A spring extends by 10 cm when a mass of 100 g is attached to it what the spring constant (K) ( calculate your answer in N/m
To calculate the spring constant (K), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Hooke's Law can be written as F = -Kx, where F is the force, K is the spring constant, and x is the displacement.
In this case, we know that when a mass of 100 g is attached to the spring, it extends by 10 cm (which is equivalent to 0.1 meters). We can convert the mass to force using the equation F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's calculate the force first:
F = (0.1 kg) * (9.8 m/s^2) = 0.98 N
Now we can rearrange Hooke's Law to solve for K:
K = -F / x
Substituting the known values:
K = -0.98 N / 0.1 m = -9.8 N/m
The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement. However, for simplicity, we commonly neglect the sign when referring to the spring constant, so the spring constant (K) is approximately 9.8 N/m.
F = kx
mg = kx