Measurement test
A 8 g object displaces 50 mL of water. What is its specific gravity?
0.16
The density of water is:
0.1g/cm^3
1 mL =
1 cm^3
0.001 kilogram equals to what?
1 gram = 1,000 milligrams
0.001 L
1 mL
1 cm^3 =
1 mL
1m^3 =
1,000 L
1 kilogram equals to what?
1,000 grams (g) = 1,000,000 milligrams (mg)
A box has a length of 5 cm, a width of 10 cm, and a height of 2 cm. The volume of the box is:
100 cm^3
1 liter =
1000 milliliters
A rock is dropped into 15 mL of water. It displaces 10 mL. The volume of the rock is:
10mL
Evan's playroom is 4 m by 3 m. The area of the room is:
12m^2
If the inside of a person's rectangular trunk measures 2 feet by 3 feet by 4 feet, what is the volume of the trunk?
24 cubic feet
2,000 mL is equal to:
2L
3 mL is equal to:
3cm^3
The specific gravity of an object is 14.5. The object displaces 4 mL of water. What is its mass?
58 g
On Earth, the average measurement of g is:
9.8 m/s^2
What does a balance measure?
A balance measures the quantity of matter independent of its form or shape. This quantity of matter is called mass.
Why is the metric system easier to use than the English system?
A typical page is 8.25 inches wide. To convert this measurement to feet requires remembering that 12 inches is equal to one foot. After division the number is .688 feet. To convert this measurement into units of a mile is even more awkward. This time the conversion factor is 5,280 feet per mile. Once again long division is required to determine that a page is .00013 miles wide. In the English system, many conversion factors have to be memorized, and many more errors are likely to occur.
Cubic centimeter
A unit of measure equal to the space enclosed by a cube 1 cm by 1 cm by 1 cm.
Cubic meter
A unit of measure equal to the space enclosed by a cube 1 m by 1 m by 1 m.
Standard
Accepted reference unit that is mutually agreed upon as the basis of measurement for that physical characteristic.
The story of Archimedes
According to an old story, King Hiero of Syracuse, recognizing the scientist's talents, asked him to determine whether the royal crown, which was supposed to be made of pure gold, contained any silver. Archimedes was puzzled for a time, but one day while taking a bath he concluded that his apparent loss of mass was equal to the mass of the water displaced. It occurred to him that he might put the crown and equal masses of gold and silver in water, one after another, and compare the volumes of water displaced. If the crown and an equal mass of gold should displace equal quantities of water, he would prove that the crown was made of pure gold. If the crown displaced more water than an equal mass of gold but less than an equal mass of silver, he would know that the crown was alloyed with silver.
Volume
All matter takes up space. The measure of this space is called volume. The standard unit of volume is the liter (L), however, this unit is usually reserved for liquids. Milliliters (mL) and cubic centimeters (cm³) are also commonly used. One milliliter is equal to one cubic centimeter.
How phase effects density:
All substances exist in one phase or another. Some substances, such as water and minerals, can exist in more than one phase, depending on the temperature and pressure of their surroundings. The density of such a substance depends upon its phase. For example, the density of liquid helium is different than the density of helium in its gas phase. The same is true of liquid hydrogen. The molecules of an element are farther apart in the gas phase. The gas will usually have less mass within a given volume.
What is the magnitude of the earth's gravity?
Among the planets of our solar system, the magnitude of the earth's gravity is selected to represent 1.0
Density
Amount of matter packed into a unit of volume; equal to mass divided by the volume of the substance. Matter has another physical property that is important to study: this quality is called density. Density is a measure of how much matter is packed into a given volume.
