Answer to Question #170140 in Mechanics | Relativity for Nad

Question

A small puck taken as a point object of mass 0.5 kg is launched with a speed of V0=10m/s from O up an inclined plane of length wpm making an angle 30 with the horizontal.

1)in the absence of friction,find the distance it covers along the inclined plane.

2)the friction force is supposed constant f=5N.determine the initial speed needed for the body to cover a length of 10m along the inclined plane.

Answer 1

1)

$v_{0y}=v_0sin \alpha=5~\frac ms,$

$t=\frac{v_{0y}}{g}=0.5~s,$

$l=v_0t=5~m.$

2)

$F_{fr}+mgsin\alpha=ma,$

$a=\frac{F_{fr}}{m}+gsin\alpha=15~\frac{m}{s^2},$

$s=\frac{v^2}{2a},\implies$ $v=\sqrt{2as}=17.3~\frac ms.$