Sir Isaac Newton deduced that the weight of an object is due to the force of gravity - Leaving Cert Physics - Question 6 - 2014

Newton's law of universal gravitation states that:

• The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

This can be expressed mathematically as:

$F \propto \frac{m_1 m_2}{r^2}$

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

$g = \frac{GM}{r^2}$

Where:

• $G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$ (gravitational constant)
• $M = 6.4 \times 10^{23} \text{ kg}$ (mass of Mars)
• $r = 3.4 \times 10^6 \text{ m}$ (radius of Mars)

Now substituting values:

$g = \frac{(6.67 \times 10^{-11}) (6.4 \times 10^{23})}{(3.4 \times 10^6)^2}$

Calculating this gives:

g ≈ 3.7 m/s² (to one decimal place).

The wheels of the rover are not as strong as those of the vehicle that would be needed for Earth because Mars has a lower gravitational pull. The mass of the Mars rover, which is considerably lesser than that of Earth vehicles, and the less force exerted on the wheels results in the need for less robust construction.

The weight of an object can be calculated using the formula:

$W = mg$

Where:

• $m = 899 \text{ kg}$ (mass of Curiosity)
• $g = 9.8 \text{ m/s}^2$ (acceleration due to gravity on Earth)

Thus:

$W = 899 \times 9.8 ≈ 8810.2 \text{ N}$

Therefore, the weight of Curiosity on Earth is approximately 8810 N.

The mass of an object remains the same regardless of the gravitational field it is in. Thus, the mass of Curiosity on Mars is still:

899 kg.

To find the weight on Mars, we again use the weight formula:

$W = mg$

Where:

• $m = 899 \text{ kg}$
• $g = 3.7 \text{ m/s}^2$ (acceleration due to gravity on Mars)

Thus:

$W = 899 \times 3.7 ≈ 3326.3 \text{ N}$

So, the weight of Curiosity on Mars is approximately 3326 N.

Radio waves are part of the electromagnetic spectrum, which also includes microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These waves share the characteristic of traveling at the speed of light in a vacuum, allowing the Curiosity rover to send and receive signals across vast distances.