Download The distance around a figure is the perimeter. Measure

Unit 8 and 9
Customary and Metric Units and Conversions
Length and Area
The distance around a figure is the perimeter.
Measure perimeter in linear units, such as inches, feet, miles, meters centimeters. These
units are one dimensional.
1. Draw dark lines to illustrate the perimeter of these figures
The formula for perimeter is P = ∑sides
This translates as Perimeter is equal to the sum of the sides
(∑ (sigma) is used in math as a symbol to mean "the sum of")
The enclosed floor of a figure is the area. This is a two dimensional quantity
Measure area square units, such as square inches, square feet, square yards, square meters
The formula for the area of a rectangle is A = L W
This translates as Area is equal to the length times the width
When you use the formula for the area of a rectangle:
you are multiplying the number of unit squares that you need to form a single row by the
number of rows it takes to fill up the figure.
2. The squares in this rectangle illustrate this
The Customary Units for length are feet, inches and miles
Find the area and perimeter of these figures, convert to the indicated units
5.0 ft
3.
8.0 in
perimeter __________in
area___________ft2 convert to ______________in2
The metric unit for length is the meter. Prefixes are used for smaller and larger units
4.
2.5m
1.2m
275cm
152cm
perimeter _____________ cm
area___________cm2 convert to ___________m2
Volumes
When calculating volume think of how many "sugar cubes fit in the box".
Volume is measured in three dimensions so the units are in cubes.
cm3, ft3, yd3, m3 etc.
To calculate work with little cubes one unit on each side. Think how many will to cover the
"floor" in one layer and then how many layer deep to fill the space.
Formula for the volume of a box is Volume = (Base Area) ⋅ height. Again the height
must be perpendicular to the base
Find the volume of these shapes
5.
4 ft
10 ft
Volume in ft3__________________
6 ft
Convert to yd3 ______________
6.
15.0mm
35.3mm
22.0mm
Volume in mm3 __________________
Convert to m3 ________________
32.0mm
The Area of a triangle is
AT =
1
bh so the volume of this right triangular prism is V = AT h
2
Conversions between Metric and English
Conversions between systems are not any harder except for the arithmetic. See the small chart below for
the equivalencies for length measurements
1 inch = 2.54 cm
1 ft = 30.5 cm
1 yd = 91.4 cm
1 mile = 1610 mm = 1.61km
7.
It is about 24.0 km to Cashmere, how many miles is this?
8.
One hectare is 10,000 m2 (The area of a square 100m on each side) How many square feet in a
hectare?
9.
How many cubic meters in 5 yd3?
Capacity
Capacity is another way to measure volume. It is usually used with liquid volume.
The Customary units are gallons, quarts, cups and fluid ounces. How to you convert between these?
Metric Units of Capacity are based on the liter. 1 mL is the same size as 1 cubic centimeter (cc)
and 1 liter = 1000mL or 1000 cc. The metric liter is a little larger than a quart.
10. An automobile engine originally has a displacement of 2.300 liters. The engine is rebored and the
displacement is increased by 150.0 cubic centimeters. What is the displacement in liters after the
engine is re-bored?
Conversions
1 L = 1.06 qt and 1 gallon = 3.785 Liters
11. Use the equivalencies to Estimate the volume of a 12.0 oz pop can in liters.
Mass
Mass is the measure of the quantity of material making up an object. Weight is the measure of the earth's
gravitational force or pull on an object. So while in orbit an astronaut's mass remains constant but his
weight changes. On earth we tend to interchange these measurements, especially in the customary units,
where mass is usually expressed in pounds (a force unit).
In the metric system mass is measured in kilograms or grams.
1 gram is the mass of 1 cubic centimeter or milliliter of water at 4°C. A common object with the mass of
one gram is a paper clip
1 kilogram = 1000 grams and is the mass of l Liter of water.
Smaller masses are expressed in milligrams mg and micrograms µg.
12. Review the prefixes and complete the equivalencies
1 gram = _____________milligrams = _________________micrograms
1 milligram = ___________micrograms
13. An extra strength Tylenol tablet is 500 mg or ______________µg or ________g
For most conversion use 1 kg = 2.20 pounds
14. Calculate the mass of the ‘ideal airline’ 160.0lb person in kilograms.
15. A dump truck can haul about 12 cubic yards of dirt. If the average specific weight of dirt is 95lb/ft3.
How pounds of dirt is this?
For very large or very small units review the metric prefixes on your conversion chart
16. 350,000 microfarads (µF) as farads (F)
17. 97,000 kilobits (kb)and gigabits (Gb)
Temperature
Customary units are Fahrenheit and Rankine.
For Fahrenheit (°F) water freezes at 32° and boils at 212°, with 180 equal divisions or degrees in between.
