A spring has a force constant of 410.0 N/m.

(a) Determine the potential energy stored in the spring when the spring is stretched 4.13 cm from equilibrium.
(b) Determine the potential energy stored in the spring when the spring is stretched 3.06 cm from equilibrium.
(c) Determine the potential energy stored in the spring when the spring is unstretched.

Correction: PE = 0.5F * d = 0.5*16.93 * 0.0413 = 0.35 Joules.

a. F = 410N/m * 0.0413m = 16.93 N.

PE = F*d = 16.93 * 0.0413 = 0.7 Joules.

b. Same procedure as a.

c. F = 410N/m * 0 = 0.
PE = F * d = 0*0 = 0.

To determine the potential energy stored in a spring, you can use the formula:

Potential Energy (PE) = (1/2)kx^2

Where:
k is the force constant of the spring (in N/m)
x is the displacement of the spring from equilibrium (in meters)

(a) To determine the potential energy when the spring is stretched 4.13 cm from equilibrium:

Step 1: Convert the displacement from cm to meters:
x = 4.13 cm = 4.13 / 100 m = 0.0413 m

Step 2: Plug the values into the formula:
PE = (1/2) * 410.0 N/m * (0.0413 m)^2

Step 3: Calculate the potential energy:
PE = (1/2) * 410.0 * 0.00170469

(b) To determine the potential energy when the spring is stretched 3.06 cm from equilibrium:

Step 1: Convert the displacement from cm to meters:
x = 3.06 cm = 3.06 / 100 m = 0.0306 m

Step 2: Plug the values into the formula:
PE = (1/2) * 410.0 N/m * (0.0306 m)^2

Step 3: Calculate the potential energy:
PE = (1/2) * 410.0 * 0.00093636

(c) To determine the potential energy when the spring is unstretched (at equilibrium), the displacement (x) is zero. Therefore, the potential energy is also zero:

PE = (1/2) * 410.0 * (0 m)^2
PE = 0 J

To determine the potential energy stored in a spring, you can use the formula:

Potential energy = 1/2 * k * x^2

where:
- k is the force constant of the spring (in N/m)
- x is the displacement from the equilibrium position (in meters)
- x^2 means x squared

(a) For a spring stretched 4.13 cm from equilibrium:
- First, convert the displacement to meters: 4.13 cm = 0.0413 m
- Now, substitute the values into the formula:
Potential energy = 1/2 * 410.0 N/m * (0.0413 m)^2
Potential energy = 1/2 * 410.0 N/m * 0.00170769 m^2
Potential energy ≈ 0.351 J

So, the potential energy stored in the spring when stretched 4.13 cm from equilibrium is approximately 0.351 J.

(b) For a spring stretched 3.06 cm from equilibrium:
- Convert the displacement to meters: 3.06 cm = 0.0306 m
- Substitute the values into the formula:
Potential energy = 1/2 * 410.0 N/m * (0.0306 m)^2
Potential energy = 1/2 * 410.0 N/m * 0.00093636 m^2
Potential energy ≈ 0.181 J

The potential energy stored in the spring when stretched 3.06 cm from equilibrium is approximately 0.181 J.

(c) For an unstretched spring (x = 0):
- Substitute x = 0 into the formula:
Potential energy = 1/2 * 410.0 N/m * (0 m)^2
Potential energy = 0 J

The potential energy stored in the spring when it is unstretched is 0 J.