STATE HOOKES LAW. WHAT IS THE FORCE REQUIRED TO PRODUCE AN EXTENSION OF 1CM. IF AN EXTENSION OF 8.0CM CAN BE PRODUCED BY A LOAD OF MASS 300G?
Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement or extension produced, as long as the elastic limit of the spring is not exceeded.
Mathematically, Hooke's Law is expressed as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant (also known as the stiffness constant),
x is the displacement or extension of the spring.
To calculate the force required to produce an extension of 1 cm, we need to determine the spring constant (k) of the spring first.
Given that an extension of 8.0 cm can be produced by a load of mass 300 g, we can determine the force applied using Newton's second law:
F = m * g
Where:
F is the force applied,
m is the mass of the load,
g is the acceleration due to gravity (approximately 9.8 m/s²).
Converting the mass from grams to kilograms:
m = 300 g = 300/1000 kg = 0.3 kg
Substituting the values into the equation:
F = 0.3 kg * 9.8 m/s² = 2.94 N (Newton)
Now, to calculate the spring constant (k), we can rearrange Hooke's Law equation:
k = F / x
Substituting the force (F) and the extension (x = 8.0 cm = 0.08 m) into the equation:
k = 2.94 N / 0.08 m = 36.75 N/m
Therefore, the force required to produce an extension of 1 cm is:
F = k * x
F = 36.75 N/m * 0.01 m = 0.3675 N (Newton)
Hooke's Law states that the force required to produce an extension or compression of a spring is directly proportional to the extension or compression, as long as the elastic limit of the material is not exceeded.
To determine the force required to produce an extension of 1 cm, we need to calculate the proportionality constant, known as the spring constant (k).
Given that an extension of 8.0 cm can be produced by a load of mass 300 g, we need to convert the mass from grams to kilograms.
Mass = 300 g = 300/1000 = 0.3 kg.
Next, we need to calculate the force applied to produce the extension.
Force = mass x acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Force = 0.3 kg x 9.8 m/s^2 = 2.94 N.
Now, we can calculate the spring constant (k).
k = Force / Extension
k = 2.94 N / 8.0 cm = 2.94 N / 0.08 m (converting cm to m)
k = 36.75 N/m.
Therefore, the force required to produce an extension of 1 cm is 36.75 N.
f = k x
one eighth the extension requires one eighth the load
300 g / 8 = ?