Sheila (m=56.8 kg) is in her saucer sled moving at 12.6 m/s at the bottom of the sledding hill near bluebird lake. she approaches a long embankment inclined upward at 16° above the horizontal. as she slides up the embankment, she encounters a coefficient of friction of 0.128. determine the height to which she will travel before coming to rest.

y = 54.9 m

Explanation:

For this exercise we can use the relationship between the work of the friction force and mechanical energy.

Let's look for work

      W = -fr d

The negative sign is because Lafourcade rubs always opposes the movement

On the inclined part, of Newton's second law

Y Axis  

      N - W cos θ  = 0

The equation for the force of friction is

      fr = μ N

      fr = μ mg cos θ

We replace at work

     W = - μ m g cos θ  d

Mechanical energy in the lower part of the embankment

      Em₀ = K = ½ m v²

The mechanical energy in the highest part, where it stopped

      = U = m g y

     W = ΔEm =   - Em₀

    - μ m g d cos θ = m g y - ½ m v²

Distance d and height (y) are related by trigonometry

     sin θ = y / d

     y = d sin θ

    - μ m g d cos θ = m g d sin θ - ½ m v²

We calculate the distance traveled

     d (g syn θ + μ g cos θ) = ½ v²

     d = v²/2 g (sintea + myy cos tee)

     d = 9.8 12.6 2/2 9.8 (sin16 + 0.128 cos 16)

     d = 1555.85 /7.8145

     d = 199.1 m

Let's use trigonometry to find the height

      sin 16 = y / d

      y = d sin 16

      y = 199.1 sin 16

      y = 54.9 m

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)