The Rankine scale has the same size of degrees but beings at ‘Absolute zero’ where there is no molecular
movement. Absolute zero is at –460°F, so The conversion is R = °F + 460
Metric units are Celsius and Kelvin
For Celsius (°C) water freezes at 0° and boils at 100°. The Kelvin scale is tied to the Celsius scale with
absolute zero (0 K) at – 273 °C, so Use the Conversion K = °C + 273
18. Convert 300 K to °C
Conversion
To convert between scales use these relationships
Apply order of operation carefully
9
F = C + 32
5
5
C = (F − 32 )
9
19. Convert 80°F to C°
Velocity or Speed
Velocity =
∆d
∆t
Average velocity is calculated using the formula
It is a ‘compound unit because it is made up of more than one unit
Velocity is expressed in metric units of m/s or for a vehicle speed in km/h (kph).
In the English system the units are normally ft/s or miles/h (mph). Your car's speedometer is probably
calibrated in both mph and km/h.
20. Find the average velocity of a marathon runner who started at 10 AM, and finished a 26 mile run at
1:15 PM
21. Convert 65mph to km/h
Acceleration
Acceleration is how quickly you are speeding up or slowing down.
Average acceleration is calculated using the formula
The units for acceleration are normally ft/s2 or m/s2.
Where does the s2 come from?
accleration =
∆V
∆t
22. Find the average acceleration of a bicycle that goes from 5ft/s to 30 ft/s in 5 s, express in ft/s2
Force
Weight is a unit of Force. In the English system mass is customarily described in pounds which are force
units. In the metric system where mass is correctly described using kilograms, the ‘weight’ or Force
required to lift an object must calculated by the formula
F = ma
This translates as Force = mass times acceleration.
A Newton is the unit of force in the metric system 1 N = 1kg m /s2
23. Calculate the force required to lift a 1000 kilograms car.
Gravitational acceleration (g) is approximately 9.81 m/s2 on the earth surface
24. What is the force required to accelerate a 1000 kg car from 0 to 30 m/s in 5 seconds?
Work
Work is a measure of accomplishment rather than effort.
The Formula used to calculate work is
Translate this as Work = Force times distance
W = F ⋅d
Force is a measure of the strength of the push. The units of force are pounds (lb) in English units or
Newtons (N) in Metric. In order for work to be accomplished, the direction of the force and the direction
of movement must be the same. This is called a 'dot product' and so multiplication is indicated with a dot
The metric unit for Work is 1 Joule = 1 N m or 1kg m2/s2
Mechanical Work has English units of foot-lbs. 1 ft lb is the work done when lifting 1 lb 1 foot up.
To convert to metric use. 1 ft lb = 1.356 J
25. Calculate the work required to lift a 65 kg man, 5 m. Caution first find Force required to lift the man
= (mass )(gravitational acceleration)
26. A man weighing 198 lb climbs a 10,000 ft mountain. How much work does he do in ft-lbs
Power
Power measures how quickly work gets done. The formula for Power is
Power =
work done
F ⋅d
=
time elapsed
∆t
The unit of power in the metric system is the watt.
It is the same unit for mechanical work and electrical work
1 watt =1 Joule/s or 1N m/s or
Electrical power is calculated with P = IV and is also a watt 1 watt = 1volt amp
27. Calculate the power required to lift our 65 kg man, 5 m, in 5 seconds. (use the results of #25)
In customary units mechanical power commonly has units of Horsepower. This unit came from how
much power an average horse could produce.
1 horsepower = 550 ft-lb/s
28. A 2 ton block is lifted 10 yards in 3 minutes.
Determine the necessary horsepower.
To convert horsepower to watts use this conversion factor 1 hp = 745.7W.
29. Determine the wattage rating of a electric motor equivalent to a 110 hp engine Express in kW
(kilowatts)
Energy
Energy is actually another word for work. It is usually associated with the expenditure of power over a
given length of time.
Electrical Energy is often measured in kilowatt-hours. (kWh). It is the work done by a device working at
a constant rate of one kilowatt for one hour.
30. Rocky reach Dam has a peak generating capacity of 1.4 GW. If the dam operates at this capacity for 3
hours how many kWh has is produced?.
Heat and Thermal Energy
Thermal Energy is the energy associated with the random motion of the atoms of a substance, which is
measured by temperature.
Heat is thermal energy being added or removed from a substance. It is a form of work. Heat has its own
special units
The metric unit is the kilocalorie and is the heat need to raise the temperature of 1 kilogram of
water 1°° C.
The kilocalorie has a mechanical work equivalent . 1 kcal = 4184 J
The English unit is the British Thermal Unit or BTU. This is the heat need to raise the temperature of
1 lb. of water 1° F
Again there is a mechanical work equivalent 1 Btu = 778 ft-lb
And of course the conversion factor between systems 1 Btu = 0.2520 kcal
Heat loss and gain calculations
When heat is added or lost from materials, other than water, the change in the temperature is different the
Btu/lb or calories/kg. The specific heat capacity of a substance is the quantity of heat required to increase a
unit mass of the substance by one degree. The units on specific heats are kcal/kg°C or Btu/lb°F. here are a
few examples
material
specific heat (c)
water
1.00
copper
0.094
The heat required to raise the temperature of a mass can be calculated using the formula
This translates as heat = specific heat x mass x change in temperature
Q = cm∆T
31. How many kilocalories are required to raise the temperature of 4 kg of copper from 35°C to 53°C.