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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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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:


F = m*a


F = 40*0,93


F = 37,2\:N

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


F = k*x


37,2 = k*0,82


0,82k = 37,2


k = (37,2)/(0,82)


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



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




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