A 220 air-track glider is attached to a spring. The glider is pushed in 12.0 against the spring, then released. A student with a stopwatch finds that 13 oscillations take 11.5s.
What is the spring constant?
Your first two numbers (220 and 12.0) require dimensions.
To find the spring constant, we need to use Hooke's Law and the formula for the period of oscillation of a mass-spring system.
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position and is given by the equation: F = -kx, where F is the force, k is the spring constant, and x is the displacement.
The period of oscillation (T) for a mass-spring system is given by the equation: T = 2π√(m/k), where m is the mass attached to the spring and k is the spring constant.
In this case, we are given information about the number of oscillations and the time it takes for those oscillations. We can use this information to find the period (T) and then use Hooke's Law to find the spring constant (k).
First, we divide the total time (11.5s) by the number of oscillations (13) to find the average time per oscillation:
Average time per oscillation = 11.5s / 13 = 0.8846s/oscillation
Next, we divide the average time per oscillation by the number of oscillations in one period to find the period (T):
T = 0.8846s / 1 = 0.8846s
Now, we can plug the values of mass (m) and period (T) into the formula for the period of oscillation to find the spring constant (k):
T = 2π√(m/k)
Rearranging the formula:
k = (4π²m) / T²
Since the mass (m) is not given, we cannot find the exact value of the spring constant. We would need the mass of the glider to calculate the spring constant.