Answer:
196.2 N/m.
Step-by-step explanation:
To find the spring constant (k), you can use Hooke's Law, which relates the force exerted by a spring to its spring constant and the displacement from its equilibrium position.
The formula for Hooke's Law is:
F = -k * x
Where:
- F is the force applied to the spring (in newtons, N).
- k is the spring constant (in newton per meter, N/m).
- x is the displacement from the equilibrium position (in meters, m).
First, you need to convert the mass from grams to kilograms:
400 grams = 0.4 kg
Now, you can calculate the force (F) acting on the spring due to the mass:
F = m * g
Where:
- m is the mass (0.4 kg).
- g is the acceleration due to gravity (approximately 9.81 m/s²).
F = 0.4 kg * 9.81 m/s² = 3.924 N
Now, you have the force (F) and the displacement (x) is 2.0 cm, which you need to convert to meters (since 1 cm = 0.01 m):
x = 2.0 cm * 0.01 m/cm = 0.02 m
Now, you can use Hooke's Law to find the spring constant (k):
3.924 N = -k * 0.02 m
Solve for k:
k = -3.924 N / 0.02 m
k = -196.2 N/m
The spring constant is approximately 196.2 N/m. Note that the negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement, which is a convention in Hooke's Law.