Transcript Example 2 - mrdsample

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)
- Without gravity, how can we distinguish
between a 1kg and a 2kg mass?
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
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?
Fan for boat with no wind?
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?
Example 4: A box (6.2kg) is pulled along a rough,
horizontal surface by a rope that is parallel to the
surface. The tension in the rope is 23N. The box
accelerates from 2.4m/s to 3.6m/s over a distance of
7.5m. Determine the size of the friction force.
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
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 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.
Example3
A 5.0kg block is pulled by a tension force of 50.0N
along a rough horizontal surface at a constant
acceleration. If the coefficient of kinetic friction is
0.40, determine the speed of the block after 3.0s if it
starts from rest.
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
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.
Example 5
A 67.5-kg sprinter exerts a force of 775N on a starting block
which makes a 20o angle to the ground as shown (relative to
west). Assume sprinter takes off perpendicular to block.
Determine the resultant
acceleration of the sprinter.
θ=?
20o
F
F
x
 max
y
 may
Equilibrium
Object is in equilibrium or is balanced when ΣF=0 in
a particular direction.
Determine the weight
of the hanging picture.
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.
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?
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.
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 between A & B
and between 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.
Example 3
If m1 is 4kg and m2 is 3kg ,
determine the tension in the
string if uk = 0.35. Assume m1
falls. Angle is 30o