An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{3}$ $(pi)/3$ , and then slides horizontally on the floor for another $25 m$ $25 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Question

An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{3}$ $(pi)/3$ , and then slides horizontally on the floor for another $25 m$ $25 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Impact of this question

1250 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-06T09:37:55

$0.264211$ $0.264211$

Explanation:

$d_{r}$ $d_r$ Distance slided down on the ramp.
$α$ $alpha$ Ramp incline.
$d_{h}$ $d_h$ Distance slided horizontally.
$μ$ $mu$ Kinetic friction coefficient.
$m$ $m$ Object mass.
$g$ $g$ Gravity acceleration.

Equating

Potential Energy = Dissipated work against friction

$d_{r} sin α m g = m g cos α μ d_{r} + m g μ d_{h}$ $d_r sin alpha m g = m g cos alpha mu d_r + m g mu d_h$

or

$d_{r} sin α = cos α μ d_{r} + μ d_{h}$ $d_r sin alpha = cos alpha mu d_r + mu d_h$

then

$μ = \frac{d_{r} sin α}{cos α d_{r} + d_{h}} = \frac{9 \sqrt{3}}{59} = 0.264211$ $mu = (d_r sin alpha)/(cos alpha d_r+d_h) =(9 sqrt[3])/59 = 0.264211$

Science

Math

Humanities

... and beyond

An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{3}$ $(pi)/3$ , and then slides horizontally on the floor for another $25 m$ $25 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

An object, previously at rest, slides 9m9 m down a ramp, with an incline of π3(pi)/3 , and then slides horizontally on the floor for another 25m25 m. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Explanation:

Related questions

Impact of this question

An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{3}$ $(pi)/3$ , and then slides horizontally on the floor for another $25 m$ $25 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?