A 100 g blob is attached to avertical spring and the spring stretched 4 cm from its original length..calculate the spring constan, k and period, t
F = 0.1kg * 9.8N/kg = 0.98N/kg = 0.98 N.
K = F/d = 0.98N/0.04m = 24.5N/m.
To calculate the spring constant (k) and period (T), we need to apply Hooke's Law and the equation for the period of a mass-spring system.
1. Calculate the spring constant (k):
According to Hooke's Law, the force exerted by a spring is proportional to the displacement from its equilibrium position. The formula for Hooke's Law is given by:
F = -k * x
where F is the force, k is the spring constant, and x is the displacement.
In this case, we are given a displacement (x) of 4 cm (which is equal to 0.04 meters) and the mass (m) of the blob is 100 g (which is equal to 0.1 kg).
Since the force exerted by the spring is equal to the weight of the blob, we can equate the two:
F = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Thus, -k * x = m * g
Substituting the values, we have:
-k * 0.04 = 0.1 * 9.8
Solving for k, we get:
k = - (0.1 * 9.8) / 0.04
Using a calculator, the value of k is approximately -24.5 N/m (Note: the negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement).
2. Calculate the period (T):
The period (T) is the time taken for one complete oscillation of the mass-spring system. The formula for the period of a mass-spring system is given by:
T = 2π * √(m / k)
where m is the mass and k is the spring constant.
Substituting the values, we have:
T = 2π * √(0.1 / -24.5)
Using a calculator, the value of T is approximately 0.717 seconds (rounded to three decimal places).
Therefore, the spring constant (k) is approximately -24.5 N/m, and the period (T) is approximately 0.717 seconds.