# Accelerating blocks connected by a spring

• XanziBar
In summary, the problem involves two 3.0 kg blocks connected by a spring with a spring constant of 1000 N/m on a frictionless surface. The left block is pushed by a horizontal force F to the right, and at t=0 seconds, both blocks are moving with a velocity of 3.2 m/s to the right. The spring's compression remains constant at 1.5 cm for the next second. The question asks for the magnitude of F during that 1.0 s interval. The approach involves using conservation of energy and momentum equations, and the final answer is 30 N.
XanziBar

## Homework Statement

Two 3.0 kg blocks on a level frictionless surface are connected by a spring with spring constant 1000 N/m. The left block is pushed by a horizonal force F to the right. At time t=0 seconds, both blocks are moving with velocity 3.2 m/s to the right. For the next second, the spring's compression is a constant 1.5 cm. What is the magnitude of F during that 1.0 s interval

## Homework Equations

KE=.5*m*v^2
SPE=.5*k*(delta x)^2
F=(delta p)*(delta t)
change in energy = force * distance

## The Attempt at a Solution

I tried to setup the following: Ei= .5*6kg*3.2^2
and Ef=Ei+F*d=.5*m*v1^2+.5*m*v2^2 +.5*k * (delta x)^2
Now I know everything about the spring potential energy at the end and the total energy (kinetic) at the beginning. But I guess the biggest problem I'm having is that I do not know the final velocities of either of the 2 blocks. I tried using conservation of momentum to relate them but got a much bigger mess with no obvious way to simplify. Would considering the center of mass of the 2 block system help? If I have the acceleration of the center of mass can I do something with that? Is this even the right approach at all? No matter what I do I get like 1 equation with 3 unknowns! Please help.

So... the change in momentum, F*(delta t)=m*v1f+m*v2f-2*m*v then that's a relationship between v1f and v2f in terms of the force (which is what I'm looking for). But with (1/2)*m*v1f^2+1/2*m*v2f^2+1/2*k*(delta x)^2=m*v^2+F*d that still leaves me with an unknown and no equation. Also, does the distance represent the distance that the center of mass travels?

Kind of struggling here, any ideas anyone?

F=-kx ?

No, the force on the spring is not the same as on the block. X1=Vo+a1/2 X2=Vo+a2/2.

a1-a2=2*1.5 cm
F-kx=ma1
kx-ma2
F=m*(a1+a2)=3*(10.03)

==>> a2=5 m/s^2
a1=5.03 m/2^2.

Anyway, the forces are not the same but this problem should be do-able with conservation of energy/momentum.

I just drew an fbd and solved and got 30n.

## 1. What is the purpose of connecting blocks with a spring in an accelerating system?

The purpose of connecting blocks with a spring in an accelerating system is to create a system where the blocks can move together in a coordinated manner, while also experiencing force from the acceleration. This allows for the study of how the spring responds to different accelerations and the relationship between acceleration and displacement.

## 2. How does the spring affect the motion of the blocks in an accelerating system?

The spring affects the motion of the blocks in an accelerating system by providing a restoring force that is proportional to the displacement of the blocks. This means that as the blocks are displaced, the spring exerts a force that tries to bring them back to their original position. This force can either aid or oppose the acceleration of the blocks, depending on the direction of the acceleration.

## 3. What factors can influence the acceleration of the blocks in a system with an accelerating spring?

The acceleration of the blocks in a system with an accelerating spring can be influenced by several factors, including the mass of the blocks, the spring constant, the amplitude of the oscillations, and the magnitude and direction of the acceleration. The relationship between these factors can be described using equations such as Hooke's law and Newton's second law.

## 4. How does the acceleration of the blocks affect the displacement of the spring in an accelerating system?

The acceleration of the blocks affects the displacement of the spring in an accelerating system by causing the spring to stretch or compress. The displacement of the spring is directly proportional to the acceleration of the blocks and the spring constant, as described by Hooke's law. Therefore, a larger acceleration will result in a larger displacement of the spring.

## 5. Can the acceleration of the blocks in an accelerating system be controlled by adjusting the properties of the spring?

Yes, the acceleration of the blocks in an accelerating system can be controlled by adjusting the properties of the spring, such as its stiffness or length. This is because the spring constant, which is a measure of the stiffness of the spring, directly affects the acceleration of the blocks. By changing the spring constant, the acceleration can be increased or decreased, allowing for different experiments and observations to be made.

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