What is meant by the term 'acceleration due to gravity'? A spacecraft of mass 800 kg is on the surface of the moon, where the acceleration due to gravity is 1.6 m s² - Leaving Cert Physics - Question 6 - 2012

A diagram should illustrate the module with arrows indicating the following forces:

• Weight (downward): Calculated as the gravitational force on the module, which is the mass times the acceleration due to gravity on the Moon (600 kg * 1.6 m/s²).
• Thrust (upward): The upward force exerted by the engine, which is given as 2000 N.

The resultant force (F) is calculated by subtracting the weight from the thrust:

$F = Thrust - Weight$

Here, Weight = 600 kg * 1.6 m/s² = 960 N.

Thus, the resultant force is:

$F = 2000 N - 960 N = 1040 N$

To find the acceleration (a) of the module, we use Newton's second law, which states:

$F = ma$

Rearranging gives:

$a = \frac{F}{m}$

Here, F is the resultant force (1040 N) and m is the mass of the module (600 kg):

$a = \frac{1040 N}{600 kg} = 1.73 m/s²$

Using the equation of motion:

$v = u + at$

Where:

• Initial velocity (u) is 0 (since it starts from rest).
• a is the acceleration calculated as 1.73 m/s².
• t is the time, which is 20 s.

So, $v = 0 + (1.73 m/s² * 20 s) = 34.6 m/s$

The engine would not be able to lift the module off the earth's surface, as the weight of the module on Earth is much greater than the thrust produced by the engine. The weight can be calculated as:

$Weight = mg = (600 kg)(9.8 m/s²) = 5880 N$

Since the thrust (2000 N) is less than the weight (5880 N), the engine could not overcome gravitational force on Earth.

The acceleration due to gravity on a celestial body depends on its mass and radius. The moon has significantly less mass and a smaller radius than Earth, resulting in a reduced gravitational pull. Therefore, the gravitational acceleration on the Moon is only 1.6 m/s² compared to Earth's 9.8 m/s².

The module does not need a streamlined shape because the Moon has a very thin atmosphere compared to Earth. The lack of significant air resistance means that aerodynamic drag is minimal during launch; therefore, a streamlined shape is not necessary to reduce drag, unlike spacecraft launched from Earth.