What is the mass of a 200 newton object?
The Correct Answer and Explanation is:
To find the mass of an object when given its weight in newtons, we can use the relationship defined by Newton’s second law of motion, which states that:
[
F = m \cdot g
]
Where:
- ( F ) is the weight (force) in newtons (N),
- ( m ) is the mass in kilograms (kg),
- ( g ) is the acceleration due to gravity, approximately ( 9.81 \, \text{m/s}^2 ) on the surface of the Earth.
In this case, the weight of the object is given as 200 N. To find the mass, we can rearrange the formula to solve for ( m ):
[
m = \frac{F}{g}
]
Substituting in the known values:
[
m = \frac{200 \, \text{N}}{9.81 \, \text{m/s}^2}
]
Calculating this gives:
[
m \approx 20.39 \, \text{kg}
]
Explanation
- Understanding Weight and Mass: It’s important to distinguish between weight and mass. Weight is a force that results from the gravitational attraction between an object and the Earth. Mass, on the other hand, is a measure of the amount of matter in an object and does not change regardless of the object’s location in the universe.
- Units: Weight is measured in newtons, which is a derived unit based on the International System of Units (SI). It is defined as the force required to accelerate 1 kilogram of mass at a rate of 1 meter per second squared. Thus, when we express weight in newtons, it is a reflection of the gravitational force acting on that mass.
- Gravity’s Role: The acceleration due to gravity (( g )) is a crucial factor in this calculation. On Earth, it is approximately ( 9.81 \, \text{m/s}^2 ), which means that for every kilogram of mass, the force of gravity exerts about ( 9.81 \, \text{N} ). Therefore, the mass of an object can be determined by dividing its weight by the gravitational acceleration.
- Practical Application: This calculation is vital in various fields, including engineering, physics, and everyday problem-solving, where understanding the mass of an object is essential for assessing its behavior under various forces, including gravitational, frictional, and tension forces.