Question

An object, previously at rest, slides `4 m` down a ramp, with an incline of `pi/4`, and then slides horizontally on the floor for another `15 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

`u_k~=0,158`

Explanation:

`"Total Energy of object:"`
`E_p=m*g*4*sqrt2/2" "E_p=m*g*2sqrt2`
`"Work doing by the Friction Force on Ramp"`
`W_f=u_k*m*g*4*sqrt2/2" "W_f=u_k*m*g*2sqrt 2`
`"Total Energy on floor"`
`Delta E=m*g*2sqrt2-u_k*m*g*2sqrt2`
`color(red)(W_f=(u_k*m*g)*15)`
`color(red)"work doing by The Friction Force on Floor"`
`Delta E=cancel(m*g)*2sqrt2-u_k*cancel(m*g)*2sqrt2=color(red)(u_k*cancel(m*g)*15`
`2sqrt2-u_k*2sqrt2=u_k*15`
`2sqrt2=15*u_k+2sqrt2*u_k`
`2,82=15*u_k+2,82*u_k`
`2,82=17,82*u_k`
`u_k=(2,82)/(17,82)`
`u_k~=0,158`