# Friction on an incline

1. Feb 21, 2016

### df102015

1. The problem statement, all variables and given/known data
A block is sliding with an initial velocity of 7.3 m/s along a frictionless horizontal surface when it then goes up an incline of 51.5 degrees that does have friction. If the kinetic friction coefficient is 0.1 then how far along the incline (hypotenuse) will the object travel before it stops?

Θ = 51.5°
µ(k) = 0.1
v(initial) = 7.3 m/s
v(final) = 0 ...because the question asks at what point will it stop, meaning there is no more speed.
g = 9.81
d = ?
m = ?
a = ? ...i do not know if i even need acceleration
F = ?
W = ?

2. Relevant equations
KE = W = 1/2mv(final) - 1/2mv(initial)
F = mg
W = Fd
Force up ramp... F = mg sinΘ
Normal Force against ramp... Fnormal = mg cosΘ
Force of friction between block and ramp... F(f) = µ Fnormal

3. The attempt at a solution
Honestly i have no clue where to even begin, i am so lost on this problem :(
Also, my equations could be wrong.

2. Feb 21, 2016

### Biker

Okay, Lets think about it together alright?

At the horizontal surface, There is no friction. So there is no change in kinetic energy Which mean there is no change in the total energy
But on the incline, I have an external force acting on it which is friction of course.
and work is W = f*d cos theta.
What does work do? if the work is positive then it adds energy to the object. If it is negative then it takes away energy.

Now think of the initial position and the final position, What kind of energy does the object have at these moments?

Hint: at the end of the movement, The velocity is zero and it is not at the ground level so there is height (What form of energy is that?)

Put it in an equation describing what happens to the total energy and volaaa you have solved it!

3. Feb 21, 2016

### df102015

Okay i think i get what you're saying, so it starts with kinetic energy and ends with gravitational potential energy. But what equations, i don't know which ones i could use...

4. Feb 21, 2016

### Biker

Well I know that
W = E2- E1
Substitute these values with what you have.
For example E1 should be kinetic energy.