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Janet wants to find the spring constant of a given spring, so she hangs the spring vertically and attaches a 0.53 kg mass to the spring's other end. If the spring stretches 3.9 cm from its equilibrium position, what is the spring constant?
M*g = 0.53 * 9.8 = 5.2 N. = Wt. of the
mass.
K = 1/0.039 * 5.2N = 133.2N/m
To find the spring constant, we can use Hooke's Law, which states that the force (F) exerted by a spring is proportional to the displacement (x) from its equilibrium position. Mathematically, this can be written as:
F = k * x
Where:
F is the force exerted by the spring
k is the spring constant
x is the displacement
In this case, we are given the mass (m) attached to the spring (0.53 kg) and the displacement (3.9 cm or 0.039 m). The force exerted by the spring can be calculated using Newton's second law, which states that the force (F) exerted on an object is equal to the mass multiplied by the acceleration (a):
F = m * g
Where:
F is the force exerted on the object
m is the mass of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Now we can substitute this force value into Hooke's Law equation:
m * g = k * x
Rearranging the equation to solve for the spring constant (k):
k = (m * g) / x
Let's plug in the given values to find the spring constant:
m = 0.53 kg
g = 9.8 m/s^2
x = 0.039 m
k = (0.53 kg * 9.8 m/s^2) / 0.039 m
Now, we can calculate the spring constant:
k = 13.54 N/m
Therefore, the spring constant of the given spring is 13.54 N/m.