Momentum fo two blocks and spring

[lando45]

Hey,

I have been set this question and I'm half-way through answering it but am stuck on where to go next...here's the question:

The m1 = 1.1 kg block at rest on a horizontal frictionless surface is connected to an unstretched spring (k = 180 N/m) whose other end is fixed. (See Fig. 10-36.) The m2 = 2.2 kg block whose speed is 4.0 m/s collides with the 1.1 kg block. Assume that the two blocks stick together after the one-dimensional collision. What maximum compression of the spring occurs when the blocks momentarily stop?

Using m1v1 = m2v2 I got:

2.2 x 4.0 = 8.8kg/m/s
The joint mass of the two blocks is 3.3kg so the velocity must be 2.66m/s

But I don't understand how to calculate the spring compression knowing only the velocity and the "k" value of the spring?

Any help appreciated,
Thanks

 

[maverick280857]

Hi

Good. You have the velocity of the composite mass which now presses against the spring.

Hint: What happens to the (composite mass + spring system) as the composite mass moves forward pressing against the spring? What happens to the velocity of the mass at maximum compression? What happens to the initial kinetic energy? Can you relate these two parameters now?

Hope that helps.

Cheers
Vivek

 

[kp]

all of your composite mass K.E. is equal to all of the compressed springs ____ energy.

(hint: You have equations that represent these energies...and they are just floating around out there waiting for you to use them...)

 

[lando45]

Oh right...so at the springs maximum compression, the velocity of the two joint blocks will be 0m/s...so does the composite mass' KE equal the compressed springs PE?

 

[lando45]

OK so I calculated the KE of the composite mass:

KE = ½mv² = ½ x 3.3 x 2.6² = 11.674J

So is this value supposed to equal the PE of the compressed spring? And if it does, I don't really see how that helps me answer the question, as mgh won't tell me the length of compression...is there a different formula I need to use?

 

[Astronuc]

The key with the spring is

an unstretched spring (k = 180 N/m)

Spring force, F = kx, and PE in spring is just the integral of F dx = 1/2 kx², where x is the displacement from fully relaxed (i.e. no force applied).

The spring reaches maximum deflection when the velocity of blocks = 0, i.e. the KE of the blocks is completely transformed into the stored mechanical energy or PE of the spring.

 

[lando45]

The key with the spring is
an unstretched spring (k = 180 N/m)
Spring force, F = kx, and PE in spring is just the integral of F dx = 1/2 kx², where is the displacement from fully relaxed (i.e. no force applied).
The spring reaches maximum deflection when the velocity of blocks = 0, i.e. the KE of the blocks is completely transformed into the stored mechanical energy or PE of the spring.

Did you mean to write something between "where" and "is"?

 

[Astronuc]

x, sorry about that. Post has been corrected.

 

[lando45]

Ah. So the 11.674J will equal ½kx² so:

½kx² = 11.674 = ½ x 180 x x² = 90 x x²

11.674/90 = x²

x = 0.36m

Is this right do you think?

 

[lando45]

Help, the deadline for this question is tomorrow, and I only have one submission left so I don't want to waste it...does 0.36m seem correct?

 

[Astronuc]

It appears to be correct.