A rubber band has a"spring constant" of 45 N/m. When the rubber band is pulled by a force of 9.8 N , how far will it stretch and what is potential energy?
Stretch X = F/k = 9.8/45 = 0.218 m
P.E. = (1/2)k X^2 = ___ J
k is the spring constant
To calculate how far the rubber band will stretch, you can use Hooke's law, which states that the force applied to a spring is directly proportional to the displacement of the spring. The formula to determine the displacement is:
Δx = F / k
Where:
Δx is the displacement (how far the rubber band will stretch)
F is the applied force
k is the spring constant
Using the given values:
F = 9.8 N (applied force)
k = 45 N/m (spring constant)
Δx = 9.8 N / 45 N/m
Δx ≈ 0.22 meters
Therefore, the rubber band will stretch approximately 0.22 meters.
To calculate the potential energy of the rubber band when stretched, you can use the formula:
PE = ½ k Δx²
Where:
PE is the potential energy
k is the spring constant
Δx is the displacement (stretch)
Using the given values:
k = 45 N/m (spring constant)
Δx = 0.22 meters (stretch)
PE = 0.5 * 45 N/m * (0.22 meters)²
PE ≈ 0.5394 Joules
Therefore, the potential energy of the rubber band when stretched is approximately 0.5394 Joules.
To calculate how far the rubber band will stretch and the potential energy, we can use Hooke's Law.
Hooke's Law states that the force needed to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's Law is:
F = kx
Where:
- F is the applied force
- k is the spring constant
- x is the displacement from the equilibrium position
In this case, the rubber band has a spring constant of k = 45 N/m and the applied force is F = 9.8 N. We need to find the displacement x.
Rearranging the formula, we have:
x = F / k
Substituting the known values, we have:
x = 9.8 N / 45 N/m
x ≈ 0.217 m
So, the rubber band will stretch approximately 0.217 meters.
To calculate the potential energy, we can use the formula:
PE = (1/2) kx^2
PE = (1/2) * (45 N/m) * (0.217 m)^2
PE ≈ 0.496 J
Therefore, the potential energy of the stretched rubber band is approximately 0.496 Joules.