Download Force in Mechanical Systems

Force in Mechanical
Systems
Measuring
Measuring
 There are several systems of
measurement.




English
Cgs (very small)
Avoirdupois (ballistics)
SI (metric)
 We will be using English and metric (SI)
Measuring Length with a ruler
 For length we use a ruler for lengths
under a foot or a tape measure for
longer lengths.
Tape Measure
 Once you can read a ruler you certainly
can use a tape measure which is used in
many different careers and activities.
 View the link on using a tape measure
 Play the ruler game
Measuring lengths with a
caliper or micrometer
 For smaller lengths we use vernier
calipers or very small lengths
(thicknesses) we use a micrometer
Metric (SI) System
Force in Mechanical System
How do we measure forces?
 The English unit for force is the
pound (lb.)

The metric unit for force is the
Newton (N)
A Newton
1 Newton is approximately 1 stick of
margarine or butter (1/4 pound)
King Henry Doesn’t Mind
Discussing Church Matters
International System (SI)
 root units : meter liter gram
 Base Units Base units are meter, kilogram, second,…
 (see table 2 on page 6)
 Kilo
 K
hecto
H
Deka (root) deci
Da
d
centi
c
milli
m
 1000 100
10
1
0.1
0.01
0.001
 103
101
100
10-1
10-2
10-3
102
Metric Activity
You will need a meter stick
Remember:
-a millimeter is slightly less than a dime
-a centimeter is width of a pinky finger
-a decimeter is about a hand width
-a meter is slightly longer than the
distance from your nose to your finger tips
Changing Prefixes- 1
 Make a chart
K / H / Da / meter, liter , gram / d / c / m
378 cm to m
The decimal moves 2 places to the left
3.78 m
Changing Prefixes - 2
Property of One
 378 cm to m
 100 cm = 1 m
 378 cm X 1 m
1
100 cm
=
3.78 m
Force in Mechanical System
What are other common units?
SI
English
Length
meter (m)
foot (ft)
Time
second (s)
second (s)
Mass
kilogram
Pound mass
Weight Newton (N)
Pound (lb)
Mass & weight conversions
- 1 pound = 4.45 Newtons
- 1 kilogram weighs 9.8 Newtons
Assignments

Measuring Activities

Linear Math 1
Mass vs Weight
What is the difference between weight and
mass?
-Mass – the amount of matter in a
object
- measured in pound mass (lbm),
grams or kg
-Weight – mass and the measure of the
Earth’s gravitational pull
- measured in pounds (lb) or newtons
Force in Mechanical System
Can mass change?
- no, mass does not change
Can weight change?
-yes, weight can change as
gravity changes
Gravity is 1/6 less on the
moon.
Weight is a force

Weight is a force caused by the Earth’s
gravity
Gravity

Varies with elevation

Mt Everest
– weigh less

Death Valley
– weigh more

Would you weigh more or less in New
Orleans?

More you are below sea level
Force in Mechanical System
Are mass and weight the same thing?
- no, mass and weight are very
different
You weigh 120 lbs on Earth. What
do you weigh on the moon?

20 lbs
In Space

Your spine lengthens by 2 inches when in
0 gravity.
Weight = mass X Gravity
Variable
English
Weight
W
lb
Mass
m
lb-mass
Gravity
g
32 ft/s2
SI
N
kg
9.81 m/s2
To convert mass to weight
In our labs we convert mass/weight in SI
EX: Use the Property of One
500 g X 0.00981 N = 4.905 N
1g
100 Kg X 9.81 N
1 Kg
= 981 N
Convert Weight to mass

EX: Use the Property of One
25 N X 1 kg
9.81 N
4N
X
= 2.55 Kg
1g
= 407.7 g
0.00981 N

Weight and mass math ws
Vectors and Systems
What two factors determine the effect
of a force?
- the strength of the force
- direction of the force
What is the strength of the force
called?
- Magnitude
Force in Mechanical System
What is the difference between
vectors and scalars?
- a vector is a physical quantity that
has both a magnitude and direction
- forces, velocity, acceleration
- a scalar quantity only has a
magnitude
- temperature, pressure, mass
Force in Mechanical System
What is the difference between
vectors and scalars?
- a vector is a physical quantity that
has both a magnitude and direction
- forces, velocity, acceleration
- a scalar quantity only has a
magnitude
- temperature, pressure, mass
Which are vectors????

