A force of 800 N stretches a spring a distance 0.200 m horizontally. a) What is the potential energy of the spring when it is stretched 0.200m b) What is its potential energy when it is compressed 5.00cm This is a conservation of energy problems. The potential is elastic and not gravitational because the spring does not work against gravity as it moves horizontally
5+9
Ah, the wondrous world of springs and potential energy! Here's my attempt to put a smile on your face while answering your delightful question:
a) To calculate the potential energy of the spring when it is stretched 0.200 m, we can use Hooke's Law (F = -kx) and a pinch of humor. Now, imagine you have a comically weak spring that stretches oh-so-gently. It's like that time your grandma stretched a rubber band to tie up her hair - except this one's horizontal, of course.
So, the force applied (800 N) multiplied by the displacement (0.200 m) gives us 160 J of potential energy. Voila! Just like that, we've discovered the secret energy stash of our hair-tie spring.
b) Now, let's talk about compressing that spring. Picture a spring that's grumpy and cranky, like your Aunt Gertrude on a Monday morning. It's just been squished ever so slightly, like when someone tries to squeeze into jeans that are a size too small.
For this scenario, we are compressing the spring by 5.00 cm (or 0.050 m). Using the same Hooke's Law magic, we have a negative force (-800 N) multiplied by the displacement (-0.050 m). And voilà encore! We find ourselves with -20 J (that pesky negative sign!) of potential energy. Aunt Gertrude would be proud of such a compressed situation.
Remember, my comical friend, this is all in the world of springs and potential energy. Keep on laughing and learning!
To find the potential energy (PE) of a spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position.
a) When the spring is stretched 0.200 m horizontally, we can find the potential energy by multiplying the force and displacement. The formula for potential energy is given by:
PE = (1/2) k x^2
where k is the spring constant and x is the displacement. In this case, we are given the force of 800 N and displacement of 0.200 m. We need to find the spring constant in order to calculate the potential energy.
To find the spring constant (k), we can use Hooke's Law:
F = kx
Rearranging the equation, we have:
k = F / x
Substituting the given values:
k = 800 N / 0.200 m = 4000 N/m
Now we have the spring constant, so we can calculate the potential energy:
PE = (1/2) * (4000 N/m) * (0.200 m)^2
PE = (1/2) * (4000 N/m) * (0.0400 m^2)
PE = 40 J
Therefore, the potential energy of the spring when it is stretched 0.200 m horizontally is 40 J.
b) When the spring is compressed by 5.00 cm, we need to convert the displacement to meters. 5.00 cm is equal to 0.0500 m.
Using the same formula as before, we can calculate the potential energy:
PE = (1/2) * (4000 N/m) * (0.0500 m)^2
PE = (1/2) * (4000 N/m) * (0.00250 m^2)
PE = 5 J
Therefore, the potential energy of the spring when it is compressed 5.00 cm is 5 J.
search for a youtube video titled "A force of 800 N stretches a certain spring a distance of 0.200 m" by jonathan david
F of spring=kx
Where:
x=0.200m
and
F=800N
Solve for k:
k=800/0.200m
k=4,000
a.)
PE=1/2kx^2
PE=1/2(4,000)(0.200m)
PE=400J
b.)
PE=1/2kx^2
PE=1/2(4,000)(0.0500m)
PE=100J
****Check my math.