Transcript Newton’s Laws of Motion

Unit 4: Newton’s Laws of
Motion
Causes of Motion
Aristotle (384-322 BC) believed that all objects
had a “natural place” and that the tendency of
an object was to reside in its “natural place.”
All objects were classified into categories
of earth, water, air, or fire.
“Natural motion” occurred when an object sought
to return to its “natural place” after being
moved from it by some type of “violent motion.”
The natural state of an object was to be
“at rest” in its “natural place.”
To keep an object moving would require a force.
These views remained widely
supported until the 1500s
when Galileo Galilei (1564-1642)
popularized experimentation.
Isaac Newton (1642–1727)
proposed that the tendency of
an object was to maintain its
current state of motion.
Forces
• A force is a push or a pull
• A force (F) can cause
– a stationary object to move
– a moving object to stop
– an object to accelerate (change speed or direction)
• Net force (Fnet)
– the combination of all the forces acting on an object.
– changes an object’s state of motion.
• Balanced Force
– Fnet = 0
– object at rest
– Or constant velocity
• Unbalanced Force
– Fnet > 0
– Object moves
– Or accelerates
Newton’s Laws of Motion
• 1st Law – (Law of Inertia) An object at rest
will stay at rest, and an object in motion will
stay in motion at constant velocity, unless
acted upon by an unbalanced force.
• 2nd Law – (F=ma)Force equals mass times
acceleration.
• 3rd Law – (action-reaction)For every action
there is an equal and opposite reaction.
INERTIA
the tendency of an object
to resist any change in its motion
Inertia is a property of matter and does not
depend on the position or location of the object. But it does depend on:
MASS
a quantitative measure of inertia
FORCE
“a push or pull”
Free Body Diagrams
• Gravity (Fg) always pulls straight down
• Normal force (FN) is perpendicular to surface and equal and
opposite to component of gravitational force (Fg)
• Applied force (Fapp) is in the direction of the motion of the
object. It is always parallel to the surface
• Frictional force (Ff) always opposes the motion. It is always
parallel to the surface opposite the Fapp.
FN
FN
Ff
Fapp
Ff
Fapp
Fg
Fg
What direction is normal force (FN).
Example 1
The net force acting on an object is the vector
sum of all the forces acting on it.
Fnet = F1 + F2 + F3 +……
Examples:
9 lb
8 lb
4 lb
8 lb
7 lb
12 lb
Fnet =
6 lb
Fnet =
If an object is remaining at rest, it is
incorrect to assume that there are no
forces acting on the object.
We can only conclude that the net force
on the object is zero.
5 lb
Fnet =
4 lb
Example 2
Fnet
magnitude _______
direction _________
Balanced or Unbalanced?
Fnet
magnitude _______
direction _________
Fnet
magnitude _______
direction _________
Balanced or Unbalanced?
Balanced or Unbalanced?
nd
2
Law
The net force of an object is
equal to the product of its mass
and acceleration
F=ma.
2nd Law
• Relates an object’s mass and acceleration to
the net force (force causes acceleration)
F=ma
• Mass is inversely related to acceleration
• Acceleration is directly related to net force
Newton’s 2nd Law proves that different masses accelerate
to the earth at the same rate, but with different forces.
• We know that objects with
different masses accelerate to
the ground at the same rate.
• However, because of the 2nd
Law we know that they don’t
hit the ground with the same
force.
F = ma
F = ma
98 N = 10 kg x 9.8 m/s2
9.8 N = 1 kg x 9.8 m/s2
Mass vs. Weight
• MASS
– How much and what
material an object is made
of
– Symbol = m
– Unit = kilograms (kg)
– Is constant for an object
independent of location
To go from mass to weight,
multiply by 9.8!
Mass conversion:
2.2 lb = 1 kg
• WEIGHT
– Force of gravity acting on
a mass (On earth a = 9.8
m/s2)
– Symbol = Fg
– Unit = Newtons (N)
Fg=ma
– 1N = 1kg· m/s2
- Changes depending on
location due to pull from
the center of earth
-1 lb = 4.5 N
Calculating force and acceleration
• Remember Force = mass x acceleration
F=ma
• If not given acceleration, find acceleration
using one of the acceleration equations
Example 3
• If a person pulls on the rope with a constant force
what is the acceleration of the system? How far will
it move in 3.02s?
