Increasing Force: Velocity, Height Calculation

[ShadowDatsas]

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

Homework Equations

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

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.

 

[Nate810]

I've been told that the hight is the same as the area of the triangle that the Force creates, but I think it's wrong...Thanks for your help.

 

[nlightner]

I would suggest that you double check the given values and equations to ensure they are correct. It is also important to clearly define the problem, including any assumptions or simplifications that are being made. Without a clear understanding of the problem and all the relevant information, it is difficult to provide an accurate solution.

That being said, I can offer some general advice on how to approach this problem. First, I would suggest using the equations of motion to analyze the motion of the body. This includes the equations for Newton's Second Law (ΣF = ma), as well as the equations for position, velocity, and acceleration (x = x0 + v0t + 1/2at^2, v = v0 + at, a = constant).

Next, I would recommend drawing a free body diagram for the body, showing all the forces acting on it. This will help you to identify the net force acting on the body, which can then be used to calculate the acceleration and ultimately the velocity and position of the body.

In terms of the given values, make sure to convert all units to the appropriate SI units (meters, kilograms, seconds, etc.) and double check that the values for mass, coefficient of friction, angle, and acceleration due to gravity are all correct.

Finally, it may be helpful to break down the problem into smaller, more manageable steps. For example, you could first solve for the velocity of the body when it takes off, and then use that velocity to calculate the height of the body after 2 meters. This will help to ensure that you are on the right track and can catch any errors along the way.

Overall, it is important to approach the problem systematically and carefully, making sure to use the correct equations and units throughout. Good luck!