The increase in spring force when a spring is stretched or compressed can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Mathematically, Hooke's Law is expressed as:
F = -k * x
Where:
F is the force exerted by the spring,
k is the spring constant (a measure of the spring's stiffness),
x is the displacement from the equilibrium position.
The spring is stretched from 5.0 cm to 8.0 cm from equilibrium. The increase in displacement (Δx) is:
Δx = final position - initial position
Δx = 8.0 cm - 5.0 cm
Δx = 3.0 cm
Now, if you're given the spring constant (k) for the specific spring, you can use Hooke's Law to calculate the increase in spring force. If you don't have the spring constant, you won't be able to calculate the exact force increase.
The negative sign in Hooke's Law indicates that the force exerted by the spring is in the opposite direction of the displacement (stretching or compression).