Example 4
• How much force must a 30,000kg jet develop
to achieve an acceleration of 1.5m/s2?
(neglecting air friction)
• F=ma
• F=(30,000 kg) (1.5 m/s2)= 45,000 N
Example 5
• If a 900 kg car goes from 0 to 60 mph (27 m/s)
in 5 seconds, how much force is applied to
achieve this?
Example 6
• If I throw a 0.145 kg baseball at 20 m/s baseball
and my ‘windup distance’ is 600 cm, how much
force am I applying?
Example 7
• A 2.2 kg book is slid across a table. If Fnet = 2.6
N what is the book’s acceleration?
• F=ma
• 2.6 N = (2.2kg) a
• a = 1.18 m/s2
Example 8
• If you drop a 20 kg object what is its
acceleration? What is its weight?
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•
•
•
acceleration = 9.8 m/s2
Weight = force
Fg=ma
Fg= (20 kg) (9.8 m/s2)
• Q: If a jet cruises with a constant velocity and
the thrust from its engines is constant
80,000 N. What is the acceleration of the jet?
– A: Zero acceleration because the velocity does not
change.
• Q: What is the force of air resistance acting on
the jet?
– A: 80,000 N in the opposite direction of the jet’s
motion
Example 9:
After a birthday party, Bozo the clown went to dinner in his
250 kg car. To save room in the car, he let the left over
balloons hang out the window. The engine of the car is
exerting a force of 360 N. The balloons are creating drag in
the air with a force of 35 N in the opposite direction of the
car’s motion.
• Draw the vector arrows on the free body diagram
• What is the net force (Fnet) acting on the car?
• What is the direction that force is acting?
• Use Newton’s 2nd Law to calculate the net acceleration of
the car.
3rd Law
• For every action, there is an
equal and opposite reaction.
3rd Law
• There are two forces resulting from this interaction
• a force on the chair (action)
• a force on your body (reaction)
action
reaction
• If all forces have equal and opposing forces,
how does anything move?
– Action-Reaction pairs are forces of objects on
different objects
– F Net is sum of external forces acting on ONE
object
3rd Law
Flying gracefully through the air, birds depend
on Newton’s third law of motion. As the birds
push down on the air with their wings, the air
pushes their wings up and gives them lift.
Other examples of Newton’s Third Law
• Action: baseball forces
the bat to the left
• Reaction: bat forces the
ball to the right
Friction & Tension
• Friction (Ff) - the force that opposes motion
• Tension (FT) - the pulling force exerted by a
string, cable, chain on another object.
Example 11
• Draw free body diagram for table
• Applied force from pusher, normal force, gravitational
force, friction force
• If applied force is greater than friction, table moves
Drawing Free Body Diagrams
Example 12
Drawing Free Body Diagrams
Example 13
Friction
• The force of friction (Ff):
1. Is always opposite to the direction of motion or
impending motion
2. Usually has a smaller value if the object is
moving than if it is stationary
- (static friction > kinetic friction);
3. Depends on the nature of the pair of surfaces
involved (the value of μ);
Friction
• The force of friction (cont’d):
4. Is proportional to the force pressing the surfaces
together (the normal force);
- static friction: Ff ≤ μs FN
- kinetic friction: Ff =μk FN
5. Is usually independent of the contact area and
speed.
Example 14
• If a 1 kg mass sits on a flat surface with a
coefficient of static friction of 0.5, what is the
force of friction (Ff) if:
– A horizontal force of 1 N is applied?
– A horizontal force of 10 N is applied?
– A horizontal force of 100 N is applied?