55 mph
55mph, E

20 ft, left
20 ft

30 N at 20 degrees
30 N

5 mm
5 mm, down
Answers to Vectors

Any number with a direction
55 mph
55mph, E

20 ft, left

30 N at 20 degrees



20 ft
30 N*
5 mm
5 mm, down
*Sometimes the unit indicates direction
How can we represent forces?
- all vectors can be represented by
arrows
- the arrow length represents the
magnitude of the force
- the arrow heading represents the
direction of the force
Tail
Head
Force in Mechanical System
Consider the example – A worker pulls
a heavy cart with a force of 30
pounds at an angle of 30o above the
floor. Draw out this vector.
30 lbs
30o
What is a balanced force?
-
-
forces that are equal in size and
opposite in direction
THERE IS NO MOVEMENT
example: two men
pushing on a fence
What is an unbalanced force?
- force that unequal in either size or
direction
- causes movement
example – man pushing lawn mower,
the mower moves
What is a net force?
- the force that is leftover when all
forces are taken into consideration
A man pulls a rope with 5 N of force to
the right. A second man pulls with
15 N of force to the left. What is the
net force on the rope?
- 10 N to the left
Are the forces on the rope
balanced or unbalanced?
- unbalanced
Will the rope move?
- Yes, because an unbalanced force
causes motion
Example – Four people are playing tug of
war. Two people on one side pull against
two people on the other side. The two on
the right each pull with 50 pounds of force.
The two on the left pull with 70 pounds of
force. What is the net force? (magnitude
and direction)
40 pounds of force to the right (net
force)
Newton’s Laws
When is a body at equilibrium?
- when all forces are
equal
- the body is at rest
What will happened to a body if it is at
rest and balanced force are applied to it?
- it will stay at rest (Newton’s First Law of
Motion)
NewtoN’s 1st Law of Motion
(also Law of Inertia)
An object at rest will remain at rest
An object in motion will remain in motion
Unless acted upon by an unbalanced force.
If a body is at rest and unbalanced forces
(net force) act on it, what will happen?
- the body will be
accelerated in the
direction of the force
(Newton’s Second
Law of Motion)
Newton’s 2nd Law
F = m a
If you push down a trampoline with
10 N of force, what how much force
will push back on you?
- 10 N of force will push you
up
- Newton’s Third Law of
Motion – for every action,
there is an equal and opposite
reaction
Newton’s 3rd Law of Motion
For every action there
is an equal and
opposite reaction
Adding Vectors
How do we add forces that act along
the same line?
- if the forces act in the same direction, we
add magnitude of the forces
- if the forces act in opposite directions, we
subtract the magnitude of the forces
Vector Addition
Joe’s car runs out of gas. Joe’s friend Anne
helps Joe push the car into the gas
station. Joe pushes with 200 lb and Anne
pushes with 180 lb. What is the net
force?
380 lb forward
What would happen if the two teams below
both pulled with a force of 750 lb?
- the rope would not move because the
forces are balanced or in equilibrium
Force in Mechanical System
How do we add forces that act at an angle?
- you cannot add forces when they act at
angles
- you can solve them graphically
What is the overall force when multiple
forces are acting on an object?
- a resultant force
- the resultant always acts in a direction
between the directions of the two forces
Graphical Analysis

Vectors are drawn as accurate as possible.

Rulers and protractors are used

Used when you don’t use trigonometry
Forces at Angles
- Step One – Look at the force vectors
- Choose scale for the line
-for ex: 1 cm = 10 lb
- use a ruler
-Step Two- Place a dot on the paper
-
Step Three –Draw the two force vectors coming
out of the dot while using the scale, ruler and
protractor (Be sure you are drawing the vectors
in the correct direction)
Force in Mechanical System
-Step Four – Draw a parallelogram
ALWAYS add the tail of the second vector to the head of
the first vector
-Step Five – Draw the resultant force- (the
diagonal line from the dot to the end corner)
-Step Six – Measure the length of the resultant
(magnitude) and measure the angle on either
side (direction)
- use the ruler and protractor
EX: Two people pull on a boat with ropes
that form a right angle. The person on the
right of the boat (on the dock) pulls with
40 pounds of force. The person in front of
the boat (on shore) pulls with 30 pounds
of force. What is the resultant force of the
boat?
Draw the 30 lb vector 3 inches long
and the 40 lb vector 4 inches long.

30 lb
40 lbs
Measure the Net Force


Make a parallelogram and measure the net force
(resultant) which is the diagonal line.
measure the angles on either side of the dot
30 lbs
40 lbs
Answer

The resultant or net force is the path that
the boat will take

Net force = 50 lbs ( the line was 5 inches)

Angles 53o, 37o
Torque
What is torque?
- the effect of a force applied on a
body at some distance from the axis
of rotation of that body
- torque causes rotation
What are two ways an object can
rotate?
- clockwise and counterclockwise
Torque
When is torque used?
- opening a paint
can, opening a door,
using a wrench to
turn a nut, turning
gears
Torque
How is torque measured?
- lb·ft (English)
- N·m (SI)
Rearranging the Torque
Equation
T
F
T= F (L)
F=T/L
L
L=T/F
Torque
How is torque calculated?
- T = (F)(L)
- torque = applied force x lever
arm
- applied force  lbs. or N
- lever arm  ft or m
Rotational Mathlab
You use a force of 20 lbs on a car lug nut.
The wrench (lever arm) is 24 inches long.
What is the torque of the lug nut?
24 inches X
T = (F)(L)
T=
1ft
12 inches
=
2 ft
20 lbs ( 2 ft) = 40 ft lbs
Linear Math Lab


You will be practicing mathematical
concepts pertaining to:
Vector and scalar quantities
1M1 lab

Pre lab- read the lab in the lab notebook
-Fill in the blanks


Lab quiz
Special Skills – reading a ruler and
graphing
1M2 Lab
 Prelab- Use the lab notebook and read
the lab
 Fill in the blanks
 Lab Quiz
 Special skill: reading a protractor
Work Cited
Thanks to My Most beautiful fantastic daughter who is just
the most wondrous young lady ever (that I shall buy
(hopefully) a present for Halloween because everyone
knows that’s like the best holiday ever besides
Christmas. And take out to dinner every night because
she’s just smexy like that) for designing the WHOLE
powerpoint and making it very beautiful.
And also thanks to the unknown person whose original
powerpoint is the basis of this one.
And thanks to the colleague who gave it to me.