The weight of an object is due to the gravitational force acting on it - Leaving Cert Physics - Question 6 - 2008

Newton's law of universal gravitation states that every point mass attracts every other point mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It can be expressed mathematically as:
$F = G \frac{m_1 m_2}{r^2}$
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the two masses.

To calculate the acceleration due to gravity on the moon, we can use the formula:
$g_{moon} = G \frac{M_{moon}}{r_{moon}^2}$
where

• $G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$,
• $M_{moon} = 7 \times 10^{22} \text{ kg}$, and
• $r_{moon} = 1.7 \times 10^6 \text{ m}$.
  Substituting the values:
  $g_{moon} = 6.67 \times 10^{-11} \frac{(7 \times 10^{22})}{(1.7 \times 10^6)^2}$
  Calculating this gives:
  $g_{moon} \approx 1.6 \text{ m/s}^2$.
  Thus, the acceleration due to gravity on the moon is approximately 1.6 m/s².

The weight of the buggy on Earth can be calculated using the formula:
$W = mg$
where m is the mass (2000 kg) and g is the acceleration due to gravity on Earth (9.8 m/s²).
Thus,
$W = 2000 \times 9.8 = 19600 \text{ N}$.
Therefore, the weight of the buggy on Earth is 19600 N.

The mass of an object remains constant regardless of location. Therefore, the mass of the buggy on the moon is the same as its mass on Earth, which is 2000 kg.

To find the weight of the buggy on the moon, we can use the same weight formula:
$W_{moon} = mg_{moon}$
Using the mass of the buggy (2000 kg) and the gravitational acceleration on the moon (approximately 1.6 m/s²):
$W_{moon} = 2000 \times 1.6 = 3200 \text{ N}$.
Thus, the weight of the buggy on the moon is 3200 N.

A less powerful rocket is required to leave the surface of the moon because the moon's gravitational pull is significantly weaker than that of the Earth. On the moon, the gravitational acceleration is approximately 1.6 m/s², compared to 9.8 m/s² on Earth. This means that objects on the moon need less force (and consequently, less rocket power) to overcome gravitational pull and achieve escape velocity.