How can I calculate the spring constant given only the following:
equilibrium length of spring: 10.5 cm
stretched length of spring (by attaching a mass): 12.5 cm
object's mass: 198.9 grams
-please help me...I'm really lost...
You need to assume that the measurement was made at a place where the accleration of gravity = g. On the surface of the Earth, that value is 9.8 m/s^2. The force stretching the spring is them
F = m g = 0.1989 kg * 9.8 m/s^2 = ? Newtons
To get the spring constant k, divide F by the strech amount: 0.020 m (which is 20 cm)
The dimensions of your answer will be N/m
k = m g / (change in length)
To calculate the spring constant, we can 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.
The formula for Hooke's Law is as follows:
F = -kx
Where:
- F is the force exerted by the spring
- k is the spring constant
- x is the displacement or change in length of the spring
In this case, we need to find the spring constant given the equilibrium length of the spring, the stretched length of the spring with an attached mass, and the mass of the object.
First, we need to determine the change in length of the spring. This can be calculated by subtracting the equilibrium length from the stretched length:
Change in length = stretched length - equilibrium length = 12.5 cm - 10.5 cm = 2 cm
Next, we need to convert the change in length to meters, as the equation for the spring constant requires it in SI units:
Change in length = 2 cm = 0.02 m
Now, we can calculate the force exerted by the spring using the mass and acceleration due to gravity:
Force, F = mass * acceleration due to gravity = 0.1989 kg * 9.8 m/s^2 = 1.94822 N
Finally, we can calculate the spring constant by dividing the force by the change in length:
Spring constant, k = force / change in length = 1.94822 N / 0.02 m = 97.411 N/m
Therefore, the spring constant of the spring is 97.411 N/m.