A spring has a force constant of 554.1 N/m. Find the potential energy stored in the spring when the spring is a) stretched 4.35 cm from equilibrium. Answer in units of J.
b) compressed 2.98 cm from equilibrium. Answer in units of J.
c) unstretched. Answer in units of J.
I did 1/2 k x^2 but its wrong
a) PE=1/2 kx^2
b) PE=1/2 k x^2
c) zero.
change stretching distance to meters. I suspect that is what you did wrong.
W
thanks bro
Ah, I see what's happening here. It seems like you're not getting the correct answer when using the formula for potential energy stored in a spring, which is indeed given by (1/2)kx^2. Don't worry, I'm here to help you out with a little bit of humor!
a) So, you've got a spring stretched 4.35 cm? Well, let's calculate the potential energy it's storing. We'll multiply half of the spring constant (which is 277.05 N/m, by the way) by the square of the distance you gave me (0.0435 m). Honey, I hope you're ready for this mind-blowing answer: it's 0.2647 J.
b) Now, onto a compressed spring. This one's squeezed 2.98 cm? Alright, let's crunch some numbers. Using the same formula, multiply half of the spring constant by the square of the distance (0.0298 m). Drumroll, please! The potential energy here is... 0.0526 J!
c) Last but not least, the unstretched spring. By definition, the potential energy of an unstretched spring is zero. It's like a really lazy spring napping in its cozy equilibrium position, not bothering to store any energy whatsoever. So, the answer is a resounding 0 J, my friend!
I hope my answers put a spring in your step! If you have any more questions, feel free to bounce them my way.
To find the potential energy stored in a spring, you need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium.
The formula to calculate the potential energy stored in a spring is:
Potential Energy = (1/2) * k * x^2
Where:
- k is the force constant of the spring (given as 554.1 N/m)
- x is the displacement of the spring from equilibrium
Now let's calculate the potential energy for each situation:
a) When the spring is stretched 4.35 cm from equilibrium:
Convert the displacement to meters:
x = 4.35 cm = 0.0435 m
Now plug the values into the formula:
Potential Energy = (1/2) * 554.1 N/m * (0.0435 m)^2
Calculate:
Potential Energy = (1/2) * 554.1 N/m * 0.00189075 m^2
Potential Energy ≈ 0.4969 J
b) When the spring is compressed 2.98 cm from equilibrium:
Convert the displacement to meters:
x = 2.98 cm = 0.0298 m
Now plug the values into the formula:
Potential Energy = (1/2) * 554.1 N/m * (0.0298 m)^2
Calculate:
Potential Energy = (1/2) * 554.1 N/m * 0.0008844 m^2
Potential Energy ≈ 0.1387 J
c) When the spring is unstretched (at equilibrium):
In this case, the displacement (x) is zero. When x is zero, the potential energy stored in the spring is also zero. This is because the spring is in its equilibrium position and has no potential energy stored.
Hence, the potential energy in this scenario is 0 J.
Make sure to double-check your calculations and unit conversions to avoid any errors.