A spring has a force constant of 590.0 N/m.
(a) Determine the potential energy stored in the spring when the spring is stretched 3.77 cm from equilibrium.
(b) Determine the potential energy stored in the spring when the spring is stretched 3.26 cm from equilibrium.
(c) Determine the potential energy stored in the spring when the spring is unstretched.
see other post.
a. F = 590N/m * 0.0377m = 22.24 N.
PE=0.5F * d = 0.5*22.24 * 3.77 = 247 J.
b. Same procedure as part "a".
c. PE = 0.5F * d = 0.5F * 0 = 0.
To determine the potential energy stored in a spring, we can use the formula:
1. Potential energy (PE) = (1/2) * k * x^2,
where k is the force constant of the spring and x is the displacement from equilibrium.
(a) For a spring stretched 3.77 cm from equilibrium:
1. Convert the displacement to meters: x = 3.77 cm = 0.0377 m.
2. Substitute the values into the formula: PE = (1/2) * 590 N/m * (0.0377 m)^2.
3. Calculate the potential energy.
(b) For a spring stretched 3.26 cm from equilibrium:
1. Convert the displacement to meters: x = 3.26 cm = 0.0326 m.
2. Substitute the values into the formula: PE = (1/2) * 590 N/m * (0.0326 m)^2.
3. Calculate the potential energy.
(c) For an unstretched spring:
1. In this case, the displacement from equilibrium is 0.
2. Substitute the values into the formula: PE = (1/2) * 590 N/m * (0 m)^2.
3. Calculate the potential energy.
Please let me know if you would like the calculations for each part.
To determine the potential energy stored in a spring, we can use the formula:
Potential energy (PE) = (1/2) * k * x^2,
where k is the force constant of the spring, and x is the displacement from equilibrium.
(a) To find the potential energy stored in the spring when it is stretched 3.77 cm from equilibrium, we need to convert the displacement to meters.
Displacement (x) = 3.77 cm = 3.77 / 100 = 0.0377 m
Now we can plug the values into the formula:
PE = (1/2) * 590.0 N/m * (0.0377 m)^2
PE = 0.5 * 590.0 * 0.0377^2 J
PE ≈ 0.418 J
Therefore, the potential energy stored in the spring when it is stretched 3.77 cm from equilibrium is approximately 0.418 J.
(b) Similarly, to find the potential energy when the spring is stretched 3.26 cm from equilibrium:
Displacement (x) = 3.26 cm = 3.26 / 100 = 0.0326 m
PE = (1/2) * 590.0 N/m * (0.0326 m)^2
PE = 0.5 * 590.0 * 0.0326^2 J
PE ≈ 0.307 J
Therefore, the potential energy stored in the spring when stretched 3.26 cm from equilibrium is approximately 0.307 J.
(c) When the spring is unstretched, the displacement (x) is 0. We can use the same formula as before:
PE = (1/2) * 590.0 N/m * (0 m)^2
PE = 0 J
Therefore, when the spring is unstretched, there is no potential energy stored in the spring.