Can anyone please explain how to do #6?

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valentin68 | College Teacher | (Level 3) Associate Educator

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The weight `G` of the sled decomposes into a normal to plane component `G_n` and a parallel to plane component `G_p` (see the figure below).

`G_n =G*cos(alpha) =m*g*cos(alpha)`

`G_p =G*sin(alpha) =m*g*sin(alpha)`

On the normal to plane axis, `G_n` is balanced by the plane normal reaction `N` (not shown in figure). On the parallel to plane axis we can write

`G_p =F_f +m*a`

`G_p =mu*G_n +m*a`

`m*g*sin(alpha) =mu*m*g*cos(alpha) +m*a`

`a =g*[sin(alpha)-mu*cos(alpha)] =9.81*[sin(38)-0.1*cos(38)] = 5.27 m/s^2`

The acceleration depends only on the friction coefficient and on the plane angle.

The acceleration is 5.27 `m/s^2` and does not depend on the masses involved.

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