Maximal Contraction & Height Reached by 2kg Mass on Spring

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Homework Help Overview

The problem involves a 2 kg mass released from a height of 0.4 m above a vertical spring with a spring constant of 1960 N/m. The discussion centers around determining the maximal contraction of the spring and the height the mass will reach after being released, assuming no energy loss during the collision.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between energy conservation and the height the mass will reach after being released from the spring. Questions arise regarding the point of separation between the mass and the spring, particularly whether it occurs at the spring's loose length and the implications of the spring force being zero at that point.

Discussion Status

Participants are actively discussing the mechanics of the spring-mass system, particularly focusing on the conditions under which the mass loses contact with the spring. There is an exploration of the forces involved and the reasoning behind the separation point, with some participants offering insights into the nature of normal forces and contact forces.

Contextual Notes

There is an ongoing examination of assumptions related to the attachment of the mass to the spring and the implications of the spring's behavior during the motion of the mass. The discussion reflects a lack of consensus on the exact mechanics of the separation point, indicating a need for further clarification.

assaftolko
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A body with a mass of 2 kg is released from rest a height of 0.4m above the edge of a vertical rested spring with k= 1960 N/m. Assume there is no energy loss in the collision:

1. what's the maximal contraction of the spring?
2. to what height will the body reach back?

about 2 - Because I have energy coservation it seems reasonble that the body will reach the same height it was released from right? but... in 1 I found that the maximal contraction with respect to the loose length of the spring is 0.1 m and that it's maximal extension with respect to the loose length is -0.08 m... so it seems that when the spring is at full strech upwards - it's still lower than the initial height of 0.4 m above the loose length of the spring... so how does it all add up? does it have anything to do with the fact that maybe the body doesn't stay attached to the spring? if it doesn't stay attached - how can I know what's the point where it is released from the spring in its way up?
 

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the body does noy stay in contact with the spring...When it loses contact with it, the spring no longer exerts an upward force on it, which occurs at what point ? Note that you don't need to find this point to solve the problem and achieve your intuitive answer to part 2.
 
PhanthomJay said:
the body does noy stay in contact with the spring...When it loses contact with it, the spring no longer exerts an upward force on it, which occurs at what point ? Note that you don't need to find this point to solve the problem and achieve your intuitive answer to part 2.

Ok thanks man! I still want to know at what point this separation happens... is it the point where the spring is at loose length? if so - why is that?
 
assaftolko said:
Ok thanks man! I still want to know at what point this separation happens... is it the point where the spring is at loose length?
yes, that is correct
if so - why is that?
When the spring rebounds to its loose length, what is the force exerted by the spring on the body, per Hookes law?
 
PhanthomJay said:
yes, that is correct When the spring rebounds to its loose length, what is the force exerted by the spring on the body, per Hookes law?

0, but how can you conclude from this that the body will separate from the spring? I mean for a mass that is attached to a spring - it will experience a lot of times 0 force from the spring and still will stay attached to it - why if the mass isn"t attached (by something) to the spring then I know for sure (either for vertical or for horizontal spring) that the mass will depart from the spring at loose length point?
 
assaftolko said:
0, but how can you conclude from this that the body will separate from the spring? I mean for a mass that is attached to a spring - it will experience a lot of times 0 force from the spring and still will stay attached to it - why if the mass isn"t attached (by something) to the spring then I know for sure (either for vertical or for horizontal spring) that the mass will depart from the spring at loose length point?
The spring force on a body is not only a conservative force, but it is also a normal contact force acting perpendicular to the body. Unattached normal contact forces always push in toward an object, never away from it. Its like a book resting on a table, with a normal force of the table acting up on it with a force of mg. When you now lift the book slowly from the table, the normal force gets less and less until it reaches zero, at which point, the book loses contact with the table because the normal force cannot act downwards.
 
PhanthomJay said:
The spring force on a body is not only a conservative force, but it is also a normal contact force acting perpendicular to the body. Unattached normal contact forces always push in toward an object, never away from it. Its like a book resting on a table, with a normal force of the table acting up on it with a force of mg. When you now lift the book slowly from the table, the normal force gets less and less until it reaches zero, at which point, the book loses contact with the table because the normal force cannot act downwards.

So the reason a body "glued" to a spring doesn't depart from it at loose length point is just the constraint from the spring? this pivot or whatever exerts a force on the body that doesn;t allow it to depart?
 
assaftolko said:
So the reason a body "glued" to a spring doesn't depart from it at loose length point is just the constraint from the spring? this pivot or whatever exerts a force on the body that doesn;t allow it to depart?

Oh no that's just because of the glue.

When it's not glued to the spring, the upward acceleration due to the restoring force causes it to move upward and finally leave the spring when the force is zero.
 

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