# Increasing Force.

1. Homework Statement

(First of all sorry for my English, I don't know any scientific expressions in English...)
A Force given by the type F=5x + 5 (x at metres, F at Newtons) is applied to a body of mass m while it creates (the Force) an angle φ with the horizontal level. The coefficient of friction is μ. (the body will move by doing the numbers) First it asks the velocity of the body, when it takes off the ground. Then, it asks the hight, h of the object, if the force stops after 2 meters (after the takeoff).
Givens: m=1kg, μ=0,2 , φ=30, g=10m/s^2

2. Homework Equations

F=5x + 5 , T=μ*N (T is friction), N=m*g - F*sinφ
I guess that's it.

3. The Attempt at a Solution
First of all I don't know how much advanced this problem is therefore I couldn't classify it.
The first question is rather easy.
We know that the body will take off when N=0 (N is the reaction from the ground)
So: F*sinφ + N = mg (the ΣF for the Vertical axis)
By zeroing N we get x=3. The by doing the diagramm of (F*cosφ)(x) and T(x)=mg - F*sinφ
and by calculating the acreage we find both Force's work. By subtracting them we get the Kinetical Energy and thus the velocity.
The second question I think it's impossible, or there is something wrong with the exercise.
I use Principal of Energy Conservation to get: WF - mgh = 1/2mv22 - 1/2mv12.
I know v(1) from the previous question and I can find WF with the same way, with the diagramm. But I can't find the velocity at the final state, or the hight to find the velocity afterwards.

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