When a mass of 28 g is attached to a certain
spring, it makes 17 complete vibrations in
3.0 s.
What is the spring constant of the spring?
Answer in units of N/m
2PI*frequency=k/m
frequency=17/3 m= .028kg
solve for k
To find the spring constant of the spring, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
The formula for Hooke's Law is: F = -kx
Where:
F is the force exerted by the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.
In this case, we are given that the mass attached to the spring undergoes 17 complete vibrations in 3.0 seconds.
To find the spring constant, we need to determine the angular frequency (ω) of the vibrating mass on the spring. The angular frequency is given by the formula:
ω = 2πf
Where:
f is the frequency of oscillation, which is the number of complete vibrations per unit time.
In this case, we can calculate the frequency f using the given information:
f = (number of vibrations) / (time)
= 17 / 3.0
Now we can calculate the angular frequency ω:
ω = 2π * f
Next, we can determine the period T, which is the time it takes for one complete vibration. Period is the reciprocal of frequency:
T = 1 / f
In this case, we can calculate the period T as follows:
T = 1 / f
Now that we have the period T and the angular frequency ω, we can use these values to find the spring constant k. Rearranging Hooke's Law, we get:
k = -(F / x)
Since the mass is attached to the spring, the force F can be calculated using Newton's second law:
F = m * a
In this case, the only force acting on the mass is the force from the spring, so F = -kx. Therefore, we can substitute -kx for F:
-(kx) = m * a
Since acceleration a is related to angular frequency ω and displacement x as follows:
a = -ω^2x
We can substitute -ω^2x for a in the equation:
-(kx) = m * (-ω^2x)
Now we can solve for the spring constant k:
k = (m * ω^2) / x
Plugging in the given values, we have:
m = 28 g = 0.028 kg
ω = 2πf = 2π * (17 / 3) Hz
x = amplitude of vibration
To find the amplitude of vibration, we need more information. Without the amplitude, we can't calculate the spring constant. Please provide the amplitude of the vibration in order to proceed with the calculation.