Transcript Mechanical Force Information

FORCE
Any push or pull that can cause change in motion. Prime
mover in mechanical systems
Gears, chains, pulleys, pistons, screws, etc. have mechanical
motion (moving parts), create mechanical force
Other forces (non-mechanical):
gravity
electric
magnetic
fluid
thermal
MEASURING IN PHYSICS
Dimensions – things that can be measured, e.g.,
length, time, mass, temperature
Described w/ units and numbers
Most common units: metric system ( Standard
International [SI]).
Based on powers of ten
Have unit term, e.g., liter, meter, second
Prefix denotes power of ten by which
unit is multiplied
English system – used only in US
Based on fractions (1/2, ¼, 1/8, 1/16)
No consistent multiples or base units
SI (METRIC) BASE UNITS
QUANTITY
UNIT
SYMBOL
Length
Mass
Force
Time
Elect. Current
Temperature
meter
kilogram
Newton
Second
Ampere
Celsius
m
kg
N
s
A
C
ENGLISH BASE UNITS
QUANTITY
UNIT
SYMBOL
Length
Mass
Force
Time
Elect. Current
Temperature
foot, mile
slug
pound
Second
Ampere
Fahrenheit
ft, mi
lb, #
s
A
F
USING METRIC PREFIXES
SI PREFIXES
Prefixes for multiples of 10 larger than 1:
Trillion
10 12
Billion
10 9
Million Thousand
10 6
10 3
T--
G--
M--
Tera, giga,
Hundred
10 2
k
mega, kilo,
Ten
10 1
1
h
da
(base unit)
hecto,
deka
Prefixes for multiples of 10 smaller than 1:
1
10 -1 10 -2
10 -3
10 -6
tenth
(base unit)
d
hundredth
c
thousandth
m
millionth
--
(gram, meter)
10 -9
billionth
--n
10 -12
trillionth
- -p
(gram, meter) deci, centi, milli, - - micro, - - nano, - - pico
SI CONVERSIONS BASED ON
PREFIXES
To convert units in SI system, move decimal. For instance:
Change 400 m to cm
(Meter is larger than centimeter)
Move decimal 2 places to right. (There are more
centimeters than meters; ea. piece is 1/100 of
meter, so moving decimal gives a bigger
number) 400 0 0 . ( Insert a “0” for ea. place
you move.) So 400 m = 40,000 cm
SI CONVERSIONS BASED ON
PREFIXES (CONT.)
Change 7.5 mg to g
Milligram is smaller than gram
Changing to grams involves moving decimal 3 places to
left.
7.5 mg = 0.0075 g
SI CONVERSIONS BASED ON
PREFIXES (CONT.)
Change 0.025 micrometers (m) to millimeters (mm)
Micrometer smaller than millimeter
Changing to micrometers:
0.025 m = 0.000025 mm
MASS VS. WEIGHT
 Mass – amount of matter in object.
 Constant in universe
 Measured with balance
 Units: kg or g (SI), slug or pound-mass (English)
 Weight – force of gravity on object’s mass.




Changes with amount of gravitational pull
Measured with scale
Differs at various locations in universe
Units: N (Newtons) (SI) or pounds (lb or #) (English)
FORCE IN MECHANICAL SYSTEMS
Mechanical force often measured with spring scale
Weight is common measurement
Units either Newtons (SI) or pounds (English)
Forces are VECTORS – have both magnitude (amount or size)
and direction showing where force is applied.
Other vectors: velocity, displacement, acceleration,
momentum
(SCALAR has magnitude only. Ex: mass, temp, pressure, time)
Forces (and all vectors) represented by symbol of arrow
Length indicates magnitude (longer = more force)
Heading = direction force is applied
BALANCED FORCES
No “leftover” force when all forces added together
Equal in amount and opposite in direction
(Newton’s 3rd Law)
Vector arrows are equal in length and opposite in
direction when forces balance.
Objects subject to balanced forces have NO NET
force (no left-over force) when combined. They are in
EQUILIBRIUM.
Balanced forces CANNOT change motion.
BALANCED FORCES (CONT.)
Moving objects may be in equilibrium; especially
true in space.
If no net force acts on object (it is in equilibrium;
all forces are balanced), it will continue moving in
a straight line at constant speed (Newton’s 1st
Law).
