Question

A block of mass 4 kg is given velocity $4\sqrt{2}$ m/s at the bottom of incline plane of angle ${37}^{\circ }$ with horizontal. Coefficient of friction between plane and block is $\frac{x}{4}$ where $x$ is distance from bottom of plane. Distance after which block stops on plane is [g = 10 m/s${}^2$ ]

Answer 1

By Work Energy Theorem: $W_G+W_f=\Delta K.E-mg\sin \theta x-\int \frac{x}{4}mg\cos \theta dx=-\frac{1}{2}m{v}^{2}g\sin \theta x+\frac{x^2}{2}\frac{gcos\theta }{4}=\frac{v^2}{2}\Rightarrow 6x+x^2=16x^2+6x-16=0\to x=2$