example2
Block m2 (5.0kg) sits on rough
surface where us= 0.65.
Determine the minimum value
of m1 to accelerate the system.
Assume a frictionless & negligible
mass pulley.
If m1 = 6.0kg, determine the
tension in the string if uk = 0.30.
Example3
Assume a frictionless & negligible
mass pulley. If the system is
released from rest, determine the
speed of the 5kg mass after it has
fallen for 1.3s.
b) Determine the tension in the string.
Inclines
Consider a block that slides
down a frictionless incline.
y
θ
x
Since the surface of the incline does not lie along
x or y, we rotate our x-y axis to meet our needs.
Draw the force of gravity vector
Example
A skier moves down a ski
slope angled at 30o.
If the length of the slope is
50m, determine the time it
takes to reach the bottom if
the skier starts from rest.
Ignore friction.
Example 2
A block of mass 2kg is projected up a rough
incline (uk = 0.40) at 6.2m/s where the angle of
the incline is 25o.
a) Determine the distance along the incline it
slides before coming to rest.
b) Determine the acceleration of the block on
the way down the incline.
Example 3
Determine the minimum value
of m1 if us = 0.70,θ = 30o, and
m2 = 3.0kg so that the system
will start to accelerate when
m1 is released.
If m1 is 4kg, determine the tension in the string if uk = 0.35.