Gravitational fields and field strength

An aircraft is flying horizontally at an altitude of 10 000 m and a constant speed of 220 m s^–1. 17

While maintaining this speed, the controls are adjusted so that the aircraft is in projectile motion until the altitude is 7500 m.

Throughout the projectile motion the passengers experience apparent weightlessness.

A condition for projectile motion is constant vertical acceleration. State the other condition.

Show that t, the time taken to reach the new altitude of 7500 m, is about 23 s.

Determine the magnitude and direction of the velocity of the aircraft at time t.

velocity =........ m s

angle to the vertical........

Explain why the engines of the aircraft must provide thrust during the projectile motion.

Explain why the passengers are described as ‘weightless’ during the projectile motion of the aircraft.

A scientist uses a rocket to study the Earth’s atmosphere.

The scientist launches the rocket from rest at the point A at t = 0 seconds. The force produced by the rocket’s engine causes it to accelerate.

At t = 50 seconds, the rocket’s engine no longer produce an accelerating force as all of the fuel has been used. The rocket has reached point B. Its velocity is now 3.1 km s^–1 at an angle of 75° to the horizontal.

The rocket engine works by expelling hot gas backwards.

Explain, using Newton’s laws of motion, how the engine causes the rocket to accelerate between t = 0 and t = 50 s.

The MAVEN spacecraft orbits Mars and studies its upper atmosphere.

The diagram below shows the orbit of MAVEN around Mars.

Mark an X on the diagram to show the point in the orbit where MAVEN has maximum

acceleration.

Explain how Kepler’s 1st law applies to MAVEN’s orbit around Mars.

The table shows data for four orbits around Mars.

Phobos and Deimos are moons of Mars.

An areostationary orbit for Mars is the equivalent of a geostationary orbit for Earth.

Show that Kepler’s 3rd law applies to this data.

Suggest two reasons why MAVEN was not placed in an areostationary orbit.

The table shows some data on the planet Venus.

Calculate the magnitude of the gravitational field strength g at the surface of Venus.

Give your answer to 3 significant figures.

=........ N kg^–1 g

Two identical space probes, A and B, land on a flat surface on Venus.

Probe A lands at the north pole. Probe B lands on the equator.

Each probe has mass 760 kg and volume 1.7 m³.

Calculate the centripetal acceleration a of probe B at the equator due to the rotation of Venus about its axis.

=........ m s^–2 a

The atmosphere exerts the same upthrust on each probe.

Using your answer to (a), calculate the upthrust acting on each probe.

Explain which probe will experience the greater normal contact force from the surface of Venus.

Both the ISS and the astronauts inside it are in free fall.

Explain why this makes the astronauts feel weightless.

Calculate the value of the gravitational field strength g at the height of the ISS above the Earth.

=........ N kg^–1 g

Use the information in (b)(ii) and the data below to show that the root mean square (r.m.s.) speed of the air molecules inside the ISS is approximately 15 times smaller than the orbital speed of the ISS.

• molar mass of air = 2.9 × 10^–2 kg mol^–1

• temperature of air inside the ISS = 20 °C

The ISS has arrays of solar cells on its wings. These solar cells charge batteries which power the ISS. The wings always face the Sun.

Use the data below and your answer to (b)(ii) to calculate the average power delivered to the batteries.

• The total area of the cells facing the solar radiation is 2500 m².

• 7% of the energy of the sunlight incident on the cells is stored in the batteries.

• The intensity of solar radiation at the orbit of the ISS is 1.4 kW m^–2 outside of the Earth’s shadow and zero inside it.

• The ISS passes through the Earth’s shadow for 35 minutes during each orbit.

The Earth is surrounded by a gravitational field.

Which of the following statements is/are correct about the gravitational field lines near the surface of the Earth.

1 They are parallel. 2 They show the direction of the force on a small mass. 3 They are equally spaced.

A Only 1

B Only 1 and 2

C Only 2 and 3

D 1, 2 and 3

Your answer

Which of the following is a correct unit for gravitational field strength?

J kg⁻¹ A

N kg⁻¹ B

N m² kg⁻² C

kg m s⁻¹ D

Your answer

A graph of y against distance r from the centre of a planet is shown below.

The graph shows that y is inversely proportional to r².

Which quantity is best represented on the y-axis of the graph?

A Period of a satellite orbiting the planet.

B Gravitational potential of the planet.

C Gravitational field strength of the planet.

D Kinetic energy of a satellite orbiting the planet.

Your answer