Question

An object, previously at rest, slides `9 m` down a ramp, with an incline of `(pi)/6`, and then slides horizontally on the floor for another `24 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

`k~=0,142`

Explanation:

`pi/6=30^o`
`E_p=m*g*h " Potential Energy of Object"`
`W_1=k*m*g*cos 30*9`
`"Lost energy because friction on inclined plane"`
`E_p-W_1": energy when object on ground"`
`E_p_W_1=m*g*h-k*m*g*cos 30^o*9`
`W_2=k*m*g*24 " lost energy on the floor"`
`k*cancel(m*g)*24=cancel(m*g)*h-k*cancel(m*g)*cos 30^o*9`
`24*k=h-9*k*cos 30^o`
`"using "cos 30^o=0,866 ;h=9*sin30=4,5 m`
`24*k=4,5-9*k*0,866`
`24*k+7,794*k=4,5`
`31,794*k=4,5`
`k=(4,5)/(31,794)`
`k~=0,142`