Question

An object, previously at rest, slides `3 m` down a ramp, with an incline of `(3pi)/8`, and then slides horizontally on the floor for another `5 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

`u_k~=0,45`

Explanation:

`"Total Energy at The Point of A: "E_p=m*g*3*sin alpha`
`"The Work doing by The Friction Force along AC:"`
`W_(AC)=3.u_k*m*g*cos alpha`
`"Total Energy at The Point of C:"`
`W_C=E_p-W_(AC)`
`W_C=m*g*3*sin alpha-3.u_k*m*g*cos alpha`
`"The Work doing by Friction Force along CD:"`
`W_(CD)=u_k*m*g*5`
`3 cancel(m. g.) sin alpha -3.u_k. cancel(m. g.) cos alpha=5. u_k .cancel(m .g)`
`3.sin alpha-3.u_k.cos alpha=5.u_k`
`2,772-u_k.1,148=5.u_k`
`2,772=5.u_k+1,148.u_k`
`2,772=6,148.u_k`
`u_k~=0,45`