Maximum extension of system with two blocks connected by a spring

[carlyn medona]

Homework Statement

Two blocks of masses m, and m2 are connected by a
spring of spring constant k.
Suppose each of the blocks is pulled by a constant force F
Find the maximum elongation spring will suffer and the distances moved by the two

Homework Equations

The Attempt at a Solution

the two forces are acting on opposite direction. so net force on the system is zero. So I applied conservation of mechanical energy. Initial and final kinetic energy is zero. and final spring potential energy is kx^2/2. this doesn't make sense to me.

 

[haruspex]

this doesn't make sense to me.

Why not, and if it does not make sense to you, why did you do it?

 

[andrewkirk]

We need to calculate the final extension $x$ of the spring. For the final system to be static, the spring tension must be $F$ to exactly cancel the applied force. Given that, what is $x$ (use Hooke's Law)?

To calculate the motion of each block, we can use conservation of momentum. Since the external forces are equal and opposite at all times, the combined momentum of the two blocks must remain constant. What does that tell us about the ratio of the distance traveled by m to that traveled by m2?

 

[haruspex]

We need to calculate the final extension x

No, we are asked for the maximum extension. It will not be static.
The OP method is correct, and very neat, though lacking a few justifying details.

 

[conscience]

We need to calculate the final extension $x$ of the spring. For the final system to be static, the spring tension must be $F$ to exactly cancel the applied force. Given that, what is $x$ (use Hooke's Law)?

Sorry , this is incorrect . Maximum extension is not a state of equilibrium . At maximum extension , spring force is greater than the applied constant force .

 

[carlyn medona]

If net force on my system is zero. Wont net work be zero. that means total mechanical energy is conserved. Initially it is zero and final is kx^2/2. Why?.Is net on the system not zero? I am so confused.

 

[haruspex]

If net force on my system is zero. Wont net work be zero

No. The forces are opposite, but so are the displacements. The work done is positive in each case.

 

[conscience]

net force on my system is zero. Wont net work be zero

Not in this case .

that means total mechanical energy is conserved.

Total mechanical energy is conserved only when total work done by non conservative forces is zero .

Total work done on an object could be zero , yet total mechanical energy may not be conserved .

Is net on the system not zero?

Go by the definition of Work done by a force .Consider each force separately . What is the direction of force on anyone block ? What is the direction of displacement of that block ? Is it positive or negative ?

Now what is the net work done by the two forces ?

 

[carlyn medona]

okay, Now it does make sense. Thanks a lot.