A woman weighs 580 N. What is her mass?
The Correct Answer and Explanation is:
To calculate the mass of a woman who weighs 580 N, we can use the formula that relates weight (force), mass, and gravitational acceleration:
[
W = m \times g
]
Where:
- ( W ) is the weight in newtons (N),
- ( m ) is the mass in kilograms (kg),
- ( g ) is the acceleration due to gravity, approximately ( 9.8 \, \text{m/s}^2 ) on Earth.
We are given that her weight ( W = 580 \, \text{N} ), and we need to find her mass ( m ).
Step 1: Rearrange the equation to solve for mass:
[
m = \frac{W}{g}
]
Step 2: Substitute the known values:
[
m = \frac{580 \, \text{N}}{9.8 \, \text{m/s}^2}
]
Step 3: Perform the division:
[
m = 59.18 \, \text{kg}
]
So, the woman’s mass is approximately 59.2 kg.
Explanation:
Weight is the force exerted by gravity on an object and is dependent on both the mass of the object and the strength of the gravitational field it is in. On Earth, gravity pulls objects downward at a rate of ( 9.8 \, \text{m/s}^2 ). Therefore, an object’s weight is a product of its mass and the gravitational acceleration.
Mass, on the other hand, is a measure of the amount of matter an object contains, and it does not change with location (it is constant regardless of where you are in the universe). The weight of an object, however, does change depending on the strength of gravity. For example, a person weighs less on the moon because the gravitational pull there is weaker.
In this case, we used the standard gravitational acceleration on Earth to convert the weight (measured in newtons) into mass (measured in kilograms). This formula helps us understand the relationship between these two important physical quantities.