CIE iGCSE Co-Ordinated Science P1.4 Density Exam Style Questions Paper 3
Question
(a) A team of students enter a competition to see who can build the highest tower from identical wooden cubes. One cube has a mass of 200 g. One cube has a volume of 250 cm3.
(i) Calculate the density of one wooden cube.
▶️Answer/Explanation
Solution:
Density is calculated using the formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Given:
Mass = 200 g
Volume = 250 cm3
\[ \text{Density} = \frac{200 \, \text{g}}{250 \, \text{cm}^3} = 0.8 \, \text{g/cm}^3 \]
Therefore, the density of one wooden cube is 0.8 g/cm3.
Answer: 0.8 g/cm3
(ii) Calculate the weight of each wooden cube. Gravitational field strength = 10 N/kg.
▶️Answer/Explanation
Solution:
Weight is calculated using the formula:
\[ \text{Weight} = \text{Mass} \times \text{Gravitational Field Strength} \]
Given:
Mass = 200 g = 0.2 kg
Gravitational Field Strength = 10 N/kg
\[ \text{Weight} = 0.2 \, \text{kg} \times 10 \, \text{N/kg} = 2 \, \text{N} \]
Therefore, the weight of each wooden cube is 2 N.
Answer: 2 N
(b) Fig. 6.1 shows the towers of cubes built by two teams. Team A’s tower is only 6 cubes tall before it falls over. Team B’s tower reaches 10 cubes tall and stays standing.
(i) Use ideas about stability and centre of mass to suggest why team A’s tower falls over.
▶️Answer/Explanation
Solution:
The stability of an object depends on the position of its centre of mass. If the centre of mass is not directly above the base of the object, it becomes unstable and may topple over. In the case of Team A’s tower, the centre of mass is likely not aligned over the base, causing the tower to fall. Team B’s tower, on the other hand, has a centre of mass that is aligned over the base, making it more stable and able to stand taller.
Answer: Team A’s tower falls over because the centre of mass is not directly above the base, making it unstable.
(ii) Explain why more work is done to lift a cube to the top of the tower as the tower gets taller.
▶️Answer/Explanation
Solution:
Work is done against gravity to lift a cube to a certain height. The work done is calculated using the formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
As the tower gets taller, the distance (height) that each cube needs to be lifted increases. Therefore, more work is required to lift each cube to the top of the tower as the tower grows taller.
Answer: More work is done because the height (distance) increases as the tower gets taller, requiring more energy to lift each cube.
(iii) State the type of energy that is greater for a cube at the top of the tower compared with a cube lower down the tower.
▶️Answer/Explanation
Solution:
The type of energy that is greater for a cube at the top of the tower is gravitational potential energy. This is because gravitational potential energy depends on the height of the object above the ground. The higher the cube is, the more gravitational potential energy it possesses.
Answer: Gravitational potential energy
(c) One student hits two cubes together. He hears the sound echo from the back wall of the room. The time interval from the student hitting the cubes to the student hearing the echo is 0.25 seconds. The distance to the wall is 39 m.
Calculate the speed of sound through the air.
▶️Answer/Explanation
Solution:
The speed of sound can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Given:
Distance to the wall = 39 m
Time for the sound to travel to the wall and back = 0.25 s
Since the sound travels to the wall and back, the total distance is twice the distance to the wall:
\[ \text{Total Distance} = 2 \times 39 \, \text{m} = 78 \, \text{m} \]
\[ \text{Speed of Sound} = \frac{78 \, \text{m}}{0.25 \, \text{s}} = 312 \, \text{m/s} \]
Therefore, the speed of sound through the air is 312 m/s.
Answer: 312 m/s