What is the weight of the mass (100g) in Newtons? Show calculation.
The Correct Answer and Explanation is:
Correct Answer:
To calculate the weight (W) of a mass in Newtons, we use the formula:W=m×gW = m \times gW=m×g
Where:
- mmm is the mass in kilograms (kg)
- ggg is the acceleration due to gravity, which is approximately 9.8 m/s29.8 \, \text{m/s}^29.8m/s2
Given:
- Mass m=100 grams=0.1 kgm = 100 \, \text{grams} = 0.1 \, \text{kg}m=100grams=0.1kg
W=0.1 kg×9.8 m/s2=0.98 NewtonsW = 0.1 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 0.98 \, \text{Newtons}W=0.1kg×9.8m/s2=0.98Newtons
Final Answer:
The weight of a 100 g mass is 0.98 Newtons.
Explanation
Weight is a measure of the gravitational force acting on an object with mass. In the metric system, weight is expressed in Newtons (N), which is the standard unit of force in the International System of Units (SI). The relationship between weight and mass is governed by Newton’s Second Law of Motion, which states that force equals mass times acceleration.
In this case, the acceleration is due to gravity. On Earth, this acceleration has a relatively constant value of approximately 9.8 meters per second squared. This means that for every kilogram of mass, the gravitational force will pull it downward with a force of 9.8 Newtons.
Since the given mass is 100 grams, it must first be converted to kilograms because SI calculations for force require mass in kilograms. To convert grams to kilograms, divide the value by 1000. Thus, 100 grams is equal to 0.1 kilograms.
By substituting the values into the weight formula W=m×gW = m \times gW=m×g, we get:W=0.1×9.8=0.98 NewtonsW = 0.1 \times 9.8 = 0.98 \, \text{Newtons}W=0.1×9.8=0.98Newtons
This calculation shows that an object with a mass of 100 grams experiences a gravitational force of 0.98 Newtons when on the surface of the Earth. This value is important in physics and engineering, as weight affects how objects behave in response to other forces. Understanding the distinction between mass and weight also helps avoid confusion, especially when working in scientific or technical fields.
