Transcript Force of Friction

Unit 2
1D Vectors &
Newton’s Laws of Motion
A. Vectors and Scalars
B. Addition of Vectors & RESULTANT
In one dimension, simple addition
and subtraction is all that is needed.
RESULTANT VECTOR
Aristotle vs Galileo
FORCES
NET FORCE
D. TYPES OF FORCES
1) Force of Gravity (Weight)
2) Normal Force (Support Force)
If the box weighed less, what
would happen to the normal force
acting on the box?
3) Tension Force
4) Friction Force
E. NEWTON’S LAWS
Newton’s 1st Law of Motion
Also called the law of inertia.
Mass
- Without gravity, how can we distinguish
between a 1kg and a 2kg mass?
Why do all objects fall
at the same rate? (|a|=g=9.8m/s2)
Newton’s 3rd Law of Motion
Explain the
movement of
a rocket
using the 3rd
Law.
Question: A loaded school bus hits a bug and kills
it. Which body receives the greater force of
impact, bug or bus?
Who pulls harder on the rope?
Who wins the tug of war?
Force Body Diagrams (FBD) using vectors
In order to solve problems involving forces, we
need to draw an FBD.
A box is dragged by a rope towards the right on a
smooth floor. Draw the force vectors on the box.
Newton’s 2nd Law of Motion
Constant velocity equates
to what in regards to Fnet?
Example 1
A crane lowers a 1306kg car by a cable 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? Draw FBD
b) How much time will it take the car to reach the
ground?
Example 2
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.
Example 3: A force of 75N pushes on 2 boxes as
shown. The mass of b1 is 20kg and the mass of b2
is 35kg. Surface is smooth.
a) Determine the acceleration of the two boxes.
b) Determine the net force on b2.
c) Determine the net force on b1 . Why is it
different?
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:
In the case of static friction, there is a maximum
value at which the static friction force will resist
motion between surfaces.
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 where we say you just have to
equal maximum static to break free.
The static frictional force increases as the applied
force increases, until it reaches its maximum.
Example1
A person crosstrains by pushing a 950N man (who sits
on a 45N metal box). The box is pushed with a force of
335N at a constant acceleration. If the coefficient of
kinetic friction is 0.30, determine the speed of the
box after 3.0s if it starts from rest.
Example2
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 and the coefficient of kinetic
friction is 0.40?
Example2
A physics book is pushed and released across a table.
The book is sent sliding 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.
a) Initially at t=0, what forces act on the skydiver?
b) Initially at t=0, what is the acceleration and velocity of
the skydiver?
c) As the skydiver begins to fall, what happens to the
force of air resistance on skydiver?
d) As the skydiver continues to fall, describe what
happens to their speed and acceleration? Why?
e) Eventually what happens to the speed of the skydiver?
2D Vectors/Forces
Vectors & Components
Any vector pointing at an angle other than multiples
of 90o can be broken down into components.
The components form the legs of a right triangle.
If a force, F, acts at an angle, θ, it can be
resolved into perpendicular components
and can be found using trigonometric
functions.
Use the Pythagorean Theorem and Right
Adding
Vectors
by
Triangle Trig to solve for resultant and θ.
Components
Know your
quadrants.
(+) angle is
moving CCW
(-) angles
mean moving
CW
Example 4
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.
Example5
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.
Example6
Suppose a 3-kg block is being pushed against a wall
by a force F = 75N acting at an angle of 30º to the
horizontal. Determine the acceleration of the block
if the coefficient of kinetic friction is 0.10.
F
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 can rotate our x-y axis to meet our needs.
Draw the force vector, Fg , on the box
y
Fg y
Fg x
θ
Fg
x
θ
Resolve the force of gravity into components
Fg
θ
What is the normal force
on the block equal to?
Example1
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
A man pushes a 39.0-kg crate, starting at rest, up a
30.0o incline that is 23.5m long with a force of 335N.
The coefficient of sliding friction between the crate
and the incline is 0.20.
a) Calculate the magnitude
of the frictional force acting
on the crate.
b) What will be the speed of the crate when it
reaches the top of the incline?