Physics Spring problem?

Question

Hello I need help for spring problem
Here is the question
Two large crates, with masses 640kg and 490kg, are connected by a stiff, massless spring (k=8.1kN/m) and propelled along an essentially frictionless, level factory floor by a force applied horizontally to the more massive crate.
If the spring compresses 5.1cm from its equilibrium length, what is the applied force?

Answer 1

Look at free body diagrams of each of the crates considering horizontal forces only, since there is no friction:

The 490 kg crate has the force of the compressed spring
F=.051*8.1 N
from which we can compute the acceleration

F=m*a
.051*8.1/490=a

Now look at the larger crate.

There are two forces acting on it:

Fh-.051*8.1=640*a
we know that
a=.051*8.1/490
so
Fh=640*.051*8.1/490
+.051*8.1

=.953 N

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