- #1
mathchimp
- 5
- 0
Homework Statement
An object is placed on a slope with initial velocity v=0m/s. Angle of the slope is 30 degrees and the coefficient of friction (or friction factor, not sure how it's said in English) is given as u=0.1*(x/m) where x is the path traversed and m is the mass of the object.
After how much time will the object stop moving?
Homework Equations
So far, what I know is:
friction: F1=u*m*g*cos(angle)
opposite of friction: F2=m*g*sin(angle)
acceleration in this case: a=(F2-F1)/m
velocity in general: v=dx/dt
acceleration in general: a=dv/dt
The Attempt at a Solution
I first tried calculating the acceleration. Since coefficient of friction is unknown and given as 0.1*(x/m), I end up with:
a=4.9-(x/m)*0.85
I checked it four times, pretty sure by now it's correct.
I now wanted to see if I can get something from a=dv/dt.
Integrating dt=dv/a, knowing that the initial velocity is zero, I wound up with t=1/a which I already knew.
I now tried using v=dx/dt which gave me:
t = (1/a)*(dx/dt)
tdt = (1/a)dx
Integrating it, again knowing that the initial path traversed is 0, I got
t^2/2=(1/a)*x
It didn't look very useful. Plugging a into the equation and making things look "pretty" gave me:
(4.9*t^2)/2 - 1/(2*m) = 1
Again, can't find the time. Mass unknown.
Since it was my 4th attempt at solving this, not knowing what to do and ready to break the laws of physics, I decide to derivate the equation and end up with t=0.204 s, which is of course false.
I'm wondering if there's anyone out there who can help me with this. The only thing I know is the solution, which is 3.41 seconds. I've tried solving this multiple times, asked my colleagues for help and searching the internet. Can't find anything useful. The book isn't very helpful with this.