A 500g mass is placed on a spiral spring and the length of the spring decreases from 13cm to 9cm.calculate the force constant of the spring
To calculate the force 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 of the spring from its equilibrium position.
Hooke's Law is given by the equation:
F = -kx
Where:
F is the force exerted by the spring,
k is the force constant of the spring, and
x is the displacement of the spring from its equilibrium position.
In this scenario, the length of the spring decreases from 13 cm to 9 cm, which corresponds to a displacement of:
x = initial length - final length
x = 13 cm - 9 cm
x = 4 cm
We know that the mass placed on the spring is 500 g, which we need to convert to kilograms:
mass in kg = mass in grams / 1000
mass in kg = 500 g / 1000
mass in kg = 0.5 kg
Now, we can plug these values into Hooke's Law equation to find the force constant:
F = -kx
-9.81 N = -k * (0.04 m)
Since the mass is experiencing a gravitational force of -9.81 N, we can equate the forces:
F = mg
-9.81 N = 0.5 kg * 9.81 m/s^2
Now, we can rearrange the equation to solve for the force constant:
-9.81 N = -0.04 k
k = (-9.81 N) / (-0.04 m)
k = 245.25 N/m
Therefore, the force constant of the spring is 245.25 N/m.
F = kx
0.5*9.8 = k*4