How pressure effects density:
Another factor that influences density is pressure. When a bicycle tire is pumped up, the volume changes very little, but the tire contains much more air. Therefore, as the pressure on a gas is increased, the density of the gas is increased. A trash compactor is another example of increased pressure that causes an increase in density. As more and more trash is added, volume does not increase. The increase in pressure results in more trash being packed into the same space. As this happens, density will increase. Density is directly proportional to pressure: D ~ P
Calculating area
Area is a measurement of the surface of an object. The standard unit is the square centimeter (cm²). The square meter (m²) and the square kilometer (km²) are also used. Area is measured by multiplying the length of an object by its width (A = L x W). For example, in the following diagram, Area 1 is equal to 2 cm x 3 cm, or 6 cm². Area 2 is equal to 1 cm x 4 cm, or 4 cm².
What happens when the distance between the masses gets altered?
As the distance between the masses increases, the force of gravity decreases by the distance squared. If the distance is doubled, the force decreases to 1/4 the original force; if the distance is tripled, the force decreases to 1/9 the original force. This is why various planets have different magnitudes of gravitational force. The primary factor is their differences in mass.
What happens as the mass of either object increases?
As the mass of either object increases, the force of gravity increases by the same proportion.
Length
Centimeters, meters, and kilometers are the metric units corresponding to the English units of inches, feet, yards, and miles. A typical piece of paper is 21 centimeters wide. To express the width of a piece of paper in meters is just a matter of moving the decimal point two places to the left to become 0.21 meters. If, for some reason, it were necessary to express a page width in kilometers, the decimal would be moved three additional places to the left and become 0.00021 kilometers.
What does this mathematical expression mean? D ~ P
Density is directly related to pressure.
What does this mathematical expression mean? D ~ 1/T
Density is inversely related to temperature.
What would effect the weight of a person on Earth?
Earth is not a perfect sphere so there are different distances to the center of Earth's mass. Variations in the density of the earth's crust affect the gravitational constant at different locations on Earth's surface.
Why is gravity on the surface of Jupiter is only two-and-a-half times the gravity on the surface of Earth?
Even though Jupiter has many times the mass of Earth. The answer is that the surface of Jupiter is farther from the center of Jupiter than Earth's surface is from its center. Therefore, while the gravity of Jupiter is greater than Earth's because of Jupiter's greater mass, the increase is relatively small because of increased distance from the center. You must always measure the distance from the center of a mass, not from the surface.
Formula for gravitational force
F=Gm1m2/r^2
The mathematical statement that shows the relationship between gravity and mass
Fg ~ m/d^2
If the weight of displaced liquid and the weight of an object are the same, the object will:
Float, but partially submerged
How is gravity measured?
Gravity is measured in meters per second squared (m/s2). The standard unit of force is the newton (N). Since weight is a measure of the force of gravity on an amount of mass, it is measured in newtons when mass is measured in kilograms.
What happens if the mass is doubled or tripled?
If one mass is doubled, the force is doubled; if one mass is tripled, the force is tripled.
What are some difficulty with measuring the volume of a gas?
It can be difficult to contain, it could be soluble in liquid, and it varies depending on the container it's in.
The space shuttle is descending through the earth's atmosphere. How is the force of gravity affected?
It will increase with descent.
Equal-arm balances are devices that are used to measure:
Mass
How do you find the volume of water?
One way to find the volume of the water is to calculate the volume of the cube. The volume of the cube is determined by multiplying the length (L), width (W) and height (H) of the cube. The mathematical equation for this type of calculation is L x W x H.The scientists' water sample was 1 x 1 x 1, or 1 cubic centimeter (cm³). Thus the space that was occupied by one gram of water, under a certain set of conditions, can be used as the basic unit of volume. The volume of complex shaped containers can be determined by measuring how many milliliters or liters of water they can hold. If an irregular shaped container is found to hold exactly 436 mL of water, then its volume is also equal to 436 cm3.
kilogram (kg)
Standard metric unit of mass; mass of 1 L of water; symbolized by kg.
Liter
Standard unit of volume, equaling a cube 10 centimeters on a side; symbolized by L.
