# Pushing on a spring connected to a block

• jolly_math
In summary, when a force is applied to a block and a spring is connected to the block, the applied force is transmitted unchanged to the spring.

#### jolly_math

Homework Statement
Is a force is applied to a block, causing the block to move, greater, or is a force is applied to a spring connected to a block, causing the spring-block system to move, greater?
Relevant Equations
spring force
For the second force with the spring, I know the spring force will exert a force back on my hand, for example, but I'm confused whether the applied force is transmitted unchanged to the block or whether it will decrease because of the opposite spring force. What happens to the block when the force is applied to the spring? Thank you.

jolly_math said:
Homework Statement:: Is a force is applied to a block, causing the block to move, greater, or is a force is applied to a spring connected to a block, causing the spring-block system to move, greater?
Relevant Equations:: spring force

For the second force with the spring, I know the spring force will exert a force back on my hand, for example, but I'm confused whether the applied force is transmitted unchanged to the block or whether it will decrease because of the opposite spring force. What happens to the block when the force is applied to the spring? Thank you.
I am not sure if I understand your problem correctly. But if you try and answer these questions, I might get a better idea of where you are at conceptually:

1. If a subsystem with 2 objects (masses m1 and m2) has a net force acting on it (F), what does Newton's Second Law tell you? Does it mean that both objects have a the same acceleration? Or does it mean that the sum of mass times the acceleration of the objects in the subsystem add up to F i.e. F = m_1 a_1 +m_2 a_2? (Hint: Which one seems more plausible given that the 2 objects in the subsystem are free to apply a force on each other?)

2. Try applying this to the spring and block system. (Assume the spring has significant mass for now). Can you write down an equation with the masses and accelerations of the block-spring system if a force is applied to it?

3. Think of the block now. With how much force does the spring have to push the block to get the desired acceleration?

4. Compare the 2. Now consider the case when the mass of the spring is way less than the mass of the block so that you can ignore the mass of the spring entirely. What would happen in this case?

decisivedove said:
1. If a subsystem with 2 objects (masses m1 and m2) has a net force acting on it (F), what does Newton's Second Law tell you? Does it mean that both objects have a the same acceleration? Or does it mean that the sum of mass times the acceleration of the objects in the subsystem add up to F i.e. F = m_1 a_1 +m_2 a_2? (Hint: Which one seems more plausible given that the 2 objects in the subsystem are free to apply a force on each other?)

It means F = (m1+m2)a, if their accelerations are the same.
decisivedove said:
2. Try applying this to the spring and block system. (Assume the spring has significant mass for now). Can you write down an equation with the masses and accelerations of the block-spring system if a force is applied to it?

Mass 1 (spring): Fapplied = ma

jolly_math said:
It means F = (m1+m2)a, if their accelerations are the same.
Yeah. That is true if their accelerations are the same, but what if their accelerations are not the same? In that case you will have F_ext=m_1 a_1 + m_2 a_2. Two objects in a system do not even need to be in contact with each other (the choice of a subsystem is arbitrary), so the accelerations are allowed to change.

In the mass spring system for example, because the spring is allowed to be stretched and compressed even if the block is stationary, the spring could theoretically be accelerating. Think of what happens to the center of the mass of the spring when the block is forcefully held fixed for example.

jolly_math said:
Mass 1 (spring): Fapplied = ma
You will have to treat the spring and block with different accelerations. Using the similar expression to what I had on my last post: F_ext=m_1 a_1 + m_2 a_2.

So basically the force you apply on the mass spring system is an external force and the sum of mass times acceleration of both the mass and the spring are equal to the force you apply. The internal force between the block and the spring has no significance, because if we write the expression for the next force of the system, the internal forces just cancel because of Newton's 3rd Law.

I don't see any need to consider accelerations if we are taking the spring to be massless. What is the net force on the spring?

haruspex said:
I don't see any need to consider accelerations if we are taking the spring to be massless. What is the net force on the spring?
The applied force by the hand. Is this fully transmitted to the block as well? Or does the spring decrease the force because of the reverse spring force? Thanks.

jolly_math said:
The applied force by the hand. Is this fully transmitted to the block as well? Or does the spring decrease the force because of the reverse spring force? Thanks.
Please try to answer my question. If the spring has no mass, what can you say about the net force on it?

decisivedove
haruspex said:
I don't see any need to consider accelerations if we are taking the spring to be massless. What is the net force on the spring?
Yeah. I was just trying to help the OP understand how Newton's 2nd Law works in a system with multiple particles. But maybe it was unnecessary. I do not even understand what the problem excepts. The reason I brought up the spring with mass and stuff was so you can relate it better with the physical intuition most people have on a spring attached to a block. But I do think the problem probably wants us to assume massless spring. I was probably just overcomplicating it for the OP.