2.1 MASS AND WEIGHT

Mass and Weight Objectives • Show familiarity with the idea of the mass of a body • State that weight is a gravitational force • Distinguish between mass and weight • Recall and use the equation W = mg • Demonstrate understanding that weights (and hence masses) may be compared using a balance

Mass and Matter •  The mass of an object depends on how much matter

there is in an object. •  Doesn’t matter if it’s a solid, liquid, or a gas

•  Two objects of the same mass contain the same amount of matter.

SI Unit •  The SI Unit of mass is the kilogram (kg). We might use

gram when it is more convenient.

• Mass: a measure of the amount of matter something contains.

Weight •  The weight of an object depends on its mass.

•  This is because weight is due to the downward pull of the Earth’s gravity on the object and the force of gravity depends on its mass.

•  The greater the mass of an object is, the greater its weight is!

•  Weight is a force!

The Newton • We measure weight in Newtons because the SI unit of

force is the Newton (N).

• We use a Newtonmeter to measure an object’s weight.

•  The weight of an object of mass 1kg near the Earth’s surface is 10N.

The Newton (cont.) •  For any object near the Earth’s surface, the force of

gravity on it is 10N for every kilogram on its mass.

• So Weight is: • mass of 1kg = 10N • mass of 5kg = 50N • mass of 20kg = 200N

Gravitational Field Strength • How much does a 50kg person weigh on earth?

• Weight = mass x GFS • Weight = 50kg x 10N/kg • Weight = 500 N

Gravitational Field Strength •  The force of gravity on any

object near the Earth’s surface is 10N for every kg of its mass.

• Gravitational Field Strength of Earth = 10N/kg

Gravitational Field Strength •  If we know the mass of an object, we can calculate its

weight using the equation:

Equation Quantities Symbols Units

W = mg Weight W Newtons (N)

Mass m Kilograms (kg)

Gravitational Field Strength

g Newtons per kilogram (N/kg)

Gravitational Field Strength • How much does a 50kg person weigh on the moon (GFS = 1.6N/kg)? • Weight = mass x GFS • Weight = 50kg x 1.6N/kg • Weight = 80 N

Think, Pair, and Share 1.  How much does a 3.5kg cat weigh on

Earth? 2.  How much does the same cat weigh on

the moon? 3.  If a man weighs 610N on earth, what is

his mass?

2.2 DENSITY

Density Objectives • Recall and use the equation ρ = mV • Describe an experiment to determine the density of a liquid and of a regularly shaped solid and make the necessary calculation • Describe the determination of the density of an irregularly shaped solid by the method of displacement • Predict whether an object will float based on density data

Density • Density of two different materials can be compared by

comparing the masses of same-sized blocks of each material. •  We can do this by using a balance. Since each block has the same

volume, the block with the greater mass has the greater density.

Density • Density: a substance’s mass per unit of volume.

•  The SI unit of density is the kilogram per cubic meter (kg/m3) although the gram per cubic centimeter (g/cm3) is often used.

Equation Quantities Symbols Units ρ = m/V Density ρ g/cm3

Mass m grams (g)

Volume V Cubic Centimeter (cm3)

Density Tests •  There are 3 ways to test the density of an object: 1.  Density of a regular solid object 2.  Density of a liquid 3.  Density of an irregular solid

Density of a regular solid object 1.  To measure the mass of

the object, use an electronic balance.

2.  To measure the volume of a regular solid, measure its dimensions using a ruler (in cm). Use the measurements and the formula to calculate volume.

3.  Then plug in ρ = m/V

Volume of a Rectangular Prism • Rectangular Prism Volume: l � w � h

Volume of a Cylinder

• Cylinder’s Volume: π � r2 � h

Solid Example 1.  A rectangular block of gold is 0.10m in length, 0.08m in

width, and 0.05m in thickness. 1.  Calculate the volume 2.  If the mass of the block is 0.76kg, what is its density?

Solution: Volume =l � w � h 0.10m � 0.08m � 0.05m = 0.0004m3

Solution:

density = mass = 0.76kg = 1,900 kg/m3 volume 0.0004m3

Density of a Liquid 1.  Use a graduated cylinder to find the

volume of the object. 2.  Find the mass of an empty beaker.

Then pour the liquid into the beaker and take the new mass. To find the mass of the liquid, use this equation:

•  Then plug in ρ = m/V

Total mass of beaker & Liquid – mass of beaker = mass of liquid

Liquid Example A graduated cylinder contained a volume of 120cm3 of a certain liquid. The liquid was then poured into an empty beaker of mass 51g. The total mass of the beaker and the liquid was then found to be 145g. a.  Calculate the mass of the liquid in grams b.  Calculate the density of the liquid in g/cm3

Solution: mass of liquid = 145 – 51 = 94g volume = 120cm3

Solution:

density = mass = 94g = 0.78g/cm3 volume 120cm3

Density of an irregular solid • Use a method called

displacement

1.  Use a balance to find the mass. 2.  Place the object graduated

cylinder with enough water to submerge the object and observe the increase in water level. This increase is the volume of the object.

3.  Then plug in ρ = m/V