# Maximal Contraction & Height Reached by 2kg Mass on Spring

• assaftolko
In summary: 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...It's more complicated than that. The spring's force does not always act perpendicular to the body. When a body is attached to a spring, the force of the spring acts perpendicular to the surface of the body. However, there is a point at which the spring's force no longer acts perpendicular to the body. This point is called the loose length of the spring. At this point, the body can separate from the spring.
assaftolko
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.

## 1. What is maximal contraction in the context of a 2kg mass on a spring?

Maximal contraction refers to the maximum compression or stretching of a spring when a 2kg mass is attached to it. This occurs when the force of gravity acting on the mass is equal to the restoring force of the spring, resulting in a state of equilibrium.

## 2. How is the height reached by a 2kg mass on a spring calculated?

The height reached by a 2kg mass on a spring can be calculated using the formula H = (kx^2)/(2mg), where k is the spring constant, x is the distance of compression or stretching, and g is the acceleration due to gravity. This formula is derived from the conservation of energy principle.

## 3. Does the height reached by a 2kg mass on a spring increase or decrease with a higher spring constant?

The height reached by a 2kg mass on a spring increases with a higher spring constant. This is because a higher spring constant means the spring is stiffer and can exert a greater restoring force, resulting in a higher height reached by the mass.

## 4. How does the height reached by a 2kg mass on a spring change as the mass is increased?

The height reached by a 2kg mass on a spring decreases as the mass is increased. This is because a heavier mass requires a greater force of gravity to be in equilibrium with the restoring force of the spring, resulting in a shorter distance of compression or stretching.

## 5. What other factors can affect the maximal contraction and height reached by a 2kg mass on a spring?

The maximal contraction and height reached by a 2kg mass on a spring can also be affected by the length of the spring, the initial position of the mass, and any external forces acting on the system. Additionally, factors such as temperature, material properties of the spring, and friction can also play a role in the height reached by the mass.

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