Cognito Quiz Questions Flashcards
Two identical 10 kg masses are placed a distance r apart. The gravitational force between them is 2.668 x 10^-10 N. Calculate the distance between the centres of the masses.
5m
Calculate the work done to move a 50 kg object through a gravitational potential difference of 5 J kg ^-1.
W = m x change in V
W = 50 x 5 = 250 J
What is escape velocity?
The minimum speed needed for an object to break free from the gravitational field of a celestial body without further propulsion.
Describe the characteristics of geostationary satellites and their applications.
- Geostationary satellites orbit Earth directly above the equator.
- Completes one orbit every 24 hours, synchronously with Earth’s rotation
- from Earth’s surface, they appear stationary in the sky
- Particularly useful for telecommunications, as the angle of the receiver does not need frequent adjustments.
- Other applications include weather monitoring, Earth observation, and global positioning systems.
What three factors determine the orbital speed of a satellite?
- Distance between two objects
- Mass of the central object
- Gravitational constant
Calculate the velocity of a satellite orbiting Mars at a distance of 9,400 km from the planet’s centre. The mass of Mars is 6.42 x 10^23 kg.
v = √GM/r
v = √6.67 x 10^-11 x 6.42 x 1-^23/ 9400000
v = 2,134 ms^-1
v = 2.1 km s^-1
What is the definition of the orbital period?
The time it takes for an object to complete one full orbit.
Which of the following typically produces noticeable gravitational fields?
Large mass like planets
What does the gravitational potential energy of an object depend on?
Both its mass and its height within the gravitational field.
What is the gravitational field strength at the surface of Mars if its mass is 6.41 × 10^23 kg and its radius is 3.4 × 10^6 m?
3.7 N kg^-1
What is the gravitational potential at a point?
The work done per unit mass to move an object from infinity to that point.
Derive the orbital period formula.
Force between two masses: F = Gm1m2/r^2
Centripetal Force: F = mv^2/r
Speed: v = s/t
Distance = circle circumference = 2π r
Orbital Period: t = 2π √r^3/GM
What is the orbital period of a satellite orbiting the Earth at an altitude of 300 km? The Earth’s radius is 6,371 km, and its mass is 5.97 x 10^24 kg?
Orbital Period: t = 2π √r^3/GM
t = 2π √(6,671,00^3/(6.67 x 10^-11) x (5.97 x 10^24)
t = 5,425 s
Calculate the gravitational potential energy of a 200kg object located 500km above the surface of a planet.
The planet’s mass is 6 x 10^24 kg and its radius is 5,000km. Use G = 6.67 x 10^-11 N m^2 kg^-2.
Calculate distance of object from centre of planet:
r = 5,000 + 500 = 5,500 km = 5.5 x 10^6
Calculate Gravitational Potential (V):
V = - GM/r = (- 6.67 x 10^-11 x 6 x 10^24) / 5.5 x 10^6
Calculate Gravitational Potential Energy (E):
E = mV
E = 200 x ( - 6.67 x 10^-11 x 6 x 10^24 / 5.5 x 10^6 )
E = -1.46 x 10^10 J
What does it indicate when gravitational field lines are close together?
A strong gravitational field.
Describe the relationship between an object’s kinetic energy and its gravitational potential energy at escape velocity.
- At escape velocity, an object’s kinetic energy is equal to its gravitational potential energy.
- This means that at escape velocity, the object has just enough kinetic energy to overcome the gravitational potential energy and break free from the gravitational field.
- Any speed less than the escape velocity would mean the object does not have enough kinetic energy to escape the gravitational field.
What is the work done in moving a 10 kg mass from a point with gravitational potential -20 J kg^-1 to another point with gravitational potential -15 J kg^-1?
Change in V = Final V - Initial V
Change in V = -15 - (-20)
Change in V = 5 J kg^-1
W = m x Change in V
W = 10 x 5 = 50 J
If the gravitational constant (G) is 6.67 x 10^-11 N m2 kg^-2, what is the gravitational field strength at a point 5,000 km from the centre of a celestial body with a mass of 7.35 x 10^22 kg?
g = GM / r^2
g =( 6.67 x 10^-11 x 7.35 x 10^22 ) / (5 x 10^6)^2
g = 0.196 N kg^-1
How does the magnitude of gravitational potential change with increasing distance from the object’s centre?
It decreases
What is the gravitational field strength at a distance of 10,000 km from the centre of a planet with a mass of 4.8 x 10^24 kg?
g = GM / r^2
g = 3.2 N kg^-1
In which direction do gravitational field lines point?
Towards the centre of the mass creating the field.
