Question
Question 6.1 [2 marks]
State Newton’s law of universal gravitation.
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
State Newton’s law of universal gravitation.
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
Answers
GPT 3.5
Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
6.2.1 Acceleration can be calculated from the slope of the velocity-time graph. From the graph, the initial velocity is 10 m/s and the final velocity is 0 m/s. The time taken is 5 s. Using the equation of motion: final velocity = initial velocity + (acceleration x time), we can rearrange to find acceleration, which is -2 m/s^2 (as the object is moving downwards).
6.2.2
To calculate the mass of planet Xenon, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where G is the gravitational constant, r is the radius of the planet, and F is the force acting between the object and the planet. Given that the force is equivalent to the weight of the object on the planet, we can use the formula:
Weight = m * g = G * (M * m) / r^2
where M is the mass of the planet, m is the mass of the object, and g is the acceleration due to gravity on the planet.
Using the weight of the object (0.01 kg * 9.8 m/s^2) = G * (M * 0.01 kg) / (6.22 x 10^5 m)^2
Solving for M, the mass of planet Xenon can be calculated.
6.2.3
To calculate the gravitational force exerted by planet Xenon on planet Yania, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where m1 and m2 are the masses of the planets and r is the distance between their centers. Given that planet Yania is half the mass of planet Xenon, we can substitute the masses into the formula and calculate the gravitational force by using the distance between their centers.
6.2.1 Acceleration can be calculated from the slope of the velocity-time graph. From the graph, the initial velocity is 10 m/s and the final velocity is 0 m/s. The time taken is 5 s. Using the equation of motion: final velocity = initial velocity + (acceleration x time), we can rearrange to find acceleration, which is -2 m/s^2 (as the object is moving downwards).
6.2.2
To calculate the mass of planet Xenon, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where G is the gravitational constant, r is the radius of the planet, and F is the force acting between the object and the planet. Given that the force is equivalent to the weight of the object on the planet, we can use the formula:
Weight = m * g = G * (M * m) / r^2
where M is the mass of the planet, m is the mass of the object, and g is the acceleration due to gravity on the planet.
Using the weight of the object (0.01 kg * 9.8 m/s^2) = G * (M * 0.01 kg) / (6.22 x 10^5 m)^2
Solving for M, the mass of planet Xenon can be calculated.
6.2.3
To calculate the gravitational force exerted by planet Xenon on planet Yania, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where m1 and m2 are the masses of the planets and r is the distance between their centers. Given that planet Yania is half the mass of planet Xenon, we can substitute the masses into the formula and calculate the gravitational force by using the distance between their centers.