Question

An object, previously at rest, slides `15 m` down a ramp, with an incline of `pi/3`, and then slides horizontally on the floor for another `12 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

`mu=(5sqrt3)/13`

Explanation:

`"Total Energy at The Point of A:"`
`E_A=m*g*h`
`"Work Doing by The Friction Force Along AB:"`
`W_"AB"=mu*m*g*cos (pi/3)*15`
`"Work Doing by The Friction Force Along BD:"`
`W_"BD" =mu*m*g*12`
`E_A=W_"AB" +W_"BD"`
`cancel(m*g)*h=mu*cancel(m*g)*cos(pi/3)*15+mu*cancel(m*g)*12`
`h=mu*15*cos(pi/3)+mu*12*`
`alpha=pi/3`
`h=15*sin(pi/3)`
`15*sin(pi/3)=mu(15*cos(pi/3)+12)`
`15*sqrt3/2=mu(15*1/2+12)`
`7,5sqrt3=mu(39/2)`
`15sqrt3=mu*39`
`mu=(15sqrt3)/39`
`mu=(5sqrt3)/13`