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Mass
In physics, mass refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties.
The inertial mass of an object determines its acceleration in the presence of an applied force. According to Isaac Newton's second law of motion, if a body of mass m is subjected to a force F, its acceleration a is given by F/m.
A body's mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass m1 is placed at a distance r from a second body of mass m2, the first body experiences an attractive force F given by
enrichment
In the International System of Units (SI), mass is measured in kilograms (kg).
The gram (g) is 1⁄1000 of a kilogram.


Mass&Weight relationship
On the surface of the Earth, the weight W of an object is related to its mass m by

where g is the acceleration due to the Earth's gravity, equal to about 9.81 m s−2. An object's weight depends on its environment, while its mass does not: an object with a mass of 50 kilograms weighs 491 newtons on the surface of the Earth; on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons.








All Physicists Agree That:
Weight and mass are not synonymous.
Weight is a force.
The weight of an object depends on its location - things can weigh differently in different places.
Weight is NOT Mass
The first thing to realize about weight is that weight is not the same as mass, even though the terms are used synonymously in everyday life. Mass measures inertia - it is a property of an object. Weight is a force - something that happens to an object.
Weight is a Force - But WHICH Force?
Physicists and engineers all agree that weight is a force, but there is considerable disagreement and confusion about what force weight is - different textbooks say different things, and some textbooks say different things in different places. Mostly, opinion is divided into two camps. For some people, "weight is the force of gravity", and for others "weight is what a scale reads". You might think that the two statements are equivalent - but they aren't. There are advantages and (unfortunately) disadvantages with either point of view.
Weight as Gravitational Force
Our text, among others, says:
Weight: The force of gravity upon a body.1
Advantages:
Weight is always easy to calculate. The weight of an object is w = mg, where m is the mass of the object, and g is the acceleration of free fall.
Disadvantages:
This is not the intuitive, laymen's definition of weight. You can't feel the force of gravity. You feel the floor pushing up on you, not the downward pull of the Earth. You don't feel pulled toward the Earth, even when you jump into the air.
Weight as What a Scale Reads:
There is a standard definition of weight, given by the International Organization for Standardization (ISO) which says:
The weight of a body in a specified reference system is that force which, when applied to the body, would give it an acceleration equal to the local acceleration of free fall in that reference system. - ISO 31-3 "Quantities and Units. Part 3, Mechanics", 19922
Can this be simplified without losing precision? Yes! It turns out that this definition of weight is equivalent to saying:
Weight is what a scale reads.3
which is equivalent to saying:
An object's weight equals the force required to support it.4
Advantages:
It seems at first that this is a much more natural, practical and useful way to look at weight than associating weight directly with the force of gravity. ("What a scale reads" and "the force of gravity" are not always equivalent - see The Elevator Problem for details...) This definition - weight is what a scale reads - also fits quite naturally with the idea of "weightlessness".
Disadvantages:
In order to use this definition effectively in applications requires a pretty sophisticated understanding of Newton's Laws - particularly Newton's Third Law - which most beginning physics students generally don't have.



Volume & Density







Weight vs. Mass







Weight







Mass & Weight

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Mass is a measure of amount of substances in a body.

SI unit kilogram (kg)

The mass of a body resists a change in the state of rest or motion of the body.

The tendency of a body to resist a change in the state of rest or motion is known as Inertia.

The greater the mass, the more resistance there will be to the change in state (or greater in inertia).

E.g.: compare to stop a metal ball & a plastic ball at the same size.

Gravitational field

A region in which a mass experience a force due to gravitational attraction.

E.g. : When you release an object from a distance above the ground , the object will drop to the ground.

*The earth has it’s own gravitational field, so does the moon and any other large planets.

Gravitational field strength, g, in defined as the gravitational force per unit mass.

SI unit: NKg-1

SI unit: m/s2

(As the GFS is infect the gravitational acceleration)

Weight

_ The product of mass and gravitational field strength

W=mg

SI unit: Newton (N)

Mass	Weight
The amount of substance in a body (a constant that is not affected by the gravitational field strength)	Due to the pull of gravity on a body (Varies according to the gravitational field strength)
Is a scalar quantity	Is a vector quantity
SI unit: Kilogram (kg)	SI unit: Newton (N)
Measured by an electronic balance or a beam balance	Measured by a spring balance or a compression balance

Density
___ The mass per unit volume of an object

p=m/v

Note that different substances have different masses even though they have the same volume. This is because different substances have different densities. A substance with a high density is said to be denser, whereas a substance with a low density is said to be less dense. This is the reason why oil (that is less dense than water) floats on water. On the other hand, honey, which is denser than water. The table on the next page shows the densities of some substances.

Substance	Density (kg/m3)
Styrofoam	100
Cork	250
Mayonnaise	910
Vegetable oil	927
Water	1000
Honey	1420
Carbon	2250
Glass	2500
Gold	19300

Denser objects sink & less dense object float.

1.A measuring cylinder contains 30 cm³ of liquid. When a stone of weight 0.92 N is dropped into the liquid, it sinks to the bottom and the liquid level rises to the 70 cm³ graduation. Taking the weight of 1 kg to be 10 N, calculate

(i) The mass of the stone,

(ii) The density of the stone.

Explain why it would not be possible to use this method to determine the density of cork which would float in the liquid.

Ans.

(i) Mass, m=W/g

=0.92/10

=0.092kg

(ii) volume of stone = change of reading on measuring cylinder

=70-30

=40cm³

Density of stone = mass of stone/volume of stone

= 92/40

= 2.3g/cm³

To find the volume of the cork accurately, it needs to be immersed completely into the liquid. Since the cork floats in the liquid, the volume of the liquid displaces would not be equal to the volume of the cork. Thus it would not be possible to use this method to determine the density of cork.

