An iron weight, suspended by a string, is motionless. The tension in the string is 4.75 newtons. What is the mass of the iron weight?
The Correct Answer and Explanation is:
To find the mass of the iron weight, we can use the formula derived from Newton’s second law of motion:
[
T = m \cdot g
]
Where:
- (T) is the tension in the string (4.75 N)
- (m) is the mass of the iron weight (unknown)
- (g) is the acceleration due to gravity ((9.8 \, \text{m/s}^2))
Rearranging the formula to solve for (m):
[
m = \frac{T}{g}
]
Substitute the given values:
[
m = \frac{4.75}{9.8}
]
Perform the calculation:
[
m \approx 0.4847 \, \text{kg}
]
Thus, the mass of the iron weight is approximately 0.485 kg.
Explanation:
This problem involves the relationship between weight, mass, and gravity. Weight is the force exerted on an object due to gravity, and it is calculated as the product of mass ((m)) and gravitational acceleration ((g)).
In this scenario, the iron weight is stationary and suspended by a string. Since it is motionless, the tension in the string equals the gravitational force acting on the weight (no other forces are involved). The gravitational force can be expressed as (F_g = m \cdot g), and in this case, the tension (T) is the same as (F_g).
Given the tension and gravitational acceleration, dividing the tension by (g) gives the object’s mass. This approach demonstrates the fundamental principles of physics and the proportionality between force, mass, and acceleration. Additionally, it highlights the importance of understanding units: tension is measured in newtons ((\text{N})), mass in kilograms ((\text{kg})), and acceleration in meters per second squared ((\text{m/s}^2)).
This calculation is critical in engineering and physics for determining the properties of objects in equilibrium, particularly in statics problems where forces must balance.