Finding Force With Angles
FN
• Horizontal
Ff
Fapp
– FN = F g
Fg
• Incline
– Fnet = Fgsinθ
– FN = Fgcos θ
FN
Ff
20°
FN
Fnet
Fg
20°
Example 15
Example 16
Example 17
Example 18
Statics
• The study of forces in equilibrium
– Balanced forces
– No acceleration
FN
Statics
• If hanging from a wire
FT1
45°
– Weight is shared equally
between each wire
– Weight is NOT equal to
Tension
– Find Tension and divide
by number of
strings/wires/etc.
cos Θ = FN
FT
FT= FN
cos Θ
Fg
FT2
Example 19
• At an art auction, you acquired a painting that
now hangs from a nail on the wall. If the
painting has a mass of 12.6 kg, what is the
tension in each side of the wire supporting the
painting?
Example 20
Example 21
Example 22
Example 23
Physics 1 Assessment 4E
1. Two forces are applied to a 2.0 kg block on a frictionless,
horizontal surface, as shown in the diagram. The acceleration
of the block is
A. 5.0 m/s2 to the right
B. 3.0 m/s2 to the right
C. 5.0 m/s2 to the left
D. 3.0 m/s2 to the left
Physics 1 Assessment 4E
2. The vector diagram below represents two forces, F1 and F2,
simultaneously acting on an object. Which vector best
represents the resultant of the two forces?
A.
B.
C.
D.
Physics 1 Assessment 4E
3. A horizontal force is used to pull a 5.0 kg cart at a constant
speed of 5.0 m/s across the floor, as shown in the diagram. If
the force of friction between the cart and the floor is 10 N,
the magnitude of the horizontal force along the handle of the
cart is
A.5.0 N
B.10 N
C.25 N
D.50 N
Physics 1 Assessment 4E
4. The diagram below shows a sled and rider sliding down a
snow-covered hill that makes an angle of 30° with the
horizontal. Which vector best represents the direction of the
normal force, FN, exerted by the hill on the sled?
A.
B.
C.
D.
Physics 1 Assessment 4E
5. An electric model of a Boeing 757, has a mass of about 12 kg.
If the owner adjusts the wing flaps to create 123 N of lift
upwards, what is the net vertical force on the plane?
A.0 N
B.5.4 N
C.10.3 N
D.111 N
E.241 N
Example
• An object is being pulled by a 3 kiloNewtons force
towards the north and a 4 kiloNewtons force
eastward on a frictionless surface. What is the net
force that will accelerate this object?
Example
• What is the applied force acting against a frictional force of 10
N, if an object is pulled with a force of 200 N at angle of 60o
from the ground? What is the net force?
• Solve for the Fa applied force along the x –axis Fa(x)
Fa(x) = 200cos60
Fa(x) = 100 N
• The force applied opposite frictional force is 100 N and not
200 N.
• We can solve for the net force Fnet then.
Fnet = Fa(x) – Ff = 100 N – 10 N = 90N
Example
• What is the normal force Fn acting on a 180 N
object on the ramp that made an angle of 60o
from the ground?
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We will solve this problem using similar triangles.
Take note Fn = Fg’ , but opposite in direction.
We will solve Fg’ using cosine.
Our hypotenuse is the weight Fg =180 N.
Fg’ is the adjacent side with respect to the angle 60o.
cos Ɵ = adjacent side / hyp.
cos 60o = Fg’ / Fg
Fg’ = 180cos60
Fg’ = 90 N
Since Fg’ = Fn
Fn = 90 N
Example
• A crate is being pulled by cables along a frictionless
surface with a force of 500 kN eastward and by
another force of 400 KN @ 120o. What is the net
force acting on the crate? Hint: must find magnitude
and direction!
Sin 30= Fx / 400 kN
Fx = 400sin30
Fx = 200 kN
Cos 30 = Fy / 400kN
Fy = 400cos30
Fy = 346.41 kN
Magnitude:
• Add all the vector forces along the x-axis.
Fxtotal = 500 kN - 200 kN
Fxtotal = 300 kN
• Add all the vector forces along the y-axis.
• Fytotal = 346.41 kN
• Use Pythagorean Theorem to solve for Fnet
Fnet = √(Fx2 + Fy2 )
= √(3002 + 346.412)
= 458.23 kN
Direction
• Tangent Ɵ = opposite side/adjancent side
Ɵ = tan-1(Fytotal/Fx total )
= tan-1346.41 kN/300 kN
Ɵ = 49.11o
Fnet = 458.23 kN @ 49.11o