2.The mass of 600 spherical lead pellets is found to be 66g and the total volume of the pellets is found to be 5.7cm³. Calculate

(i) the total weight of the pellets

(ii) the volume of one pellets,

(iii) the density of the pellets in kg/m³,

(iv) the number of pellets which has a mass of 1.00 kg. The force of gravity acting on a mass of 1.00 kg is 10.0 N

Ans.

(i) weight of the pellets = mg

= (66/1000) x 10

= 0.66 N

(ii) volume of one pellets = 5.7/600

= 9.5 x 10^-3 cm³

= 9.5 x 10^-9 m³

(iii) density of the pellets = total mass/ total volume

= 66/5.7

= 11.6 g/ cm³

= 11.6 x 10³ kg/ m³

(iv) number of pellets = 1.00 / (0.066 / 600)

= 9090 (3 s.f.)

3.The acceleration due to gravity near the surface of the moon is 1.6 m s ^–2.

(a) what is the gravitational field strength?

(b) What is the weight of an astronaut on the moon if his mass is 80 kg?

Ans.

(a) gravitational field strength = acceleration due to gravity

= 1.6 N kg^-1

(b) weight = mg

= 80 kg x 1.6 m s^-2

= 128 N

4. The table below shows the densities of a few substances.

Substance	Density (kg/m3)	Substance	Density (kg/m3)
Styrofoam	100	Cork	250
Mayonnaise	910	Oil	927
Water	1000	Honey	1420
Carbon	2250	Glass	2500
Gold	19 300

State whether each of the following statements is true of false.

(a) A cork will float in water, honey and oil.

(b) Water will float in honey.

(c) When we have honey, oil and water in a glass, oil will be at the top layer, followed by honey and water will be at the bottom of the glass.

(d) Carbon is denser than gold.

(e) Glass will float on honey.

(f) When we have mayonnaise, oil and water in a glass, mayonnaise will be on top, followed by oil and then water.

Ans.

(a) True

(b) True

(c) False

(d) False

(e) False

(f) True

5. Two balls of different materials are of the same size. Do they necessarily have the same weight? Explain.

Ans.

Two balls of the same size need not have the same weight. The reason behind is because they are made of different materials and hence, they have different densities.

From the equation density = mass/volume, we get mass = density x volume.

Therefore, even though the two balls have the same volume, different densities will cause them to have different masses. Since weight = mass x gravitational field strength, hence, the two balls will have different weights.

6. Objects A and B are thrown into the sea. Object A floats but object B sinks. When the two objects are thrown into a swimming pool, both of them sink. Given that the densities of sea water and water in the swimming pool are 1000 kg/m³ and 1030 kg/m³ respectively, what can be concluded about the densities of object A kg/m³ and object B kg/m³?

Ans.

Since object A floats in sea water buy sinks in pure water, we know that it is less dense than sea water but denser than pure water. Since object B sinks in both sea and pure water, object B is denser than sea water. Hence, we conclude that the density of object A is between the densities of pure water and sear water. The density of object B is higher than of sea water and pure water.

1.The gravitational field strength on the surface of the Moon is 1.6N/kg. Which values of mass and weight are correct for an object placed on the Moon’s surface?

	Mass/kg	Weight/N
A	10	1.6
B	10	16
C	16	10
D	16	160

Ans. B

2.Three objects are cut from the same sheet of steel. They are different shapes but they all have the same mass.

Which object has the greatest density?

A the disc

B the L-shape

C the square

D all have the same density

Ans. D

3.A quantity of gas in a sealed balloon cooled sown. No gas is allowed to enter or leave the balloon. How do the listed properties of the gas change?

	Mass	Volume	Density
A	Decreases	Stays the same	Increases
B	Increases	Stays the same	Decreases
C	Stays the same	Decreases	Increases
D	Stays the same	Increases	Decreases

Ans. C

4.What is mass?

A. The weight of an object

B. The amount of substance in a body

C. The volume of the substances in a body

D. The density of the substance in the body

Ans. B

5.The weight of a man on a certain planet is 50MN. His mass on the Earth is 50kg. What is the gravitational acceleration due to the planet?

A.10⁶ m/s²

B.10³ m/s²

C.10 m/s²

D. None of the above

Ans. A

6.Planet A has gravitational acceleration of 10 m/s². Planet B has twice the gravitational acceleration of planet A. An identical steel ball is released from the same distance above the ground on both planets respectively. Which

of the following statements is true?

A. They both land on the planets at the same time because they accelerate at the same rate.

B. They both land on the planets at the same time because they both have the same mass.

C. Ball A reaches first because it accelerates faster.

D. Ball B reaches first because it accelerates faster.

Ans. D

7.The mass of a glass sphere is 900g. The radius is 5cm. calculate the density of the sphere. (Take volume of sphere = 4/3 πr³

A. 1920 kg/m³

B. 1720 kg/m³

C. 1500 kg/m³

D.600 kg/m³

Ans. B

8.Compression balance may be used anywhere in the Universe to accurately measure __________.

A. mass

B. weight

C. density

D. kinetic energy

Ans. B

9.What will happen to the density and weight of an object that is launched from the Earth into the Space?

A.It’s the density stays constant while its weight decreases.

B.Its weight stays constant while its density decreases.

C.Both its density and weight remain constant.

D.Both its density and weight decrease.

Ans. A

10.The weight of a man on the Moon is 96N. Given that the gravitational acceleration of the man on the Earth and the Moon are 10 m/s² and 1.6 m/s² respectively, what is his weight on the Earth?

A. 60 N

B.96 N

C. 600 N

D. 960 N

Ans. C

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