Answer: the length of the rough patch is 4.9 m.
Explanation:
The work - energy theorem, in simple words, expresses that the change in the kinetic energy in an object, is equal to the work done on the object by non-conservative forces, like frictional ones.
In the question, we know that the skater is moving at a given speed, and due to the effects of friction, her speed is reduced to 40%.
Added to this, we are told that the friction force is equal to 22% of her weight so we can write the following:
Ff = 0.22 m. g.
Now the work done by this force, is equal to the product of the force times the distance during which the force acted, i.e,. the distance that we are looking for.
So, we can write the following in a brief:
ΔK = Wf ⇒ 1/2 m (vf² - v₀²) = -Ff . x
(The negative sign explains that the friction force always opposes to the relative movement between the two surfaces in contact).
Replacing by the values, and solving for x, we get:
1/2 ( 2² - 5²) = -0.22. 9.8. x ⇒ x = 4.9 m
In this exercise, we have to use non-conservative system knowledge to calculate the path that will be taken, so we have to:
the length of the rough patch is 4.9 m.
In a non-conservative force system, the total mechanical energy changes. In an explosion, chemical potential energy or nuclear energy is released, resulting in an increase in mechanical energy.
Organizing the information given in the statement we have that:
So the formula for doing the calculations for this exercise will be given by:
[tex]\Delta K = Wf \\ 1/2 m (vf^2 - v_0^2) = -Ff * x[/tex]
Replacing by the values, and solving for x, we get:
[tex]1/2 ( 2^2 - 5^2) = -0.22* 9.8* x\\ x = 4.9 m[/tex]
See more about non-conservative system at brainly.com/question/14315104
