This is about Elastic Springs.. so far I've answered every question. This is the only one I don't get. It's so confusing for me..
In the laboratory, you attach 300 g mass to a spring of negligible mass and start oscillating it. The elapsed time from when the mass first moves through the equilibrium position to the second time it moves through that position is 2 s. Find the force constant of the spring
The oscillation period is P = 2.0 s.
Use the formula
P = 2*pi*sqrt(M/k)
with M = 0.300 kg
Solve for k in Newtons per meter
k = 4*pi^2*M/P^2
To find the force constant of the spring, you need to use Hooke's Law. Hooke's Law states that the force exerted by an elastic spring is directly proportional to the displacement of the spring from its equilibrium position.
The equation for Hooke's Law is given by F = -kx, where F is the force exerted by the spring, k is the force constant (also known as the spring constant), and x is the displacement from the equilibrium position.
In this case, the mass attached to the spring is 300 g, which is equivalent to 0.3 kg. In the equilibrium position, the net force on the mass is zero.
When the mass moves through the equilibrium position for the first time, it starts oscillating. The elapsed time from the first time it moves through the equilibrium position to the second time is given as 2 s.
During this time, the mass completes one full oscillation (i.e., it moves from one extreme position to the other and then back to the equilibrium position). Therefore, the displacement of the mass from the equilibrium position is twice the amplitude of the oscillation.
To find the force constant of the spring, we need to determine the amplitude of the oscillation.
From the information given, we cannot directly determine the amplitude. However, we can make use of the fact that the time period of the oscillation is related to the spring constant and the mass attached.
The time period of an oscillating mass-spring system is given by the equation T = 2π√(m/k), where T is the time period, m is the mass attached, and k is the spring constant.
Rearranging this equation, we get k = (4π²m) / T².
Substituting the values m = 0.3 kg and T = 2 s into the equation, we can now calculate the force constant of the spring:
k = (4π² * 0.3) / (2²)
= (4π² * 0.3) / 4
= 3π² * 0.3
≈ 9.42 N/m
Therefore, the force constant of the spring is approximately 9.42 N/m.