Define the term force and give the unit in which force is measured - Leaving Cert Physics - Question 6 - 2006

Being a vector quantity means that force has both magnitude and direction. This implies that the effect of the force not only depends on how strong it is (the magnitude) but also on the direction in which it acts. For example, a force of 10 N acting to the right is different from a force of 10 N acting to the left.

The size of the gravitational force between two bodies depends on:

1. The mass of each body: The greater the mass of either body, the stronger the gravitational force between them.
2. The distance between the two bodies: The gravitational force decreases as the distance between the two bodies increases; this relationship is described by the formula: $F = G \frac{m_1 m_2}{r^2}$ where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.

Acceleration due to gravity, denoted as 'g', is the acceleration that an object experiences when it is in free fall towards the Earth (or another celestial body) due to gravity. On Earth, this value is approximately 9.81 m/s². It represents how fast an object will speed up as it falls, and it can vary slightly based on location.

To calculate the acceleration due to gravity on the moon, we can use the kinematic equation for free fall:

$s = ut + \frac{1}{2} a t^2$

where:

• $s$ is the distance fallen (1.6 m),
• $u$ is the initial velocity (0 m/s, since it is dropped),
• $a$ is the acceleration due to gravity, and
• $t$ is the time of fall (1.4 s).

Substituting the known values:

$1.6 = 0 + \frac{1}{2} a (1.4)^2$

This simplifies to:

$1.6 = \frac{1}{2} a (1.96)$

Rearranging gives:

$a = \frac{1.6 \times 2}{1.96} \approx 1.63 m/s²$

This closely approximates the accepted value of 1.6 m/s² for the moon.

The weight of an object can be calculated using the formula: $W = mg$ where:

• $W$ is the weight,
• $m$ is the mass (120 kg), and
• $g$ is the acceleration due to gravity on the moon (1.6 m/s²).

Substituting the known values: $W = 120 \times 1.6 = 192 \text{ N}$ Thus, the astronaut's weight on the surface of the moon is 192 Newtons.

The astronaut's weight is greater on Earth than on the moon because gravitational acceleration on Earth (approximately 9.81 m/s²) is significantly higher than that on the moon (1.6 m/s²). Weight is directly proportional to the gravitational field strength; therefore, an object will weigh less where gravity is weaker.

The moon does not have a significant atmosphere because it lacks sufficient gravity to retain atmospheric gases. The lower mass of the moon results in weaker gravitational pull, making it unable to hold on to lighter gases, which tend to escape into space. Additionally, the moon's lack of geological activity means there are no processes that would produce or recycle atmospheric components.