Answer:
k = 101.2 N / m
Explanation:
For this exercise we can use the relationship between work and energy
W = ΔK (1)
Where the work of the friction force is
W = fr x cos θ
As the friction force opposes the movement, the angle is 180º, so the kinetic product remains
W = - fr x
The friction force is given by the equation
fr = μ N
Let's use Newton's second law
Axis y
N - W = 0
N = W
We substitute
fr = μ mg
So the work is
W = - μ m g x
On the other hand, the variation in energy is
ΔEm = Em_final - Em_inicial
ΔEm = ½ k x² - ½ m v²
We substitute in our initial equation 1
-μ m g x = ½ k x² - ½ m v²
k = 2m / x² (- μ g x + ½ v²)
k = 2 2.00 / 0.190² (- 0.660 9.8 0.190 + ½ 2.07²)
k = 101.2 N / m