Moving objects move because they have inertia
(tendency to resist change in motion) , not
because something pushes or pulls object.
UNBALANCED FORCES
Unbalanced forces are unequal in amount or
direction.
There IS a NET force.
Objects not in equilibrium
Unbalanced forces cause change in motion.
Object speeds up, slows down, changes
direction. They accelerate
Vector arrows are unequal in length, or do not
show opposite directions
UNBALANCED FORCES (CONT.)
What is net force if each of 3 people on
left pulls with force of 230 N,
and each of people on right
pull with force of 300 N?
1. Draw a diagram of EACH person’s force
2. Add forces going in same direction to find total force in each
direction
+
=
3. Add opposite directions to determine NET force. (Left is
negative direction, and right is positive direction.)
+
=
UNBALANCED FORCES (CONT.)
Forces not in line can be combined to find net force by graphing
using “tail-head” method, or using mathematics
Example: A person on a dock pulls eastward with a force of 40#. At
the same time, a person on the shore pulls northward with a force of
30#. Find the net force on the boat.
1.
2.
Draw the 40# east force to scale. Put arrowhead on right since
force is to east.
At tip of arrowhead, draw the 30# force
northward, using same scale. Place
arrowhead on the top (north).
UNBALANCED FORCES (CONT.)
3. To find resultant vector, connect open ends of
vectors to form a triangle.
4. Draw the arrowhead adjacent to the 2nd
arrow’s head to indicate direction. Final
magnitude + direction of the vector =
DISPLACEMENT
5. Measure or calculate length of RESULTANT
to determine its magnitude.
UNBALANCED FORCES (CONT.)
Algebraic method for vectors at right angles:
1. Determine direction of each given vector.
1. Use Pythagorean theorem to determine resultant
amount
A plane flies 5.0 km west, then 2500 m south.
Calculate:
• a) distance traveled
• b) displacement
UNBALANCED FORCES (CONT.)
Trigonometric method for vectors:
1. Measure angle of a hypotenuse (vector) from
vertical (y axis) or horizontal (x axis).
2. Use sine and cosine of angle to determine
how much of the vector is in x direction and
how much is in y direction
UNBALANCED FORCES (CONT.)
3. Repeat for each vector.
4. Add all x’s together, keeping track of + and
– directions.
5. Repeat for y components.
6. Draw the new vector from the beginning
point to the (x,y) coordinates at end and
determine magnitude and direction of
resultant.
Determine x & y components
(adjacent and opposite side lengths)
y-axis
Hypotenuse
Opposite side
37o
Adjacent side
y-axis
Determine x & y components
Hypotenuse
= 100 m
Opposite side
= hyp(sin q)
q = 37o
Adjacent side = hyp(cos q)
UNBALANCED FORCES (CONT.)
Summary of ways to solve for unbalanced forces:
1. Add vectors going in same direction
2. Subtract vectors going in opposite directions. Larger
vector will determine resultant’s direction
3. Solve using
(A) Tail-head graphing method
(B) Pythagorean theorem
(C) Trigonometry
INERTIA
 Depends on mass; more massive objects have
more inertia
 First described by Galileo
 Resistance to change in motion
 Objects at rest tend to stay at rest
 Objects in motion tend to stay in motion in a
straight line at a constant speed
NEWTON’S FIRST LAW OF MOTION
 Based on Galileo’s work
 Objects in motion tend to keep doing what
they are already doing (moving in straight
line at constant speed, or staying motionless)
unless an outside force makes that motion
change
TORQUE
 Force-like quantity causing rotation or
turning
 Effect of force applied some distance from an
axis
 Directions are clockwise (cw) or
counterclockwise (ccw)
 Measured in pound-feet (lb.ft) or newtonmeters (Nm)
TORQUE CALCULATIONS
 t = F * L Note: t is Greek letter Tau
 Torque = force * length of lever arm that is
being turned
 Force measured perpendicular to lever arm
 Increase torque by increasing force or
increasing length of lever arm
TORQUE (CONT.)
 In gears, increasing diameter of drive gear
(one that applies force) increases torque
 Torques are in equilibrium when equal in
amount and opposite in direction
 Torque changes rotational speed (faster or
slower)