How much does a suitcase weigh if it has a mass of 22.5 kg?
The Correct Answer and Explanation is:
To determine how much a suitcase weighs, we need to convert mass into weight using the formula:Weight=Mass×Acceleration due to gravity\text{Weight} = \text{Mass} \times \text{Acceleration due to gravity}Weight=Mass×Acceleration due to gravity
Given:
- Mass = 22.5 kilograms
- Acceleration due to gravity (on Earth) = 9.8 meters per second squared (m/s²)
Weight=22.5 kg×9.8 m/s2=220.5 Newtons (N)\text{Weight} = 22.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 220.5 \, \text{Newtons (N)}Weight=22.5kg×9.8m/s2=220.5Newtons (N)
Final Answer:
The suitcase weighs 220.5 newtons (N).
Explanation
Weight and mass are related but different concepts in physics. Mass is the amount of matter in an object and is measured in kilograms (kg). It remains the same regardless of location. On the other hand, weight is the force that gravity exerts on an object due to its mass. Weight varies depending on the gravitational pull of the place you are in. For example, an object will weigh less on the Moon than on Earth because the Moon’s gravity is weaker.
The standard acceleration due to gravity on Earth is approximately 9.8 meters per second squared. When we multiply the mass of an object by this gravitational constant, we calculate its weight in newtons (N), which is the standard unit for force in the International System of Units (SI).
In this case, the suitcase has a mass of 22.5 kilograms. By multiplying this mass by 9.8, we find that the suitcase weighs 220.5 newtons. This weight tells us how much force the suitcase exerts downward due to Earth’s gravity. It is important to note that if you were to weigh the suitcase on a different planet or in space, the number of newtons would change because the gravitational acceleration would be different. However, the mass would still remain 22.5 kilograms.
Understanding the distinction between mass and weight helps in various scientific and engineering contexts, such as designing equipment for space missions or calculating structural loads in construction.
