Question

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?

Answer 1

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

$F = k*x$

$37,2 = k*0,82$

$0,82k = 37,2$

$k = \frac{37,2}{0,82}$

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



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