Mass, Weight and Density

Facts to KnowState what mass is.

. Mass is a measure of the amount of matter in a body

Q:

Q: What is gravitational field?

. A gravitational field is a region in which a mass experiences a force due to gravitationalattraction.

Q: Define gravitational field strength.

. The gravitational field strength at any point in a gravitational field is the gravitational force per

unit mass exerted on anv bodies.

i$ProUems to Solve1. The weight of a rock on Earth is 20 N.

(The gravitational acceleration on Earth and on the Moon are 10 m/s2 and l.'7 n/s2 respectively.)

a. What is the mass of the rock on Earth? ( 2 marks )

b. What is the mass of the rock on the Moon? ( l mark)

c. What is the weight of the rock on the Moon? ( 2 marks )

41 Chapter 4 Mass, Weight and Density

Danya

l Edu

catio

n

2. An attempt to determine the volume of air trapped in a block of sponge is done by measuring themass of a piece of dry sponge and then measuring its mass again after it is soaked with water. Theexperiment assumes that the water will take up the air space in the sponge without changing its size.

Some data for the experiment is given below.

Mass of dry sponge 2oe

Volume of dry sponge 1000 cm3

Mass of wet sponge 980 g

Gravitational fields strength on Earth 10 N/ kg

Densitv of water I glcm3

Density of air 0.0012 g/cm3

a. Let the volume of trapped air in the dry sponge be V. Calculate the mass, in g, of the trapped airin the dry sponge in term of V. ( 2 marks )

b. Let the volume of trapped air in the dry sponge be V. Calculate the mass, in g, of the water whichoccupies the space of the trapped air. ( 2 marks )

c. Determine the value of Y in cm3 ( 3 marks )

rl

42 Chapter 4 Mass, Weight and Density

Danya

l Edu

catio

n

d. An extension of the experiment is to determine the density of the pure sponge material.Calculate the density of the pure sponge material (without air space). ( 4 marks )

3. To determine the density of an eel, the eel is first lowered into a measuring cylinder filled with waterand then the measuring cylinder is placed on an electronic balance.

Some data for the experiment is given below.

Volume of water in the measuring cylinder 100 cm3

Mass of measuring cylinder 0.5 kg

Volume of water and eel in the measuring cylinder 400 cm3

Mass of measuring cylinder with eel and water l.2kg

Gravitational fields strength on Earth 10 N/kg

Density of water 1000 kg/m3

Density of air l.2kglm3

a. Calculate the mass of the eel. ( 3 marks )

b. Calculate the volume of the eel. ( 2 marks )

( 3 marks )c. Calculate the density of the eel in kg/m3.

43 Chapter 4 Mass, Weight and Density

Danya

l Edu

catio

n

4. The mass of an object on Earth is 10 kg but the object has a weight of 100 N.

a. What is the difference between mass and weight? ( 2 marks )

b. What is the gravitational fleld strength on Earth? ( 2 marks )

c. List two separate equipment used to measure mass and weight of an object respectively.( 2 marks )

5. When anything is placed in a liquid, it experiences an upward force known as upthrust. A man feelslighter in water because the upthrust acts against the weight of the man producing a smaller downwardresultant force.

In an experiment to investigate the relationship between the upthrust and the weight of the liquiddisplaced, the following data is recorded.

t(

Weight of stone hanging in the air = 5.00 NWeight of stone hanging in the water = 3.15 NDensity of air = 0.001 kg/m3Density of water = 1000 kg/m3Density of stone = 2700 kglm3Density of oil = 800 kg/m3Density of steel = 8000 kg/m3Volume of stone = 1.85 x 104 m3

Gravitational fleld strength on Earth = 10 N/kg

5.0 N

3.1 N

Volume of stone = 1.85 x l0-5 m3

44 Chapter 4 Mass, Weight and Density

stone

Danya

l Edu

catio

n

a. Calculate the upthrust acting on the stone when the stone is hanging in water. (lmark)

b. Calculate the weight of water displaced by the stone when it is lowered into the displacementcan. (3marks)

6. Archimedes' principle states that: When a body is completely or partially immersed in a fluid, itexperiences an upthrust equal to the weight of the liquid displaced. Upthrust is the upward force actedby the liquid on the object.

A steel cube of sides 2 cm is lowered into a measuring cylinder partially filled with water and oil as

shown in Diagram I and Diagram 2.

wateroil

Diasram 2 Diagram 2

a. What is the value recorded in the spring balance when the cube is immersed in water? ( 3 marks )

45 Chapter 4 Mass, Weight and Density

Danya

l Edu

catio

n

b. What is the upthrust acting on the cube when the cube is oil? ( 2 marks )

What is the upthrust acting on a toy boat which weighs 8 N floating on water as shown below?( l mark)

C

46 Chapter 4 Mass, Weight and Density

Danya

l Edu

catio

n

1

Misconceptions to Clarifr

The diagram below shows a box full of bigmarbles and a box full of small marbles.Given that the two boxes are identical and themarbles are of the same density, which of thefollowing statements is true?

box full of big marbles box full of small marbles

A The box with big marbles is heavier thanthe box with small marbles.

B The box with small marbles is heavier thanthe box with big marbles.

C The box with big marbles is as heavy as

the box with small marbles.D The box with big marbles has the same

density as the box with small marbles.()

It is indicated on a spring balance that themeasurement taken is in kilograms.

Which of the following statements about thisspring balance is correct?

A It measures the mass of an object directly.B It measures the weight of an object.C It estimates the mass of an object through

measuring the weight of the object.D It estimates the weight of an object through

measuring the mass of an object. ( )

2

kg

ll

3. Which of the following experiences the samegravitational field strength?

(1) A 50 kg mass resting on the floor(2) A 50 kg mass hanging on a 20 m tall tree(3) A 50 kg mass dropping down from a20 m

tall tree(4) A 100 kg mass resting on the floor

A (1) and (2) onlyB (l),(2), and (3) onlyC (1), (2), and (4) onlyD (r),(2), (3) and (4) ( )

4. Which of the following statement(s) is/arealways true?

(1) The inertia of an object is dependent onthe size of the object.

(2) Metal is heavier than feather.(3) When the mass of an object increases, the

weight of the object will also increase.

A (3) onlyB (1) and (3) onlyC all ofthe aboveD none ofthe above ( )

41 Chapter 4 Mass, Weight and Density

Danya

l Edu

catio

n