If the weight of an object on the Earth's surface is 2.5 x 10 ^3 N, what is its weight on the moon's surface…

Analysis

The question asks us to calculate the weight of an object on the Moon, given its weight on Earth and the relationship between the gravitational pull of the Moon and the Earth.

Concept

Weight ($W$) is the force of gravity acting on an object's mass ($m$). It is calculated using the formula: $W = mg$ where $g$ is the acceleration due to gravity.

Since the mass ($m$) of an object remains constant regardless of its location, the weight of an object on the Moon ($W_m$) is directly proportional to the gravitational acceleration on the Moon ($g_m$). Given that $g_m = \frac{1}{6} g_e$ (where $g_e$ is gravity on Earth), it follows that: $W_m = \frac{1}{6} W_e$

Solution

1. Identify the given values: • Weight on Earth ($W_e$) = $2.5 \times 10^3\text{ N} = 2500\text{ N}$ • Gravitational relationship: $g_m = \frac{1}{6} g_e$

2. Apply the formula: $W_m = \frac{W_e}{6}$ $W_m = \frac{2500}{6}$

3. Calculate the result: $W_m = 416.666... \text{ N}$ Rounding to two decimal places, we get 416.67 N.

Conclusion

Comparing our result to the provided options, the correct value is 416.67 N.

Exam Tip

Always remember that mass is a scalar quantity that stays the same everywhere in the universe, while weight is a vector quantity (a force) that changes depending on the gravitational field strength of the location. If a question asks for mass, ensure you divide the weight by $g$ ($10\text{ m/s}^2$) first!