Answer to Question #226323 in Mechanics | Relativity for Coco

Question

1kg block is placed at an inclined sloped at 10 degrees with the horizontal and is pushed up by a 150N force for 3 seconds from which then the 150N force is then removed. The block will continue sliding upward due to is momentum until it will completely stop. How far has the block traveled? if the coefficient of friction is 0.3 between the block and the inclined plane.

Answer 1

Solution.

$m=1kg;$

$\theta=10^o;$

$F=150N;$

$t=3s;$

$\mu=0.3;$

$ma=F-F_f-mgsin\theta;$

$ma=F-\mu mgcos\theta-mgsin\theta;$

$a=\dfrac{F-\mu mgcos\theta-mgsin\theta}{m}$ ;

$a=\dfrac{150-0.3\sdot1\sdot9.8\sdot0.1736-1\sdot9.8\sdot0.9848}{1}=138.84m/s^2;$

$v=v_0+at;$

$v=0+138.84\sdot3=416.52m/s;$

$ma=-(F_f+mgsin\theta);$

$a=-\dfrac{F_f+mgsin\theta}{m};$

$a=-\dfrac{0.3\sdot1\sdot9.8\sdot0.1736+1\sdot9.8\sdot0.9848}{1}=-10.16m/s^2;$

$s=\dfrac{v^2-v_0^2}{2a};$

$s=\dfrac{0-416.52^2}{2\sdot(-10.16)}=8455.8m;$

Answer: $s=8455.8m.$