Question

an inclined plane making an angle of 30° with the horizontal placed in a uniform horizontal electric field 200N/C. A body of mass 1kg and a charge 5mC is allowed to slide down from a rest at a height of 1m. if the coefficient friction is 0.2, find the time taken to reach the bottom.

Answer 1

Given quantities:

$\alpha=30^o$

$E = 200\frac{N}{C}$

$m =1kg$

$q=5mC=5*10^{-3}C$

$h=1m$

$\mu=0.2$

$t \space - \space?$

$ma = Fsin\alpha-\mu Fcos\alpha = F(sin\alpha-\mu cos\alpha)=Eq(sin\alpha-\mu cos\alpha)$

$m\frac{2h}{t^2}= Eq(v\sin\alpha-\mu cos\alpha) \to t = \large\sqrt{\frac{2mh}{Eq(sin\alpha-\mu cos\alpha)}}$

$t = \large\sqrt{\frac{2*1*1}{200*5*10^{-3}*(0.5-0.1*\sqrt3)}}$ $=3.26s$