Volume
Teaspoons, tablespoons, cups, quarts, and gallons are the basic units of volume in the English system. The metric system makes use of milliliters and liters. Although most American recipes are still given in the English system, new cookbooks are listing metric units in the margin. Multiplying a recipe to serve a crowd requires cumbersome conversions in the English system. Most cooks would have to search through a cookbook to find the table of conversions, which states that 3 teaspoons equals 1 tablespoon, and that 16 tablespoons will fill 1 cup. If a multiplied recipe called for 40 teaspoons of an ingredient, dividing by 3 would be necessary to determine that 13.3 tablespoons were needed. Since 16 tablespoons equals one cup, by dividing 16 into 13.3 the cook would learn that a quantity of .83 cups is needed.
How temperature effects density:
Temperature greatly affects volume. As temperature increases, the volume of most solids and gases increases. Therefore, when density of a substance in any particular phase is given, its temperature must also be given. As temperature increases, density will decrease. Therefore, density is inversely proportional to temperature. This relationship is inverse, or opposite: as the temperature increases, the molecules bounce further apart, and density decreases. D = 1/T. The relationship of density to temperature and pressure is: D = p/t
Density is affected by:
Temperature. This relationship is inverse, or opposite: as the temperature increases, the molecules bounce further apart, and density decreases. Pressure is directly related to density. As the pressure increases, matter is crushed into a smaller volume, thus increasing the density. As a substance changes from a solid to a liquid to a gas, its density generally decreases. Water is a notable exception. Icebergs float, and freezing water expands in cracks of rocks, forcing them to break and crumble. The solid form of water is less dense than the liquid form.
buoyancy
The apparent loss of weight of a substance when in a liquid.
Archimedes' Principle
The buoyant force exerted by a liquid is exactly equal to the weight of the liquid displaced.
What is a common use for density?
The comparison of one substance to another. Density compares masses of equal volumes, such as the mass of a cubic centimeter of iron with the mass of a cubic centimeter of wood.
precision
The consistency with which the same result is achieved when an object is repeatedly measured or an experiment is repeatedly performed.
Why is the equal-arm balance the most accurate measurement of mass?
The formula for weight can be rearranged to calculate mass. However, the accuracy of this calculation is dependent on the accuracy of the measurement of weight. For this reason, the equal-arm balance remains the most accurate measurement of mass.
When finding the volume of a regularly shaped solid, you can usually use what method?
The formula method
How about other planets?
The gravitational forces of other planets, depending on their relative masses, will be greater or less than that of Earth. Mercury's force of gravity (relative to Earth) is .38. Jupiter is 2.5 on this relative scale.
accuracy
The measure of exactness to the true and actual value.
The Metric System
The metric system was first developed by Gabriel Mouton in 1670. It was later revised by French scientists, primarily Antoine Lavoisier and Joseph-Louis Lagrange. The system was called metric from the Greek word metron, which means measurement.
The principle of density and buoyancy
The principles of density and buoyancy were devised by the Greek scientist Archimedes ( 287- 212 B.C.. Unlike most other thinkers of his time, he believed in experimental evidence rather than conclusions formed by thought processes alone (philosophy). Consequently he experimented widely and made many contributions to science.
specific gravity
The ratio of the density of an object divided by density of water.
meter
The standard unit of length in the metric system (m).
liter
The standard unit of volume in the metric system (L).
Calculating volume
The volume of many objects can be calculated by multiplying length by width and height (V = L x W x H). For example, the volume of an aquarium that is 50 cm long, 40 cm wide, and 30 cm high is 50 cm x 40 cm x 30 cm, or 60,000 cm³. The volume of irregularly shaped objects, like rocks, is more difficult to find. The displacement method can be used to find the volume of these objects. The object is placed in a measured amount of water. The amount of water moved, or displaced, by the object is then measured. The volume of the object is equal to the volume of water displaced.
Which factors can be changed for a gas without changing its mass?
Volume, pressure, temperature, and density.
The equation used to describe weight is:
W = mg; the W stands of weight, the M stands for mass, and the G stands for Gravity
Calculating Buoyant Force
We can calculate buoyant force by comparing the weight of the displaced water to the weight of the object. If the weight of the displaced water (the buoyant force) is greater than the weight of the object, then the object will float. If the weight of the displaced water (the buoyant force) is less than the weight of the object, then the object will sink. If an object does float, then part of the object will rise above the water. As it rises above water, less and less of the object is below the water line, displacing less and less water, generating less and less buoyancy. Eventually, the object will rise until the part of the object still under water generates the same buoyant force as the weight of the entire object and it reaches equilibrium.
