Question
Question 6.2
A 10 g ball is thrown upwards and then allowed to fall downwards on planet Xenon. It takes 5 s for the ball to reach the ground. The velocity-time graph shown below describes the motion of an object as it falls downwards on Planet Xenon for 5 s. Assume that the only force acting on the falling object is the gravitational force of Planet Xenon.
Figure 9: Graph of velocity vs time.
Question 6.2.1 [2 marks]
Use the graph to calculate the acceleration of the falling object on Planet Xenon.
Question 6.2.2 [3 marks]
15
The radius of planet Xenon is 6,22 x105 m. Use an appropriate and relevant formula to calculate the mass of planet Xenon.
Question 6.2.3 [4 marks]
Planet Yania, a neighbouring planet of Planet Xenon is half the mass of Planet Xenon. The distance between their CENTRES is 1,5 x108 m.
Figure 10: Diagram showing the distance between two planets Xenon and Yania. Calculate the gravitational force exerted by planet Xenon on Planet Yania.
TOTAL: 11
A 10 g ball is thrown upwards and then allowed to fall downwards on planet Xenon. It takes 5 s for the ball to reach the ground. The velocity-time graph shown below describes the motion of an object as it falls downwards on Planet Xenon for 5 s. Assume that the only force acting on the falling object is the gravitational force of Planet Xenon.
Figure 9: Graph of velocity vs time.
Question 6.2.1 [2 marks]
Use the graph to calculate the acceleration of the falling object on Planet Xenon.
Question 6.2.2 [3 marks]
15
The radius of planet Xenon is 6,22 x105 m. Use an appropriate and relevant formula to calculate the mass of planet Xenon.
Question 6.2.3 [4 marks]
Planet Yania, a neighbouring planet of Planet Xenon is half the mass of Planet Xenon. The distance between their CENTRES is 1,5 x108 m.
Figure 10: Diagram showing the distance between two planets Xenon and Yania. Calculate the gravitational force exerted by planet Xenon on Planet Yania.
TOTAL: 11
Answers
GPT 3.5
Question 6.2.1:
The acceleration of the falling object can be calculated using the slope of the velocity-time graph. The slope is equal to the acceleration. From the graph, the velocity increases from 0 m/s to 10 m/s in 5 seconds. Therefore, the acceleration can be calculated as:
Acceleration = Change in Velocity / Time taken
Acceleration = (10 m/s - 0 m/s) / 5 s
Acceleration = 2 m/s^2
Therefore, the acceleration of the falling object on Planet Xenon is 2 m/s^2.
Question 6.2.2:
The formula to calculate the mass of a planet based on the radius and acceleration due to gravity is:
Acceleration due to gravity (g) = GM / R^2
Where:
g = acceleration due to gravity on the surface of the planet
G = gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2)
M = mass of the planet
R = radius of the planet
From the given data, the acceleration due to gravity on Planet Xenon is approximately 2 m/s^2 and the radius is 6.22 x 10^5 m. Substituting these values into the formula:
2 = (6.67 x 10^-11 * M) / (6.22 x 10^5)^2
Solving for M (mass of Planet Xenon) gives:
M = 1.99 x 10^25 kg
Therefore, the mass of Planet Xenon is approximately 1.99 x 10^25 kg.
Question 6.2.3:
The gravitational force between two masses can be calculated using the formula:
Force = (G * m1 * m2) / r^2
Where:
G = gravitational constant
m1, m2 = masses of the two objects
r = distance between the centers of the two objects
Given that Planet Yania is half the mass of Planet Xenon, the mass of Planet Yania is half of the mass of Planet Xenon:
m2 = (1/2) * m1 = (1/2) * 1.99 x 10^25 kg
Substitute the values into the formula:
Force = (6.67 x 10^-11 * 1.99 x 10^25 * (1/2) * 1.99 x 10^25) / (1.5 x 10^8)^2
Solving for Force gives:
Force = 2.11 x 10^15 N
Therefore, the gravitational force exerted by Planet Xenon on Planet Yania is approximately 2.11 x 10^15 N.
Total: 11 marks
The acceleration of the falling object can be calculated using the slope of the velocity-time graph. The slope is equal to the acceleration. From the graph, the velocity increases from 0 m/s to 10 m/s in 5 seconds. Therefore, the acceleration can be calculated as:
Acceleration = Change in Velocity / Time taken
Acceleration = (10 m/s - 0 m/s) / 5 s
Acceleration = 2 m/s^2
Therefore, the acceleration of the falling object on Planet Xenon is 2 m/s^2.
Question 6.2.2:
The formula to calculate the mass of a planet based on the radius and acceleration due to gravity is:
Acceleration due to gravity (g) = GM / R^2
Where:
g = acceleration due to gravity on the surface of the planet
G = gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2)
M = mass of the planet
R = radius of the planet
From the given data, the acceleration due to gravity on Planet Xenon is approximately 2 m/s^2 and the radius is 6.22 x 10^5 m. Substituting these values into the formula:
2 = (6.67 x 10^-11 * M) / (6.22 x 10^5)^2
Solving for M (mass of Planet Xenon) gives:
M = 1.99 x 10^25 kg
Therefore, the mass of Planet Xenon is approximately 1.99 x 10^25 kg.
Question 6.2.3:
The gravitational force between two masses can be calculated using the formula:
Force = (G * m1 * m2) / r^2
Where:
G = gravitational constant
m1, m2 = masses of the two objects
r = distance between the centers of the two objects
Given that Planet Yania is half the mass of Planet Xenon, the mass of Planet Yania is half of the mass of Planet Xenon:
m2 = (1/2) * m1 = (1/2) * 1.99 x 10^25 kg
Substitute the values into the formula:
Force = (6.67 x 10^-11 * 1.99 x 10^25 * (1/2) * 1.99 x 10^25) / (1.5 x 10^8)^2
Solving for Force gives:
Force = 2.11 x 10^15 N
Therefore, the gravitational force exerted by Planet Xenon on Planet Yania is approximately 2.11 x 10^15 N.
Total: 11 marks