Potential Energy of a Spring Contradiction?

AI Thread Summary
The discussion revolves around the potential energy of two identical springs in different orientations and the resulting speed of a box released from them. In the first scenario, the springs are angled, causing horizontal force components to cancel, while in the second scenario, the springs are vertical, providing a direct upward force. The confusion arises from the assumption that both setups would yield the same speed for the box due to equal potential energy. However, it is clarified that the energy required for compression differs between the two orientations, affecting the box's speed. The conversation highlights the importance of understanding the forces involved in each scenario to resolve the apparent contradiction.
dtseng96
Messages
13
Reaction score
0
Hi everyone, I'm a bit confused about the concept of the potential energy. Let's say we have the following scenarios here: https://dl.dropbox.com/u/29312856/Springs.jpg

In the first scenario, we have two identical springs with spring constant 5000 N/cm angled at 20 degrees below the horizontal, and a box of 2 kg is compressed against the two springs, causing each spring to be compressed 2 cm. The entire system is in space, with no sources of gravity nearby. If we release the box from the spring, the box have a speed of y m/s.

In the second scenario, we have the same two springs as before, except placed vertically upwards. The box is compressed against the two springs, causing each spring to be compressed 2 cm. The entire system is in space, with no sources of gravity nearby. If we release the box from the spring, the box have a speed of z m/s.

Using the law of conservation of energy, it seems like the speed y and the speed z in the two scenarios are the same (meaning that it does not matter which way you position the two springs) because the potential energy of the two springs in each scenario are the same.

Yet, it seems illogical that it would be that way. In the first scenario, the horizontal components of the force from the springs would cancel out, so only the vertical components of the force from the springs would propel the box forward. In the second scenario, the force from the two springs are completely vertical, so they do not cancel each other out. It seems like the box would have a higher speed in the second scenario because there is more force propelling the box forward in the second scenario.

Can anyone explain my confusion? Any help would be appreciated. Thanks!
 
Last edited by a moderator:
Physics news on Phys.org
In the second scenario, you need more energy for compression, as 2cm height corresponds to 2cm of compression (this is different in the first setup).
 
Thanks for the reply, mfb! That makes sense, I did not think of that. I realized I made a mistake in my question though, so I just changed my question a bit right now.
 
Last edited:

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Average velocity as a weighted mean'

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »

Similar threads

I Work-Energy Theorem for Moving Block and Spring System?
Replies
4
Views
2K
B E.P.E. -> ? when 2 masses are attached to a spring
Replies
2
Views
1K
B Why in two block systems do both blocks tend to have the same velocity?
Replies
6
Views
1K
Why gravitational potential energy is a system property?
Replies
45
Views
3K
Does the potential energy of a spring do work on the both
Replies
3
Views
1K
Does the spring force do work on the spring itself?
Replies
9
Views
3K
Does Compressing a Spring Decrease Its Potential Energy?
Replies
4
Views
2K
Invariance of elastic potential energy
Replies
6
Views
2K
How long will the ball and the spring be in contact?
Replies
7
Views
2K
Calculating Final Positions & Velocities for M1, M2 & Spring After DeltaT
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top