1. ## Mechanics Homework Help Please :D

Hey i was wondering if anyone could help me work this 1 out. Just got it set as homework.

3.
The tile on a roof becomes loose and slides from rest down the roof. The roof is modeled as a plane surface inclined at 30 degrees to the horizontal. The coefficient of friction between the tiles and the roof is 0.4. The tile is modeled as a particle of mass m KG.

(a) Find the acceleration of the tile as it slides down the roof.

The tile moves a distance 3m before reaching the edge of the roof

(b) find the speed of the tile as it reaches the edge of the roof

(c) Write down the answer to part (a) if the tile had mass 2m KG.

Thanks

2. Hi

First you need to define a referential (x and y axis and time = 0 when the tile starts sliding)

$m\:\overrightarrow{a} = \overrightarrow{P} + \overrightarrow{T} + \overrightarrow{N}$

Projection on x and y axis

$m\:a_x = mg\sin\alpha - T$

$0 = -mg\cos\alpha + N$

Therefore $N = mg\cos\alpha$ and $T = f N = fmg\cos\alpha$

Substituting in first equation gives

$m\:a_x = mg\sin\alpha - fmg\cos\alpha$

$a_x = g\sin\alpha - fg\cos\alpha = 1.5 ms^{-2}$