# Compression of a spring by an object in free fall

• hawkeye1029
In summary: It would be a lot more confusing if you were starting out with incorrect information and having to un-learn it later :smile:
hawkeye1029

## Homework Statement

A 2.0 kg object starting at rest falls 3.0 m onto a 4.0 N/m spring. How far will the spring be compressed?

m = 2.0 kg
vo = 0 m/s2
y = 3 m
k = 4 N/m
g = -9/8 m/s2

## Homework Equations

eq1: Fg = mg
eq2: Fspring = -kx

## The Attempt at a Solution

[/B]
eq1: Fg = mg
Fg = (2.0kg)(9.8m/s2)
Fg = 19.6N

Fspring = -kx
19.6N = (-4N/m)x
x = -4.9m -> compressed 4.9m

Since they gave y = 3m, I feel like I need to use it, but I'm not sure where. The answer key says the correct answer is 5.42m.

Thank you for any help.

hawkeye1029 said:
I feel like I need to use it, but I'm not sure where
Well, you can kind of imagine the amount of compression depends on the height from which the object is dropped ...

What you describe is placing the object on the spring and gently lower it until equilibrium is reached.

hawkeye1029 said:
Looks to me like the answer key didn't account for the additional GPE converted as the spring compresses.

BvU said:
Well, you can kind of imagine the amount of compression depends on the height from which the object is dropped ...

What you describe is placing the object on the spring and gently lower it until equilibrium is reached.

OK, so then I would need to use Conservation of Energy? Potential energy of block -> kinetic energy -> potential energy in spring?

mgh = 1/2kx2
x2 = 2mgh/k
x = 5.42m

gneill said:
Looks to me like the answer key didn't account for the additional GPE converted as the spring compresses.

Do you mean the GPE of the block when it's resting on the spring?

hawkeye1029 said:
OK, so then I would need to use Conservation of Energy? Potential energy of block -> kinetic energy -> potential energy in spring?

mgh = 1/2kx2
x2 = 2mgh/k
x = 5.42m
Do you mean the GPE of the block when it's resting on the spring?

Yes, energy is the easiest way to solve a problem like this. It gains kinetic energy from the GPE of falling 3.0 meters plus the additional distance ##x## as it compresses the spring. All of that energy is converted into spring compression energy.

As @gneill says above, it looks like the answer key didn't account for the additional energy ##mgx## from falling that extra distance ##x##.

hawkeye1029 said:
Do you mean the GPE of the block when it's resting on the spring?
No, I mean the GPE that is converted to KE (and hence to spring PE) while the block is still dropping and compressing the spring. The spring doesn't just fall through 3 m. That 3 m fall just brings it into first contact with the spring. As the spring compresses, the block continues to drop along with the top of the spring.

gneill said:
No, I mean the GPE that is converted to KE (and hence to spring PE) while the block is still dropping and compressing the spring. The spring doesn't just fall through 3 m. That 3 m fall just brings it into first contact with the spring. As the spring compresses, the block continues to drop along with the top of the spring.

Ohh I see. As I'm in beginning physics and this is a problem at the start of a new unit, I think the teacher didn't want to confuse us.
If I did want to take that into account, how would I go about doing that?

hawkeye1029 said:
Ohh I see. As I'm in beginning physics and this is a problem at the start of a new unit, I think the teacher didn't want to confuse us.
If I did want to take that into account, how would I go about doing that?
It would be a lot more confusing if you were starting out with incorrect information and having to un-learn it later

The ball falls an extra distance equal to the compression distance of the spring. It's the same x that you're looking for.

hawkeye1029 said:
Ohh I see. As I'm in beginning physics and this is a problem at the start of a new unit, I think the teacher didn't want to confuse us.
If I did want to take that into account, how would I go about doing that?

See my answer. Add a term on the left to account for the object falling an extra distance ##x##.

## 1. How does the mass of the object affect the compression of the spring?

The mass of the object does not have a significant effect on the compression of the spring. The compression is mainly determined by the force of gravity and the spring constant.

## 2. Does the height from which the object falls affect the compression of the spring?

Yes, the higher the object falls from, the greater the force of gravity acting on it, resulting in a greater compression of the spring.

## 3. Is the compression of the spring affected by the shape of the object?

No, the shape of the object does not affect the compression of the spring. As long as the object has mass and falls freely, it will compress the spring the same amount.

## 4. What factors affect the spring constant in this scenario?

The spring constant is determined by the material and shape of the spring. It is not affected by the object in free fall.

## 5. Does air resistance have an impact on the compression of the spring?

Yes, air resistance can slightly decrease the compression of the spring as it acts against the object's motion and reduces its speed. However, this effect is often negligible in most cases.

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