A box with two springs on a frictionless table

In summary: The force from the left spring is compressed in the counterclockwise direction. The force from the right spring is stretched in the counterclockwise direction. These two forces do not cancel out.
  • #1
BrainMan
279
2

Homework Statement


upload_2016-10-17_21-22-10.png


Homework Equations

The Attempt at a Solution


[/B]
I'm having trouble visualizing what is going on in this problem. I imagine that the box is in a position like this with a spring on each end of the box. Then a force F is applied that compresses the springs. What I'm wondering is: How does the force parallel to the springs compresses both springs? It would seem that one would be compressed, while the other would not be effected.
upload_2016-10-17_21-26-45.png
 

Attachments

  • upload_2016-10-17_21-24-53.png
    upload_2016-10-17_21-24-53.png
    1.4 KB · Views: 640
Physics news on Phys.org
  • #2
The springs are attached to the box, so if the box moves, the attached ends of the springs move with it. The outer ends of the springs are clamped to some fixed supports. So when the box moves, one spring is compressed while the other is stretched.
 
  • #3
gneill said:
The springs are attached to the box, so if the box moves, the attached ends of the springs move with it. The outer ends of the springs are clamped to some fixed supports. So when the box moves, one spring is compressed while the other is stretched.
So more like this? Where the black rectangles are the supports?

upload_2016-10-17_21-37-39.png
 
  • #4
Yup. Here's my version:

upload_2016-10-17_21-40-13.png
 
  • #5
Hi, going back to this. Wouldn't the spring constant just be 2.6N/.3m? Making it 8.66 N/m? Why is this wrong, do I need to take into account another spring?
 
  • #6
CRobinson said:
Hi, going back to this. Wouldn't the spring constant just be 2.6N/.3m? Making it 8.66 N/m? Why is this wrong, do I need to take into account another spring?
1. The force is 2N, not 2.6N
2. The displacement is 3cm., not 30cm.
3. There are two springs. What force does each exert?
 
  • #7
I need more clarification on this; there's only one force and one distance unit for the motion of two springs, would those two springs traveling in opposite directions not cancel out? I've tried the difference and the sum, nothing is right.
 
  • #8
dgood said:
I need more clarification on this; there's only one force and one distance unit for the motion of two springs, would those two springs traveling in opposite directions not cancel out? I've tried the difference and the sum, nothing is right.

Look at the drawing in #4. In what direction is the force from the left spring that is compressed? What about the force from the right spring that is stretched? This should tell you whether the forces cancel out.
 

1. How does the number of springs affect the motion of the box?

The number of springs affects the motion of the box by altering the spring constant and the force applied to the box. In a box with two springs, the force applied is double that of a box with one spring, resulting in a faster and more oscillatory motion.

2. What is the significance of a frictionless table in this scenario?

A frictionless table eliminates the external force of friction, allowing for more accurate observations and analysis of the springs' behavior. It also simplifies the mathematical equations involved in studying the motion of the box.

3. Can the springs ever reach equilibrium on a frictionless table?

No, on a frictionless table, there is no external force to counteract the oscillatory motion of the springs. Therefore, the springs will continue to oscillate indefinitely without reaching a state of equilibrium.

4. How does the mass of the box affect the motion of the springs?

The mass of the box affects the motion of the springs by altering the period of oscillation. A heavier box will have a longer period, while a lighter box will have a shorter period. However, the amplitude of oscillation remains the same regardless of the mass of the box.

5. What happens to the motion if one spring is stronger than the other?

If one spring is stronger than the other, the box will experience a net force in the direction of the stronger spring. This will result in a faster and more oscillatory motion, as the stronger spring will have a greater influence on the box's movement.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
907
Replies
5
Views
178
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
368
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
31
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
911
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
9K
Back
Top