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 another point mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. It can be mathematically expressed as:

$F = G \frac{m_1 m_2}{r^2}$

where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the two masses, and $r$ is the distance between their centers.

To find the acceleration due to gravity on the moon, we use the formula:

$g_{moon} = G \frac{M_{moon}}{R_{moon}^2}$

Substituting the given values:

• Mass of the moon, $M_{moon} = 7 \times 10^{22} \text{ kg}$
• Radius of the moon, $R_{moon} = 1.7 \times 10^6 \text{ m}$
• Gravitational constant, $G = 6.7 \times 10^{-11} \text{ N m}^2/\text{kg}^2$

We have:

$g_{moon} = 6.7 \times 10^{-11} \frac{7 \times 10^{22}}{(1.7 \times 10^6)^2}$

Calculating that gives:

g_{moon} \approx 1.6 \text{ m/s}^2.

The weight of an object is given by the formula:

$W = mg$

For the buggy on Earth:

• Mass, $m = 2000 \text{ kg}$
• Acceleration due to gravity, $g_{earth} = 9.8 \text{ m/s}^2$

Therefore, the weight is:

$W_{earth} = 2000 \times 9.8 = 19600 \text{ N}$

The mass of an object does not change regardless of its location. Therefore, the mass of the buggy on the moon remains the same as its mass on Earth, which is:

$m = 2000 \text{ kg}$

The weight of the buggy on the moon can be calculated using the formula:

$W_{moon} = mg_{moon}$

Using the mass of the buggy and the acceleration due to gravity on the moon:

• Mass, $m = 2000 \text{ kg}$
• Acceleration due to gravity on the moon, $g_{moon} \approx 1.6 \text{ m/s}^2$

Thus, the weight is:

$W_{moon} = 2000 \times 1.6 = 3200 \text{ N}$

Less powerful rockets are needed to leave the surface of the moon compared to those required on Earth due to the lower gravitational pull exerted by the moon. The acceleration due to gravity on the moon is about $1.6 \text{ m/s}^2$, while on Earth it is approximately $9.8 \text{ m/s}^2$. This means that the force required to overcome gravity and launch a spacecraft from the moon is significantly lower, thus allowing for less powerful rockets.