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A crate attached to a spring is being pulled across a flat frictionless surface. The spring is stretched 0.82 m, the crate is accelerating at 0.93 m/s squared and the mass of the crate is 40 kg. What is the spring constant?

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dexteright02
Hello!

We have the following data:
 
F (force) =? m (mass) = 40 kg
a (acceleration) = 0.93 m / s²
k (spring constant) =?
x (spring deformation) = 0.82 m

Let us first find the applied force, through the following formula:

[tex]F = m*a[/tex]

[tex]F = 40*0,93[/tex]

[tex]F = 37,2\:N[/tex]

Now let's find the spring constant, using Hooke's formula

[tex]F = k*x[/tex]

[tex]37,2 = k*0,82[/tex]

[tex]0,82k = 37,2[/tex]

[tex] k = \frac{37,2}{0,82} [/tex]

[tex]\boxed{\boxed{k \approx 45,3\:N/m}}\end{array}}\qquad\checkmark [/tex]



Answer:
We have a spring constant with about 45 N / m



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