A light spiral spring is suspended from its upper end. A mass of 7.5*10^-2, hung from the lower end produces an extension of 0.15 m. The mass is pulled down to a furthur 8.0*10^-2 m and released so that it oscillates
calculate the spring constant.
To calculate the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the extension or compression of the spring.
The formula for Hooke's Law is:
F = k * x
Where:
F is the force applied to the spring (in Newtons),
k is the spring constant (in Newtons per meter),
x is the extension or compression of the spring (in meters).
We are given:
Mass (m) = 7.5 * 10^-2 kg
Extension (x) = 0.15 m
Step 1: Calculate the force applied to the spring.
The force applied to the spring can be calculated using the formula:
F = m * g
Where:
m is the mass (in kg),
g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values into the formula, we get:
F = (7.5 * 10^-2 kg) * 9.8 m/s²
F = 0.735 N
Step 2: Calculate the spring constant.
Using Hooke's Law, we can rearrange the formula to solve for the spring constant:
k = F / x
Substituting the values obtained in step 1, we have:
k = 0.735 N / 0.15 m
k = 4.9 N/m
Therefore, the spring constant is 4.9 N/m.
To calculate the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its extension (or compression) from its equilibrium position. Mathematically, Hooke's Law can be expressed as:
F = -kx
Where:
F is the force exerted by the spring,
k is the spring constant,
x is the displacement from the equilibrium position.
In this case, we are given the mass (m) and the extension (e) of the spring, so we can use these values to calculate the spring constant.
First, let's calculate the force exerted by the mass:
F = mg
F = (7.5 * 10^-2 kg) * 9.8 m/s^2 (acceleration due to gravity)
F = 7.35 * 10^-1 N
Next, we can use the force and the extension to calculate the spring constant:
F = -kx
k = -F / x
k = -(7.35 * 10^-1 N) / (0.15 m)
k ≈ -4.9 N/m (rounded to one decimal place)
Therefore, the spring constant of the light spiral spring is approximately 4.9 N/m.