Math, asked by HARI2503, 1 year ago

an object starts from reat and is acted upon by a variable force F. if Fo is the initial value of force then the position of the object where it again comes to rest will be

Answers

Answered by abhi178
13
here in figure, we can see that force is function of x , graph between force and displacement is straight line with intersects at -F_0 on y-axis.
so, F_{net}=F(x) 

we know from Newton's law of motion,
Fnet = ma = mv\frac{dv}{dx}
so, mv\frac{dv}{dx}=F(x)
but F(x)=(tan\alpha)x-F_0
\implies m\int\limits^v_0{v}\,dv=\int\limits^x_0\{(tan\alpha)x-F_0\}\,dx
\implies m\frac{v^2}{2}=(tan\alpha)\frac{x^2}{2}-F_0x

for again come to rest , v = 0
then, tan\alpha\frac{x^2}{2}-F_0x=0

x=\frac{2F_0}{tan\alpha}
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