Weight
Weight is a measure of the pull or attraction between two objects.
Is mass universal?
Yes. The quality of matter called mass is universal. No matter where in the universe a kilogram of matter exists, it will always be a kilogram.
Finding the volume of a sphere
You can measure the radius and use the formula v = 4/3 π r^3
A liter is equal to _______
a cube 10 centimeters (10 cm) on each side (1,000 cm3)
Matter is _______
anything that has mass and volume.
The length of a pencil would most likely be measured in:
centimeters
When using water displacement to measure the volume of an irregularly shaped solid, like a rock, which of the following would be a more appropriate unit to convert milliliters to?
cubic centimeter
The metric system is based on _______________.
decimals. The United States dollar can be compared to metrics. The dollar is divided into dimes and pennies. To convert from one dollar ($1.00) to one dime ($.10), all that is required is to move the decimal point to the left one place. In converting from one dime ($.10) to one penny ($.01) the decimal point is simply moved again one place. To move from penny to dime and back to dollar is only a matter of moving the decimal point to the right rather than to the left.
If the weather forecaster tells you that the pressure is falling, what is the air density doing?
decreasing
Archimedes used the _____ method to determine the king's crown was made of gold.
displacement
A metric recipe is:
easy to multiply for service to a crowd. If a recipe must be tripled and if it called for 20 milliliters of sugar, multiplying by three would indicate that 60 milliliters were needed. If 500 milliliters of flour were required for one recipe, then 1,500 milliliters would be needed for a triple recipe. Since 1,000 milliliters equals a liter, this amount of flour would be equal to 1.5 liters. Metric recipes require no awkward mathematics or charts when a cook wishes to alter a recipe.
Metric units for density
g/cm3
If the combined mass of two objects increases by a factor of 10, how will F g be affected?
increased by 10 times
When a cold front passes your location, the temperature drops rapidly. What happens to the air density?
increases
The displacement method for measuring volume:
is not always accurate, can be used to measure the volume of solids, and may yield incorrect results if the matter is soluble in liquid.
A cubic meter (m³) is _________________ a cubic centimeter (cm³).
larger than
The weight of an object is 200 N. The object sinks in tub of water. The bouyant force is:
less than 200 N
At the top of a high mountain, the weight of an object is:
less than at sea level
The density of ice is:
less than that of water
The standard unit of measurement for volume is the:
liter
Density equals:
mass/volume
The standard unit of measurement for length is the:
meter
Which combination of units expresses volume?
m³, cm³, km³
Gravity causes:
objects to attract one another
A granulated solid like salt, sugar, or sand can be measure directly using a method similar to the liquid method:
pour the solid into a graduated contained and record the volume.
To find the volume of a solid:
put a solid into liquid
Archimedes' Principle is commonly stated as:
the buoyant force exerted by a liquid is exactly equal to the weight of the liquid displaced. This means that if we immerse an object in water, the water will push up on the object with a certain force. We find that this force is always equal to the weight of the water that we have displaced (pushed out of the way). The displaced water has the same volume as the object.
The unit that is defined as the standard unit for volume is _________.
the cubic meter
The standard liter can be divided into many subdivisions. The most common subdivision is _________
the milliliter (mL)
The weight of an object on the surface of a planet is determined by:
the radius of the planet as well as its mass. The magnitude of gravitational force is inversely proportional to the square of the distance between the objects. As you ascend above the surface, the force of gravity (weight) decreases as the distance to the center of mass increases.
The liter is commonly accepted as ________
the standard unit for volume
If a substance besides water is changed from a gas to a liquid and then to a solid, what happens to the particles?
they get closer together
What is the equivalent volume occupied by three milliliters of water?
three cubic centimeters
