Date post: | 03-Jan-2016 |
Category: |
Documents |
Upload: | rosamund-sims |
View: | 218 times |
Download: | 0 times |
How are contact forces different from long range forces? Contact forces - touching - example:
hand on desk
Long range forces - act at a distance - gravitational forces, electrostatic, magnetic
What is Newton’s First Law of Motion? Law of Inertia: tendency to resist
change An object at rest remains at rest, and an
object in motion remains in motion (same direction, constant speed) unless acted upon by an unbalanced force.
Forces are balanced: Equilibrium
Newton’s 1st Law - Types of Equilibrium
1. Static Equilibrium
object is at rest 2. Dynamic Equilibrium
object is moving at constant velocity
What is Newton’s Second Law of Motion? Unbalanced forces produce
acceleration **Acceleration is directly proportional to
force and inversely proportional to mass Fnet = ma
a = Fnet/m in reference table Units 1 kgm/s2 = 1 Newton
Example: An artillery shell with a mass of 5.5 kg is
fired from a gun with a velocity of 770 m/s. The barrel of the gun is 1.5 m long. Find the force on the shell.
Solution:
m = 5.5 kg
vf = 770 m/s
vi = 0 m/s
d = 1.5 m
€
F = ma
€
=5.5kg(2x105m /s2) =1.1x106N
€
v f2 = v i
2 + 2ad
€
(770m
s)2 = 2(a)(1.5m)
€
a = 2 x105 m
s2
Special Case - weight W = mg is a special case of F = ma,
where weight is the force, and gravity is the acceleration (can be written as Fg)
Example: What is the weight of a 5 kg object?
€
W = mg
€
=5kg(−9.8m
s2) = − 49N
Two Kinds of Mass 1. Gravitational mass - using a balance
- comparing the gravitational force on two objects (one has a known mass).
2. Inertial mass - using Newton’s 2nd law - find the force necessary to produce a specific acceleration for a given mass
Gravitational mass = inertial mass
Free Body Diagrams Used to show forces on an object Sketch and Equations:
€
Fnet = ma What is Fnet?
Fnet is the sum of the forces acting in the direction of motion (vertical or horizontal)
€
+↑ −↓
Free Body Diagrams: Vertical
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Lifted object
(Ftens is tension)
€
Fnet = Ftens + Fgrav
Example:A 50 Newton force is used to lift a 2 kg object. What is the acceleration of the object?
Lift
Weight
€
Fnet = ma
€
Fnet = lift + weight50 N
€
W = mg
€
=2kg(−9.8m
s2)
€
=−19.6N€
Fnet = 50N + (−19.6N)
€
Fnet = 30.4N
€
a =Fnetm
=30.4N
2kg=15.2
m
s2
Lift
Weight
€
Fnet = ma
€
9000N = lift + (−44,100N)
? N
€
W = mg
€
=4500kg(−9.8m
s2)
€
=−44,100N€
=4500kg(2m
s2) = 9000N
€
lift = −53,100N€
Fnet = lift + weight
Example:A 4500 kg helicopter accelerates upward at 2 m/s2. What lift force is exerted by the air on the propellers?
Alternate Solution to helicopter problem:
€
Fnet = ma
€
Fnet = lift + weight
€
ma = lift + weight
€
ma = lift + mg
€
lift = 4500kg[2m
s2− (−9.8
m
s2)]
€
=m(a− g)
€
lift = ma−mg
€
lift = −53,100N
What is Newton’s 3rd Law of Motion?
For every action, there’s an equal and opposite reaction. The force on one object is equal and opposite to the
force on the other. Object resting on a table: weight pushes back on table.
Table pushes back with an equal and opposite force called Normal force (FN). If no other vertical forces are present: normal force equals weight
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Falling objects: what are the forces on an object falling through the air?
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Object in freefall(with air resistance)
€
Fnet = Fair + Fgrav
Object in freefall(no air resistance)
€
Fnet = Fgrav
Falling Objects: What are the forces on an object falling is the
air? What happens when they are equal? Drag force (Fair) - air resistance - depends on
size/shape of the object, air density, speed. When drag force = weight, forces are
balanced (Fnet=0) No net force means no acceleration! You
have reached TERMINAL VELOCITY.
Free Body Diagrams Free body diagram - horizontal motion
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
€
Fnet = maFf
FN
FA
Fg or W
€
Fnet = FA + Ff
What if…. FA is greater than Ff
acceleration is positive FA is equal to Ff then
no acceleration (constant velocity) FA is less than Ff
acceleration is negative (you can slow down, but friction won’t make you move backwards!)
Free Body Diagrams Free body diagram - horizontal motion
with no friction:
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
€
Fnet = ma
€
Fnet = applied force only
Example: If you apply a 50 Newton force to a mass of 5
kg, what is the acceleration?
€
a =Fnetm
€
=50N
5kg
€
=10m
s2
Example (continued): What if a frictional force of 20 N opposes the applied
force? Find a.
€
Fnet = 50N + (−20N) = 30N
€
a =Fnetm
€
=30N
5kg
€
=6m
s2
What is friction?Friction - force opposing motion between 2
surfaces in contact and parallel to the surface How can you calculate frictional force? Equation:
€
Ff = μFNFf = frictional force (N)FN = normal force (N) coefficient of friction (no units)
What variables affect friction?
Weight? YES Surface area? NO Type of surfaces in contact? YES Velocity? NO Normal force - force pushing objects together- is
normal force always equal to weight? NO - they are not equal if other vertical forces are
present.
What are two types of friction? 1. Static - objects are NOT in relative motion
- static friction opposes the START of motion 2. Kinetic (sliding) - force between surfaces
in motion - resists motion Which is greater? Static friction is greater - it is harder to start
motion that it is to keep an object moving.
€
Fstatic > Fkinetic
Example #1: A block is place on a table. It has a weight of 50 N.
You must exert a force of 20 N to keep the block moving at a constant velocity.
1. What is coefficient of sliding friction?
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
€
Fg = 50N€
FA = 50N
€
FN = 50N
€
Ff = 50N
€
a = 0m
s2(FA = Ff )
€
=FfFN
€
=20N
50N
€
=0.4
2. Place a 10 N brick on the block. What force is required to keep the block moving at constant velocity?
Same surfaces, so = 0.4
€
FA = Ff = μFN
€
=0.4(60N) = 24N
Example #2 A 10kg box made of wood is pushed on
a wood floor with a force of 100 N. (a.) Will the box slide? (b.) What force must be applied to
move the box at a constant velocity? (c.) What force must be applied for the
box to accelerate at a rate of 5 m/s2?
Solution:
(a.) Will it move? It will move if the applied force exceeds the static frictional force.
€
Ffs = μFN From reference table: static = 0.42
€
FN =W = mg
€
=10kg(9.8 m /s2) = 98N
€
Ffs = μFN
€
=0.42(98N) = 41.2N
€
Is FA > Ffs ? Yes, 100N>41.2N, box will slide.
Solution: (b). To move box at a constant velocity….. Use
KINETIC friction.
From reference table: kinetic = 0.30
Since a = 0, then Fnet = ma =0
€
FA = Ffk
€
Ffk = μFN = 0.30(98N) = 29.4N
€
FA = Ffk = 29.4N